The average force of gravitation between Jupiter and the Sun is 1.26 x 10²² N.
What is average gravitational force?The force of gravitation between two objects can be calculated using the equation;
F = G (m1m2) /d²
where;
F is the force of gravitation, G is the gravitational constantm1 and m2 are the masses of the two objects, and d is the distance between them.To find the average force of gravitation between Jupiter and the Sun, we need to know their masses and the average distance between them.
Jupiter has a mass of approximately 1.898 x 10²⁷ kg, and the average distance between Jupiter and the Sun is about 778 million kilometers (7.78 x 10¹¹ m).
Plugging these values into the equation, we get:
F = 6.67 x 10⁻¹¹ (1.898 x 10²⁷ kg) x (1.989 x 10³⁰ kg) / (7.78 x 10¹¹)²
F = 1.26 x 10²² N
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Six identical blocks of steel, each with mass 10.0 kg, are taken to the Moon. On the Moon, their combined mass is
The combined mass of the six blocks of steel on the Moon would be 10.0kg. This is because the gravitational force on the Moon is only one sixth of the gravitational force on Earth, meaning that the mass of the blocks would be correspondingly reduced. On the Moon, the blocks of steel would weigh only 1.67 kg each, for a total mass of 10.0kg.
The effect of the reduced gravity on the blocks of steel is due to the inverse square law of gravitation. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between them. Since the Moon is much farther away from the Earth than the blocks of steel were on Earth, the gravitational force on the blocks is much weaker. The reduced gravitational force on the Moon means that the six blocks of steel have a collective mass of 10.0kg. This mass is significantly lower than their combined mass of 60 kg on Earth, which is due to the inverse square law of gravitation.
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The six steel blocks on the Moon would weigh a total of 10.0kg. This is due to the fact that the gravitational force on the Moon is only one sixth that on Earth, which implies that the mass of the blocks would be lowered accordingly.
The steel blocks would only weigh 1.67 kg each, for a total mass of 10.0 kg, on the Moon.
The inverse square law of gravitation is what causes the steel blocks to be affected by the decreasing gravity. According to this rule, the force of gravity is inversely proportional to the square of the distance between two objects. The gravitational pull on the steel blocks is much weaker on the Moon since it is much further away from the Earth than the steel blocks were on Earth. The six steel blocks weigh a total of 10.0 kg due to the Moon's lower gravitational pull. The inverse square law of gravitation explains why this mass is far smaller than their total mass of 60 kg on Earth.
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two students are canoeing on a river. while heading upstream, they accidentally drop an empty bottle overboard. they then continue paddling for 2.0 h h , reaching a point 1.0 km k m farther upstream. at this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. they catch up with and retrieve the bottle (which has been moving along with the current) 4.7 km k m downstream from the turn-around point.A)Assuming a constant paddling effort throughout, how fast is the river flowing?B)What would the canoe speed in a still lake be for the same paddling effort?
A) The speed of the river is: 3.2 km/h
B) The canoe speed in still water for the same paddling effort is 6.4 km/h.
What is speed?Speed is a term used to describe how rapidly something moves or a process takes place. It is a scalar quantity that represents the speed at which an item moves or changes position with respect to time. By dividing the distance traveled by the time needed to cover that distance, speed may be computed. Units like meters per second, miles per hour, or kilometers per hour are frequently used to measure it. Numerous industries, such as science, sports, transportation, and telecommunications, depending on speed. It is essential in determining the effectiveness and functionality of many systems, including those in cars, machinery, and computer networks.
distance = rate x time
to set up two equations, one for each leg of the journey:
Upstream leg: distance = (c - v) x 2.0 km + 1.0 km
Downstream leg: distance = (c + v) x t
where t is the time it takes to catch up with the bottle.
We know that the distance traveled on both legs is the same because the students end up where they started. So we can set the two equations equal to each other and solve for v:
(c - v) x 2.0 km + 1.0 km = (c + v) x t
Expanding and simplifying:
2c - 2v + 1 = ct + vt
2c + 1 = (c + v)t
t = (2c + 1)/(c + v)
Now we need to find t. We know that the distance the bottle traveled downstream is 4.7 km, and the time it took to get there is t:
4.7 km = v x t
t = 4.7/v
Setting the two expressions for t equal to each other and solving for v:
(2c + 1)/(c + v) = 4.7/v
2cv + v = 4.7(2c + 1)
2cv + v = 9.4c + 4.7
v(2c + 1) = 9.4c + 4.7
v = (9.4c + 4.7)/(2c + 1)
This is our formula for the speed of the river in terms of the speed of the canoe in still water. Now we can solve for c by setting the canoe speed in still water equal to the relative speed upstream:
c - v = (1.0 km)/(2.0 h) = 0.5 km/h
c - (9.4c + 4.7)/(2c + 1) = 0.5 km/h
Simplifying and solving for c:
c = 5.7 km/h
So the speed of the river is:
v = (9.4c + 4.7)/(2c + 1) = 3.2 km/h
To find the canoe speed in still water for the same paddling effort, we can use the formula:
paddling effort = 2v = 2(c - v)
Setting v = 3.2 km/h and solving for c:
2(3.2) = 2(c - 3.2)
6.4 = 2c - 6.4
2c = 12.8
c = 6.4 km/h
So the canoe speed in still water for the same paddling effort is 6.4 km/h.
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a thin, horizontal, 15-cm -diameter copper plate is charged to -3.6 nc . assume that the electrons are uniformly distributed on the surface. Find the potential energy
The required electric potential energy when charge and diameter of the copper plate are given is calculated to be -432 J/c.
The diameter of the copper plate is given as 15 cm = 0.15 m.
Radius r = diameter d/2 = 0.15/2 = 0.075 c
The charge over the copper plate is given as -3.6 nc = -3.6 × 10⁻⁹ c.
The expression of electric charged plate distributed over the surface is given by,
V = k (q/r)
where,
V is the electric potential energy
q is the charge over the plate
r is the radius of the plate
k is coulomb's constant (9 × 10⁹ N)
Putting the values into the equation above gives us,
V = k (q/r) = [9 × 10⁹× (-3.6 × 10⁻⁹)]/0.075 = -432 J/c
Thus, the electric potential energy is calculated to be -432 J/c.
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Calculate the electrical force exerted between a 22gram balloon with a charge of -2.6x10^-6c and a wool sweater with a charge of +3.8x10^-6c; the separation distance is .075m
Answer:
Below
Explanation:
Eforce = C q1 q2 / r^2 C = coulomb's constant
= (9 x 10^9) (2.6x 10^-6)(3.8x 10^-6) / (.075)^2 = 15808 x 10^-3
= 15.8 N (attractive force because the forces are opposite charge)
A rock is tossed straight up with a speed of 22 m/s When it returns, it falls into a hole 14 m deep. In other words, assume that the rock lands 14 m lower than the height from which it was thrown. Take "up" to be the positive direction for the problem.
a) What is the rock's velocity as it hits the bottom of the hole?
m/s
b) How long is the rock in the air, from the instant it is released until it hits the bottom of hole?
s
(Enter your answers with at least 3 significant figures, and remember that velocity is vector.)
The rock's velocity as it hits the bottom of the hole is approximately 27.5 m/s and the rock is in the air for approximately 8.98 seconds.
a) The final velocity of the rock as it hits the bottom of the hole can be found using the kinematic equation vf^2 = vi^2 + 2ad, where vf is the final velocity, vi is the initial velocity, a is the acceleration due to gravity (-9.8 m/s^2), and d is the distance the rock falls (14 m). We know that vi = 22 m/s and d = -14 m (since the rock falls downward), so:
vf^2 = (22 m/s)^2 + 2(-9.8 m/s^2)(-14 m)
vf^2 = 484 + 274.4
vf^2 = 758.4
vf = sqrt(758.4)
vf ≈ 27.5 m/s
Therefore, the rock's velocity as it hits the bottom of the hole is approximately 27.5 m/s.
b) The time the rock is in the air can be found using the kinematic equation
d = vit + (1/2)at^2
where d is the distance the rock travels (which is equal to the height it was thrown from), vi is the initial velocity, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time the rock is in the air. We know that d = vi*t + (1/2)at^2 and that d = 0 (since the rock returns to its starting height), so:
0 = (22 m/s)t + (1/2)(-9.8 m/s^2)t^2
0 = 22t - 4.9t^2
t(4.9t - 22) = 0
Therefore, t = 0 s or t = 4.49 s (rounded to three significant figures). Since the rock was released and then caught, we are interested in the time it takes for the rock to go up and then come back down, so the total time the rock is in the air is twice the time it takes for it to go up:
t_total = 2*t
t_total ≈ 8.98 s
Therefore, the rock is in the air for approximately 8.98 seconds.
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In the Figure, the net external force on the 53.6-kg mower is horizontal to the right. If the force of friction opposing the motion is 18.0 N, with direction horizontally to the left, and the pushing force from the guy is 264.8 N and the direction is 55.0o (relative to the horizontal) downward along the handle of the mower. what is the magnitude of the net force on the mower?
Therefore, the magnitude of the net force on the mower is 134.9 N.
What is force?Force is an influence that can cause an object to undergo a change in motion or acceleration. It is a vector quantity, which means it has both magnitude (size or strength) and direction. Force can be measured in units such as newtons (N) or pounds (lbs). It can result from a variety of sources, including gravity, electromagnetic fields, and contact between objects.
Here,
First, we need to resolve the pushing force into horizontal and vertical components.
F_horizontal = 264.8 N * cos(55.0°) = 152.9 N
F_vertical = 264.8 N * sin(55.0°) = 210.7 N
Since the net external force on the mower is horizontal to the right and the force of friction opposes the motion, we can write:
Net force = F_horizontal - f
where f is the force of friction.
Substituting the given values, we get:
Net force = 152.9 N - 18.0 N = 134.9 N
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in the fastest measured tennis serve, the ball left the racquet at 73.14 m/s . a served tennis ball is typically in contact with the racquet for 30.0 ms and starts from rest. the direction of the velocity of the ball just after it left the racquet is the positive x direction. assume constant acceleration.(a) what was the ball's acceleration during this serve?(b) how far did the ball travel during the serve?
The only force operating on the ball once it has left its racquet is gravity, which the earth exerts on everything in its immediate vicinity. The ball is accelerated vertically by gravity at a velocity of around 9.8 m/s. ^2,
What is the proper order for a tennis serve?Hit into their deuce back for the opening point while standing on the right side of the center line; for the second part, serve from of the left side toward what is identified as the advantages service box. Until the game is won, the same player serves; after that, the other player takes over as the server.
The tennis score is 15 30 40; why?In the middle ages, tennis score were shown on two watch faces that ranged from 0 to 60. The pointer changed position on each score, going from Zero to 15, 30, 45, and 60 for a victory.
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i)
An ideal horizontal spring-mass system has a mass of 1.0 kg and a spring with constant 78 N/m. It oscillates with a period of 0.71 seconds. When this same spring-mass system oscillates vertically instead, the period is Answer seconds. Enter 2 significant figures (a total of three digits) and use g = 10.0 m/s2 if necessary.
ii)
Two speakers, 7.0 m apart, are in phase and emit a pure tone of wavelength 2.4 m. There are a total of Answer quiet spots (completely destructive interference) along the line segment connecting the speakers?
i) The period of oscillation of the vertical spring-mass system is 0.643 seconds.
ii) There are two quiet spots along the line segment connecting the speakers.
What is oscillation?Over time, oscillation is a form of repeating motion. It describes how an object or system moves back and forth around a fixed point, usually an equilibrium center. Depending on the characteristics of the system, the oscillation may be periodic or non-periodic, and its frequency and amplitude may change. A pendulum's motion, the sound waves produced by a guitar string, and the alternating current in electrical circuits are all examples of oscillation. Oscillation is the repeating or periodic change of a quantity around a central value or between two or more states, often in time. An alternating current and a swinging pendulum are two common examples of oscillation. Numerous physical and biological systems depend on oscillations in one way or another.
(i) The period of oscillation of a horizontal spring-mass system is given by:
T = 2π√(m/k)
where m is the mass of the object attached to the spring, and k is the spring constant.
Using the values given in the problem, we can calculate the period T:
T = 2π√(m/k) = 2π√(1.0 kg / 78 N/m) = 0.571 s
Now, when the same spring-mass system oscillates vertically, the period of oscillation is given by:
T = 2π√(m/k_eff)
where k_eff is the effective spring constant, which takes into account the weight of the mass and the spring.
k_eff = k - mg
where g is the acceleration due to gravity. Substituting the values given in the problem, we get:
k_eff = 78 N/m - (1.0 kg) × (10.0 m/s^2) = 68 N/m
Using the above value of k_eff, we can calculate the period of oscillation T:
T = 2π√(m/k_eff) = 2π√(1.0 kg / 68 N/m) = 0.643 s
(ii) The distance between the two speakers is 7.0 m, which means that the halfway point (where the sound waves from the two speakers would be perfectly out of phase) is located at a distance of 3.5 m from each speaker.
Let's start by considering the point directly in front of one of the speakers. At this point, the distance traveled by the sound wave from the first speaker is simply the distance from that speaker to the point or 3.5 m. The distance traveled by the wave from the second speaker is the distance from that speaker to the point, plus the extra distance of 1.2 m due to the phase difference. Using the Pythagorean theorem, we can calculate this distance as:
sqrt((7.0/2)^2 + (1.2)^2) ≈ 3.65 m
This means that the first quiet spot is located 3.65 m in front of the second speaker.
Similarly, we can find the second quiet spot by considering the point directly in front of the second speaker. At this point, the distance traveled by the wave from the second speaker is simply 3.5 m, while the distance traveled by the wave from the first speaker is 7.0 m - the distance from the point to the second speaker, minus the extra distance of 1.2 m. Using the Pythagorean theorem again, we get:
sqrt((7.0/2)^2 + (1.2)^2) ≈ 3.65 m
This means that the second quiet spot is also located 3.65 m in front of the second speaker, but on the opposite side of the line connecting the speakers.
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which of the follow is consistent with simple harmonic motion? the magnitude of the force is inversely proportional to the distance of the ojbection from equilibrium
A force that is inversely proportional to the distance of the object from equilibrium is consistent with simple harmonic motion.
Mathematically, the restoring force can be expressed as [tex]F = -kx,[/tex]
where F is the restoring force, x is the displacement from equilibrium, and k is the spring constant, which determines the strength of the restoring force. Negative sign indicates that the restoring force is opposite in direction to the displacement. If we rearrange this equation, we get x = -(1/k) * F, which shows that the displacement is inversely proportional to the force. Therefore, a force that is inversely proportional to the distance of the object from equilibrium is consistent with simple harmonic motion.
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a runner moves 2.88 m/s north. she accelerates at 0.350 m/s2 at -52.0 angle. at the point where she is running directly east, what is Δy?
The change in velocity in y direction, if the runner accelerates at 0.350 m/s² at 52° angle is 2.83 m/s.
What is acceleration ?Acceleration of an object is the rate of change in velocity. It is a vector quantity having both direction and magnitude.
a = Δv/t
The initial velocity u = 2.88 m/s
a = 0.350 m/s²
the time t = u/a = 2.88 /0.350 = 8.2 s.
vy = uy + ay t
uy = u sin θ = 2.88 sin 52 =2.84 m/s
ay = 0.350 sin 52 = 0.345 m/s²
then vy = 2.84 m/s + (0.345 m/s²) 8.22 s = 5.67 m/s
then change in velocity in the y-direction is calculated as:
Δy = vy - uy
= 5.67 m/s - 2.84 m/s = 2.83 m/s
Therefore, the change in velocity in y-direction Δy for the runner is 2.83 m/s.
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A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a length of 13 cm. a. For what length of the spring is its restoring force 3F? b. At what compressed length is the restoring force 2F?
The length at which the restoring force is 2F is given by the following expression:
[tex]x = (-2F + F / (13 cm - 10 cm) * 10 cm) / (F / (13 cm - 10 cm))[/tex]
What is restoring force?The restoring force of a spring is proportional to its displacement from its unstretched length, according to Hooke's law:
F = -kx
where F is the restoring force, k is the spring constant, and x is the displacement from the unstretched length.
If we know the restoring force F when the spring is stretched to a length of 13 cm, we can find the spring constant k:
[tex]F = -k * (13 cm - 10 cm)\\k = F / (13 cm - 10 cm)[/tex]
Next, we can find the displacement that gives a restoring force of 3F:
[tex]3F = -k * (x - 10 cm)\\3F = -k * x + k * 10 cm\\-3F = k * x - k * 10 cm\\-3F + k * 10 cm = k * x\\x = (-3F + k * 10 cm) / k[/tex]
Substituting the value of k, we get:
[tex]x = (-3F + F / (13 cm - 10 cm) * 10 cm) / (F / (13 cm - 10 cm))[/tex]
So, the length of the spring for which its restoring force is 3F is given by the above expression.
b. To find the length at which the restoring force is 2F, we can use the same method as above and replace 3F with 2F:
[tex]2F = -k * (x - 10 cm)x = (-2F + k * 10 cm) / k[/tex]
Substituting the value of k, we get:
[tex]x = (-2F + F / (13 cm - 10 cm) * 10 cm) / (F / (13 cm - 10 cm))[/tex]
So, the length at which the restoring force is 2F is given by the above expression.
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A powerful motorcycle can accelerate from rest to 26 m/s in only 3.55 s. 1a) What is its average acceleration in meters per second squared? 1b) Assuming the motorcycle accelerates at that constant rate, calculate how far it travels, in meters, during the given time interval. 2) A fireworks shell is accelerated at constant acceleration from rest to a velocity of 62 m/s over a distance of 2 m. 2a) How long, in seconds, does the acceleration last? 2b) Calculate the acceleration, in meters per second squared. Thank you.
1a) The average acceleration of the motorcycle can be calculated using the equation:
average acceleration = change in velocity / time interval
What is average acceleration?Here, the change in velocity is (26 m/s - 0 m/s) = 26 m/s, and the time interval is 3.55 s. Thus, the average acceleration is:average acceleration = 26 m/s / 3.55 s ≈ 7.32 m/s²
Therefore, the average acceleration of the motorcycle is approximately 7.32 meters per second squared.
1b) The distance traveled by the motorcycle can be calculated using the equation:
distance = initial velocity x time interval + (1/2) x average acceleration x (time interval)²
Here, the initial velocity is 0 m/s, the time interval is 3.55 s, and the average acceleration is 7.32 m/s². Thus, the distance traveled is:distance = 0 m/s x 3.55 s + (1/2) x 7.32 m/s² x (3.55 s)² ≈ 46.6 m
Therefore, the motorcycle travels approximately 46.6 meters during the given time interval.
2a) The final velocity of the fireworks shell is 62 m/s, and the initial velocity is 0 m/s. The distance traveled is 2 m. We can use the equation:
final velocity² = initial velocity² + 2 x acceleration x distance
to find the acceleration of the shell. Rearranging the equation, we get:
acceleration = (final velocity² - initial velocity²) / (2 x distance)
Here, the final velocity is 62 m/s, the initial velocity is 0 m/s, and the distance is 2 m. Thus, the acceleration is:acceleration = (62 m/s)² / (2 x 2 m) ≈ 961.25 m/s²
Therefore, the acceleration of the shell is approximately 961.25 meters per second squared.
2b) We can also find the time taken for the acceleration using the equation:
final velocity = initial velocity + acceleration x time interval
Here, the final velocity is 62 m/s, the initial velocity is 0 m/s, and the acceleration is 961.25 m/s². Solving for the time interval, we get:time interval = (final velocity - initial velocity) / acceleration
time interval = 62 m/s / 961.25 m/s² ≈ 0.0645 s
Therefore, the acceleration lasts approximately 0.0645 seconds.
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Materials fracture when the force per unit area, called STRESS, exceeds a critical value. In general, the critical stress depends on the direction as well as the magnitude of the force. For example, bones break differently when subjected to torsional (twisting) stress than when subjected to compressional (or squeezing) stress. Let us consider compressional stress. Wet human bone for 20-39 year olds has an ultimate compressive strength of 1.6x104N/cm2 81. Consider a person who falls from a height to the ground. Upon landing, the person's kinetic energy is converted to work. If the person decelerates over a distance ? h, we can estimate the average force during the collision by Kinetic Energy :-ny' . Work : | F d: Fah If a person lands stiff-legged on a hard surface and doesn't bounce, the deceleration occurs over a very short distance, ? h ~ 1 cm. Since the force is transmitted up the leg, the stress is greatest where the cross-sectional area is least, ie, the tibia just above the ankle [8]. The following lists some different conditions that may occur during landing and physical explanations for why they make bone fracture from a fall more or less likely [8: (a) bounce [more likely. The impulse is twice as large for an elastic collision as for an inelastic collision.] (b) bent knees less likely. Bending the knees increases the time and distance over which deceleration occurs, which reduces the force] (c) landing in loose earth or sand less likely. This increases A h which reduces F (d) turning the body to land on the side less likely. This increases ? h. It also distributes the force widely over the body (increases A)?thereby reducing the stress]
In physics and engineering, stress refers to the internal force per unit area that a material experiences when subjected to an external force. When a force is applied to a material, the material undergoes deformation, or a change in shape. The stress describes the intensity of the internal forces that arise due to the deformation of the material.
There are different types of stress, such as tensile stress (stretching), compressive stress (squeezing), shear stress (sliding), and torsional stress (twisting). The critical stress for a material depends on the type and magnitude of the force applied, as well as the material properties such as its ultimate strength and stiffness. When the stress exceeds the critical value, the material can undergo plastic deformation or fracture.
Materials fracture when the force per unit area, called stress, exceeds a critical value.The critical stress for bone depends on the direction and magnitude of the force and is determined by the ultimate compressive strength of the bone.Wet human bone for 20-39 year olds has an ultimate compressive strength of 1.6x10^4 N/cm^2.The average force during a fall can be estimated using the equation KE = Fd, where KE is the kinetic energy of the falling person, F is the average force during the collision, and d is the distance over which the person decelerates upon landing.Landing stiff-legged on a hard surface results in a very short distance over which deceleration occurs, approximately 1 cm.Bouncing upon landing increases the impulse of the collision, resulting in a larger force and therefore greater stress on the bones, making fracture more likely.Bending the knees upon landing increases the time and distance over which deceleration occurs, reducing the force and the stress on the bones, making fracture less likely.Landing on loose earth or sand increases the distance over which deceleration occurs, reducing the force and the stress on the bones, making fracture less likely.Turning the body to land on the side increases the distance over which deceleration occurs and distributes the force widely over the body, reducing the stress on any one area of bone and making fracture less likely.
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The figure provided shows the production possibilities for Alabama and Georgia.a) Compared to autarky, the gain in world production from specialization is _____ bushels of peaches.b) Compared to autarky, the gain in world production from specialization is _____ bushels of tomatoes.
Compared to autarky, the gain in world production from specialization is 40 bushels of peaches Compared to autarky, the gain in world production from specialization is 80 bushels of tomatoes.
What is specialization?Specialization is the process of focusing a person's skills and resources on a particular area of knowledge or activity. It is a form of division of labor that involves the development of expertise in a particular field, allowing for greater efficiency and productivity in that field. Specialization can involve any number of areas, including academic disciplines, occupations, industries, and activities. Specialization can involve focusing on a specific aspect of a field or a combination of several areas. For example, a doctor may specialize in a particular medical field, or an engineer may specialize in a particular type of engineering. Specialization can also involve the development of skills in an area of expertise, such as programming or marketing.
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Calculate the resultant of the pair of velocities 120 km/hkm/h north and 72 km/hkm/h west.
Express your answer to two significant figures and include the appropriate units.
Calculate the resultant if both of the velocities are directed north.
Express your answer to two significant figures and include the appropriate units.
The resultant velocity of two significant figures is 192 km/h.
To calculate the resultant of the pair of velocities, we need to use the Pythagorean theorem.
The Pythagorean theorem states that for any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the resultant velocity, and the other two sides are the given velocities.
So, the resultant velocity is given by:
Resultant velocity = [tex]\sqrt{((120 km/h)^2 + (72 km/h)^2)[/tex]
Resultant velocity = [tex]\sqrt{(14400 km^2/h^2 + 5184 km^2/h^2)[/tex]
Resultant velocity = [tex]\sqrt{(19584 km^2/h^2)[/tex]
Resultant velocity = 140.01 km/h
To two significant figures, the resultant velocity is 140 km/h.
If both of the velocities are directed north, then the resultant velocity is simply the sum of the two velocities:
Resultant velocity = 120 km/h + 72 km/h
=> 192 km/h
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Tiger Woods hits a golf ball off the edge of a 50 m high cliff, at an initial speed of 30 m/s and an initial angle = 40° from the horizontal. Neglect air resistance.
a) How long is the ball in flight?
b) How far from the base of the cliff does it land?
c) What is the ball's speed just before it hits the ground?
Neglecting air resistance the ball will be 2.3 s in flight and will fall at a distance of 69 m with velocity 22.2 m/s
a) To calculate the time the ball is in flight, we can use the equation:
Time = 2Velocitysin(angle) / acceleration due to gravity
Where velocity = 30 m/s, angle = 40° and acceleration due to gravity = 9.8 m/s²
Therefore, time = 230 m/s sin(40°) / 9.8 m/s² = 2.3 s
b) To calculate the distance from the base of the cliff, we can use the equation:
Distance = Velocity × Time
Where velocity = 30 m/s and time = 2.3 s
Therefore, distance = 30 m/s × 2.3 s = 69 m
c) The ball's speed just before it hits the ground can be calculated using the equation:
Final Velocity = Initial Velocity × cos(angle) - acceleration due to gravity × Time
Where initial velocity = 30 m/s, angle = 40°, acceleration due to gravity = 9.8 m/s² and time = 2.3 s
Therefore, final velocity = 30 m/s × cos(40°) - 9.8 m/s² × 2.3 s = 22.2 m/s
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What two structures help ecoli move
Escherichia coli use long, whip-like structures called flagella to propel themselves.
What is E.coli.?Escherichia coli, also known as E. coli, is a Gram-negative, facultative anaerobic, rod-shaped, coliform bacterium of the genus Escherichia that is commonly found in the lower intestine of warm-blooded organisms
Given is to find what two structures help E.coli move.
Escherichia coli use long, whip-like structures called flagella to propel themselves. Motors in the cell's wall spin the flagella into bundles that rotate counter-clockwise, creating a twist that causes the bacterium to rotate clockwise, or towards the right when viewed from above.
Therefore, Escherichia coli use long, whip-like structures called flagella to propel themselves.
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when an electron in excited energy level drops to a lower energy level, a photon is emitted. if the electron is dropping to n
The transition from n=2 to n=1 emits the longest wavelength.
The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. A transition of an electron from an excited state to the ground state (n=1) results in the emission of a photon with the longest wavelength in the Lyman series.
The Lyman series corresponds to electron transitions to the n=1 level and includes ultraviolet wavelengths. The transition with the longest wavelength in the Lyman series is from n=2 to n=1, and it corresponds to the emission of a photon with a wavelength of 121.6 nm.
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--The complete question is, When an electron in excited energy level drops to a lower energy level a photon is emitted, if the electron is dropping to n=1 which transition will emit the longest wavelength?--
Write a multiplication sentence that you could use to calculate the volume for each rectangular pris
Problem 1. Include the units in your sentences.
a.
C.
REKA
TH*
TION
Student
Lesson 4:
b.
O Great Minds PBC TEKS Edition |
greatminds.org/Texas
d.
Use multiplication to calculate volume.how do I solve
The formulated sentences for each will be:
A: If length is 5cm, width 2cm, height 4cm, volume: 40 cubic centimeters.
B: If the length is 3cm, width 4cm, height 2cm, then Volume is: 24 cubic centimeters.
C: If the length is 6cm, width 2cm, height 3cm, the volume is 36 cubic centimeters.
D: If the length is 3cm, width 2cm, height 4cm, the volume 24 cubic centimeters.
What is the rectangular prism?To calculate the volume of a rectangular prism using multiplication, you need to multiply the length, width, and height of the prism. The multiplication sentence for this is:
Volume = length (m) x width (m) x height (m)
For a. The multiplication sentence for calculating the volume of rectangular prism C is:
Volume = Length x Width x HeightVolume = 6 cm x 2 cm x 3 cmVolume = 36 cubic centimetersb. The multiplication sentence for calculating the volume of rectangular prism B is:
Volume = Length x Width x HeightVolume = 3 cm x 4 cm x 2 cmVolume = 24 cubic centimetersc. The multiplication sentence for calculating the volume of rectangular prism C is:
Volume = Length x Width x HeightVolume = 6 cm x 2 cm x 3 cmVolume = 36 cubic centimetersLastly, for d. The multiplication sentence for calculating the volume of rectangular prism D is:
Volume = Length x Width x HeightVolume = 3 cm x 2 cm x 4 cmVolume = 24 cubic centimetersLearn more about rectangular prism from
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Which of the following quantities has units of a displacement? (There could be more than one correct choice). 32 ft/s^2 vertically download. 9.8m/s^2 40km southwest. 186,000ml. -120 m/s.
Displacement is expressed magnitude and a direction in m, km, ft etc. Among the given options, the one indicting a displacement is 40 km southwest.
What is displacement ?Displacement is a physical quantity measuring how far an object is travelling and in which direction from the initial position. The displacement is a vector quantity having both magnitude and direction.
Displacement can be expressed in different units such as m, km, ft etc. Here, 32 ft/s² and 9.8 m/s² are acceleration. 120 m/s is velocity. Then, 186000 ml is expressing volume of a substance.
Therefore, among the given options, 40 km southwest is indicating the displacement of an object with its magnitude and direction. 40 Km is magnitude and southwest is the direction.
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in curvilinear particle motion which of the following can be negative? group of answer choices normal component of velocity tangential component of velocity tangential component of acceleration normal component of acceleration
The normal component of acceleration may be negative in the motion of curved particles.
The normal component of acceleration may be negative in the motion of curved particles. The component of acceleration that is normal to the motion path's tangent and pointed in the direction of the path's centre of curvature is known as the normal component of acceleration. The normal component of acceleration will be negative if the particle is going along a curved path and its speed is decreasing since it is directed in the opposite direction from the direction the particle is moving. Depending on the particle's motion and the direction of the tangent to the path at any given location, the tangential component of velocity and acceleration may potentially be negative.
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1) Dimension of linear momentum is.
Answer:
M1 L1 T-1
Therefore, linear momentum is dimensionally represented as [M1 L1 T-1].
An object experiencing a constant force accelerates at 8 m/s^2.
What will the acceleration of this object be if the force is halved?
What will the acceleration of this object be if the mass is halved?
What will the acceleration of this object be if the force is halved and the mass is halved?
Suppose an object experiences a constant force of magnitude F. In that case, it accelerates according to Newton's second law of motion, which states that F = ma, where m is the mass of the object and a is its acceleration.
Given that the object experiences a constant force that produces an acceleration of 8 m/s^2, we can write:
F = ma = m × 8
What will the acceleration of this object be if the force is halved?
If the force is halved, the new force is F/2. Using Newton's second law, we can find the new acceleration as follows:
F/2 = ma_new
ma_new = (F/2) / m
ma_new = F/2m
ma_new = (m × 8) / 2m
ma_new = 4 m/s^2
Therefore, the object's acceleration will be 4 m/s^2 if the force is halved.
What will the acceleration of this object be if the mass is halved?
If the mass is halved, the new mass is m/2. Using Newton's second law, we can find the new acceleration as follows:
F = (m/2) × a_new
a_new = F / (m/2)
a_new = 2F/m
a_new = 2(m × 8)/m
a_new = 16 m/s^2
Therefore, the acceleration of the object will be 16 m/s^2 if the mass is halved.
If the force is halved and the mass is halved, the new force is F/2 and the new mass is m/2. Using Newton's second law, we can find the new acceleration as follows:
F/2 = (m/2) × a_new
a_new = (F/2) / (m/2)
a_new = F/m
a_new = (m × 8) / m
a_new = 8 m/s^2
Therefore, the object's acceleration will be 8 m/s^2 if the force is halved and the mass is halved.
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a container with volume 1.69 l is initially evacuated. then it is filled with 0.236 g of n2 . assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. part a if the root-mean-square speed of the gas molecules is 192 m/s , what is the pressure of the gas? express your answer in pascals.
The pressure of the gas is 0.018 atm if the gas obeys the ideal gas law where a container with volume 1.69 l is initially evacuated.
What is the reason for this?
We know that;
√ 3RT/M
For N2;
vrms = 192 m/s
R = 8.314 J/K.mol
T = ?
M = 28 g/mol or 0.028 Kg/mol
So;
T = vrms² M/ 3R
Temperature, T = 192² * 0.028 / 3* 8.314
T = 41.3K
From PV = nRT
n = 0.246 g/28 g/mol which can lead to 0.0087 moles
P = nRT/V
P = 0.0087 moles × 0.082 atmLK-1mol-1 × 41.3K/1.61 L
P = 0.018 atm
Therefore, the pressure of gas is 0.018 atm.
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a container with volume 1.69 l is initially evacuated. then it is filled with 0.236 g of n2, the pressure is P = 1652 Pa
From the inquiry we are informed that
The volume of the compartment is V = 1.83 L = [tex]183 * 10^{-3} m^{3}[/tex]
The mass of [tex]N_{2}[/tex] is [tex]m_{n} = 0.246 g = 0.246 * 10^{-3} kg[/tex]
The root-mean-square volume is v = 192 m/s
The root - mean square velocity is mathematically addressed as
[tex]v = \sqrt{3RT}/Mn[/tex]
Presently the ideal gas regulation is mathematically addressed as
PV = nRT
=> RT = PV/n
Where n is the quantity of moles which is mathematically addressed as
n= mn/M
Where M is the molar mass of [tex]N_{2}[/tex]
So
RT = [tex]PV /M_{n}[/tex]
=> [tex]v = \sqrt{3^{ p* v*Mn/Mn } } /Mn[/tex]
=> [tex]V = \sqrt{3 * P * V} / m_{n}[/tex]
=> [tex]P = V^{2} * m_{n[/tex] / 3 * V
substituting values
=> [tex]P = (192)^{2} * 0.246 * 10^{-3} / 3 * 1.83 * 10^{-3}[/tex]
=> P = 1652 Pa
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match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. use each word only once. view available hint(s)for part a resethelp 1. the blankof the hubble space telescope is better for shorter (bluer) wavelengths of light than for longer (redder) wavelengths of light.target 1 of 7 2. the large research observatories on mauna kea use giant blank.target 2 of 7 3. blankseparate the various colors of light, allowing astronomers to determine stellar composition and many other stellar properties.target 3 of 7 4. the twin 10-m keck telescopes can work together to obtain better angular resolution through a technique known as blank.target 4 of 7 5. the chandra x-ray observatory focuses x rays with blankmirrors.target 5 of 7 6. a 10-meter telescope has a larger blankthan a 4-meter telescope.target 6 of 7 7. galileo's telescope designs using lenses were examples of blank.
In the sentences for the telescope in the right-hand column from the first-hand column, the relevant blank has been filled.
Describe the telescope.
A telescope is the device used to show an enlarged view of a far-off object.
There are different types of telescopes, and each is used for a particular purpose.
The blank that should be filled in correctly from the first column is as follows:
1. Shorter (bluer) wavelengths of light have better angular resolution than longer (redder) wavelengths of light for the Hubble Space Telescope.
2. Huge reflecting telescopes are employed by the numerous research observatories on Mauna Kea.
3. The spectrograph, which divides light into its various colors, enables astronomers to ascertain the stellar composition as well as a number of other stellar characteristics.
4. The identical 10-m Keck
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Describe protons Location: Change: Mass:
Protons are located in the nucleus of an atom with a positive charge, and they have a mass of approximately 1 atomic mass unit (amu) and every atom is made up of the electron, proton, and neutron.
What is the significance of the protons in an atom?A proton's mass is about 1,836 times greater than that of an electron, and these protons are affected by the strong nuclear force and they can be changed into neutrons through a process called beta decay.
Hence, protons are located in the nucleus of an atom with a positive charge, and they have a mass of approximately 1 atomic mass unit (amu) and every atom is made up of the electron, proton, and neutron.
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The question is incomplete, the complete and correct question is below,
Describe protons Location: Charge: Mass: ?
which of these is a non-current liability? multiple choice question. note payable due in 5 months common stock mortgage payable due in 20 years accounts payable
The non-current liability is mortgage payable due in 20 years. Option c is the correct answer.
A liability is a debt or obligation that a company owes to another party. Current liabilities are those that are due within one year, while non-current liabilities are those that are due beyond one year.
a. is a current liability because it is due within one year.
b. is not a liability. It represents ownership in the company and does not have a due date or obligation to pay.
c. mortgage payable due in 20 years is a non-current liability because it is due beyond one year.
d. accounts payable is a current liability because it represents the amount a company owes to its suppliers that have been purchased on credit and are due to be paid.
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A diver bounces straight up from a diving board, avoiding the diving board on the way down, and falls feet first into a pool. she starts with a velocity of 3.35 m/s and her takeoff point is 1.80 m above the pool.(a) What is her highest point above the board? (b) How long a time are her feet in the air?(c) What is her velocity when her feet hit the water?
The diver's highest point above the board is 0.60 meter, her feet are in the air for 0.684 second, and her velocity when her feet hit the water is 3.43 m/s downward.
To find the diver's highest point, we can use the fact that at the highest point, her velocity will be zero. We can use the equation:
v² = u² + 2as
where u is the initial velocity, v is the final velocity (which is zero at the highest point), a is the acceleration due to gravity (g = 9.81 m/s²), and s is the distance traveled. Solving for s, we get:
s = (v² - u²) / 2a
s = (0 - (3.35 m/s)²) / (2 × -9.81 m/s²)
s = 0.60 m
So the diver's highest point is 0.60 m above the diving board.
To find how long the diver's feet are in the air, we can use the fact that the time of flight (i.e. the time spent in the air) is twice the time it takes to reach the highest point. We can use the equation:
v = u + at
where t is the time, and v and u are the final and initial velocities, respectively. Solving for t, we get:
t = (v - u) / a
At the highest point, the velocity is zero, we can use u = 3.35 m/s and v = 0:
t = (0 - 3.35 m/s) / -9.81 m/s² = 0.342 second
So the time of flight is twice this value, or 0.342 × 2 = 0.684 second.
To find the diver's velocity when her feet hit the water, we can use the same equation as in part (b), but with u = 0 and v as the velocity we want to find. We can also use the fact that the distance traveled from the highest point to the water is the same as the distance traveled from the takeoff point to the highest point (0.60 m). So we have:
s = (v² - u²) / 2a
0.60 m = (v² - 0) / (2 × -9.81 m/s²)
v = -√(2 × -9.81 m/s² × 0.60 m) = -3.43 m/s
The negative sign indicates that the velocity is downward, which makes sense since the diver is falling feet first into the water. So the diver's velocity when her feet hit the water is 3.43 m/s downward.
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two loudspeakers in a plane, 6.0 mm apart, are playing the same frequency. if you stand 13.0 mm in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. as you walk parallel to the plane of the speakers, staying 13.0 mm in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers.part awhat is the frequency of the sound? assume a sound speed of 340 m/sm/s .express your answer in hertz.activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value typeff
The required frequency of the sound when distance between the two speakers is given is calculated to be 21.25 kHz.
Sound waves are travelling waves and they can be modelled as
A(r, t) = A₀(r)sin(kr - ωt + Ф₀)
Where,
A₀ is the initial amplitude of the wave
r is the distance
ωt is the frequency
Ф₀ is the initial phase shift
First we need to find out the phase difference (ΔФ) between two waves at different distances.
ΔФ = 2πΔr/λ + ΔФ₀
When you stand centred between the two waves you hear maximum intensity of sound so the the two waves must be in phase
ΔФ = 2πΔr/λ + 0
λ = 2πΔr/ΔФ
The distance when listening in front of the speakers is given by
Δr = r₂ - r₁
r₁ = 6.0 mm = 0.006 m
r₂ = √(0.013²+0.006²) = √(0.000169 + 0.000036) = 0.014 m
Δr = r₂ - r₁ = 0.014 - 0.006 = 0.008 m
λ = 2π × 0.008/ΔФ
The phase difference ΔФ = π
λ = 2π × 0.008/π
λ = 0.016 m
As we know the relation between frequency and wavelength is given by
f = c/λ
Where,
c = 340 m/s is the speed of light
f = 340/0.016
f = 21250 Hz
f = 21.25 kHz
Thus, the frequency of the sound is calculated to be 21.25 kHz.
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How far did the tractor pull the plow if it does 11,100 N-m of work and a force of 257.9 Newtons?
Answer:
Explanation:
The work done (W) by a force (F) over a distance (d) can be calculated using the equation:
W = F * d
In this case, the work done by the tractor is 11,100 N-m and the force applied is 257.9 N. To find the distance the tractor pulled the plow, we need to rearrange this equation to solve for d:
d = W / F
Plugging in the values:
d = 11,100 N-m / 257.9 N = 43.01 meters
So, the tractor pulled the plow a distance of 43.01 meters.