part a.
the work done by gravity is approximately 1690 J.
part b.
the work done by the normal force is 0.
part c.
the work done by friction is approximately -671 J
part d.
the total work done is approximately 1019 J
What is work done?work done is described as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement.
For part a, the work done by gravity can be found using the formula:
W_gravity = mgh
h = dsin(37°) = 8sin(37°) = 4.83 m
W_gravity = (35 kg) * (9.81 m/s^2) * (4.83 m) ≈= 1690 J
In conclusion, the same pattern can be followed to calculate for b, c and d.
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Given the displacement vector D = (5î − 8ĵ) m, find the displacement vector (in m) R so that D + R = −5Dĵ. (Express your answer in vector form.)
It is possible to write d = (x2 - x1)i + (y2 - y1)j to represent the displacement vector d from P1 to P2. (x2 - x1) units in the x-direction plus (y2 - y1) units in the y-direction make up the displacement d.
How do you determine the displacement that results?S = x2+y2 is the formula for the displacement that results. S stands for displacement. The item is moving in two directions, with the first being X and the second being Y. Y = 0 if the motion of your item is restricted to one direction.
The vector's magnitude is thus a| r|. A vector's magnitude only changes when it is multiplied by a scalar; its direction remains unchanged unless the scalar is negative.
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What is the average force of gravitation between Uranus and the Sun?
Answer:
1.41 10 21 newtons
Explanation:
which of the following forms of light can be observed with telescopes at sea level? select all that apply.
(a) X rays. (b) ultraviolet light. (c) visible light.
Ultraviolet light and visible light can be observed with telescopes at sea level.
What does Ultraviolet light mean?
Ultraviolet (UV) light is a type of electromagnetic radiation with a shorter wavelength than visible light but longer than X-rays. It is located in the spectrum between violet light and X-rays and has a wavelength range of about 10 to 400 nanometers. UV light can cause chemical reactions and can be harmful to living organisms, but it also plays important roles in many natural processes, such as the formation of Vitamin D in the skin and the survival of certain species of plants.
In astronomy, UV light provides important information about the hot, high-energy regions of stars and galaxies, and it can be used to study the atmospheres of planets, comets, and other celestial objects. To observe ultraviolet light, specialised telescopes and detectors are often used, as much of it is absorbed by the Earth's atmosphere.
Ultraviolet light and visible light can be observed with telescopes at sea level. X-rays are not typically observed with telescopes because they are highly energetic forms of electromagnetic radiation that cannot penetrate the Earth's atmosphere. X-rays are typically observed with specialised telescopes that are launched into space or with X-ray detectors in satellites.
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a water balloon dropped from the top of a building accelerates at 9.8 meters/second/second. If it starts from rest, and falls for 6 seconds before it hits the ground, what will its speed be just before it hits?
The final speed is 58.8 m/s.
What is the final speed?We have to note that if we are to solve the problem that we have here, we have to look at the equations of motion and this is how we can be able to get the final velocity of the object.
Thus we are going to have that;
v = u + gt
v = final speed
u =- initial speed
g = acceleration
t = time
v = gt
v = 9.8 * 6
= 58.8 m/s
The object is going to have a final speed of about 58.8 m/s when we look at the calculations above here.
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If two sound waves (frequencies f1 and f2) produce a beat frequency, which of the following is true?A. The beat frequency is equal to the sum of f1 and f2.B. The beat frequency is equal to the difference of f1 and f2C. The beat frequency is equal to the average of f1 and f2.
The beat frequency will be equal to the difference between f1 and f2. Option B.
Beat frequency from two sound wavesIf two sound waves with frequencies f1 and f2 produce a beat frequency, the beat frequency will be equal to the absolute value of the difference between the two frequencies, i.e., |f1 - f2|.
For example, if f1 = 400 Hz and f2 = 405 Hz, the beat frequency would be |400 - 405| = 5 Hz.
The beat frequency is the difference between the two frequencies that the human ear can perceive as a pulsing or beating sound. The rate of the beating sound corresponds to the beat frequency, which is measured in Hertz (Hz).
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In a classroom demonstration the pressure inside a soft drink can is suddenly reduced to essentially zero. Assuming the can to be a cylinder with a height of 15 cm
and a diameter of 7.0 cm
, find the total inward force exerted on the vertical sides of the can due to atmospheric pressure.
The total inward force exerted on the vertical sides of the can due to atmospheric pressure is calculated as 4053 N.
What is pressure?Pressure may be defined as the amount of force that is correspondingly applied perpendicular to the surface of an object per unit area. The symbol for it is "p" or P. It is generally calculated with the help of the formula, pressure, P = F/A.
According to the question,
The atmospheric pressure acts on the outer surface of the can. In order to calculate this inward force we need to know the total surface area of the can available to the air outside the can. Since the can is a cylinder with a total surface area given by 2πrh + 2πr².
A = 2πr(r + h)
where h = height of the cylinder = 15cm.
r = radius of the can = 7 cm/2 = 3.50 cm. (as r = diameter /2)
A = 2π×3.50 ×(3.50 + 15) = 406.6 cm² = 406.6 × 10-⁴ = 0.040m².
Atmospheric pressure, P = 101325Pa = 101325 N/m²
F = P × A
F = 101325 × 0.040 = 4053 N.
Therefore, the total inward force exerted on the vertical sides of the can due to atmospheric pressure is calculated as 4053 N.
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1. Find the minimum magnitude of the acceleration amin of the car.2. Find the maximum acceleration amax of the car.Express your answer in meters per second per second to the nearest integer.3. Find the distance d0,2 traveled by the car between t=0s and t=2s.Express your answer in meters to the nearest integer.
The minimum magnitude of the acceleration of the car is 0.
The maximum acceleration will be 30m/s².
The distance traveled is 55m.
How to calculate the distanceMinimum magnitude of acceleration of the car is 0. This is because in a V-t graph slope of tangent on the of car and at t=us slope is zero.
Maximum acceleration of car is from o tois where slope is steepest.
= V - u / t
= 30 - 0 / 1
= 30m/s²
The distance will be:
d1 = 15
d2 = 1/2(30 + 50) = 40
Distance = 15 + 40 = 55m
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fill in the blank. the phenomenon of perceptual set underscores the contribution of___processes to perception. please choose the correct answer from the following choices, and then select the submit answer button. answer choices bottom-up top-down sensory innate
The phenomenon of perceptual set underscores the contribution of top-down processes to perception.
Phenomenon of perceptual set highlights the important role of top-down processing in perception, as it shows how our past experiences, expectations, and preconceptions can shape and bias our interpretation of incoming sensory information. Perceptual set is a classic example of top-down processing, as our prior knowledge and expectations about the world can shape how we perceive incoming sensory information. For instance, if we see a group of objects arranged in a particular way, we may perceive them as a familiar shape or pattern even if they are actually different objects.
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A reaction has an activation Energy of 20 kJ and E = -60 kJ/mol. What would be the activation Energy for the REVERSE reaction?
A.) 40 kJ
B.) 80 kJ
C.)100 kJ
D.) 20 kJ
E.) 60 kJ
The activation energy for the reverse (backward) reaction would be 20 + 60 = 80 kJ/mol.
From the question, we are told that the activation energy of the reaction is 20 kJ and its E is -60 kJ/mol. A negative number for E means that it is an exothermic reaction, a reaction in which energy is released instead of absorbed.
The energy graph for an exothermic reaction is attached below. You can see that the activation energy for a backward reaction is EQUAL to the activation energy for the forward reaction + energy released.
Since we know the activation energy and E, the activation energy for the reverse (backward) reaction would be 20 + 60 = 80 kJ/mol.
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8) A projectile fired from the ground has a velocity = 24.0 î-8.00 m/s at a height of
9.10 m. Find: (a) the initial velocity; (b) the maximum height.
(a) The initial velocity of the projectile is 42.23 m/s.
(b) The maximum height reached by the projectile is 91 m.
What is the magnitude of the initial velocity of the projectile?
The initial velocity of the projectile is calculated by applying the following kinematic equation.
v = ( 24.0 î - 8.00j ) m/s
The angle of projection is calculated as;
θ = arc tan ( Vy / Vx )
θ = arc tan ( 8 / 24 )
θ = 18.43⁰
h = ( u² sin²θ ) / 2g
u² = 2gh / (sin²θ)
u² = ( 2 x 9.8 x 9.1 ) / ( sin 18.43 )²
u² = 1783.6
u = √1783.6
u = 42.23 m/s
The maximum height reached by the projectile is calculated as follows;
v² = u² - 2gh
where;
v is the final velocity at maximum height = 0u is the initial velocityg is acceleration due to gravityh is the maximum height2gh = u²
h = ( u² ) / ( 2g)
h = ( 42.23² ) / ( 2 x 9.8 )
h = 91 m
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The Saturn V rocket had a mass of 2.45x10 kg, 65% of which was fuel. In the absence of gravity and starting at rest, what would be the maximum velocity attained (the "burnout velocity")? The fuel exhaust velocity was 3100m/s.
Answer:
Approximately [tex]5800\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
Let [tex]m[/tex] denote the initial mass of the rocket and the fuel. The question states that the mass of the fuel is [tex]65\%[/tex] of the total mass, which is [tex]0.65\, m[/tex]. The mass of the rocket without the fuel would be [tex](1 - 0.65)\, m[/tex].
When an object of mass [tex]m[/tex] travels at a velocity of [tex]v[/tex], the momentum [tex]p[/tex] of that object would be [tex]p = m\, v[/tex].
Initial momentum of the rocket and the fuel, combined, would be [tex]0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] since initial velocity was [tex]0\; {\rm m\cdot s^{-1}}[/tex].
Let [tex]v(\text{rocket})[/tex] and [tex]v(\text{fuel})[/tex] denote the final velocity of the rocket and the fuel. Final momentum of the rocket would be [tex]((1 - 0.65)\, m)\, (v(\text{rocket}))[/tex]. Final momentum of the fuel would be [tex](0.65\, m)\, (v(\text{fuel}))[/tex].
The total final momentum of the rocket and the fuel, combined, woul dbe:
[tex]((1 - 0.65)\, m)\, (v(\text{rocket})) + (0.65\, m)\, (v(\text{fuel}))[/tex].
Under the assumptions, momentum would be conserved. In other words, the total momentum of the rocket and the fuel would stay the same:
[tex](\text{total final momentum}) = (\text{total initial momentum})[/tex].
[tex]((1 - 0.65)\, m)\, (v(\text{rocket})) + (0.65\, m)\, (v(\text{fuel})) = 0[/tex].
Given that [tex]v(\text{fuel}) = 3100\; {\rm m\cdot s^{-1}}[/tex]:
[tex]\begin{aligned}v(\text{rocket}) &= \frac{0.65}{1 - 0.65}\, v(\text{fuel}) \\ &= \frac{0.65}{1 - 0.65}\, (3100)\; {\rm m\cdot s^{-1}} \\ &\approx 5800\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
RI V1 12 V R1 3.30 RO 33 100 Key-A Fig. 4 Norton' Theorem 1. Using Ohm's law, calculate the current flowing through potentiometer R for an R. value equal to 1.0 k 5.0 kN and 10.0 k22 (show sample calculations). Appropriately report your results. 2. Using Norton' Theorem, calculate the current flowing through potentiometer Rį for an RL value equal to 1.0 KA2, 5.0 K2 and 10.0 kN (show sample calculations). Appropriately report (resistance and Norton current values). 3. Using NI-Multisim, measure the current flowing through potentiometer R for an Rz value equal to 1.0 1. 5.0 kN and 10.0 k (show sample calculations). Appropriately report your results.
The current flowing through potentiometer R is 0.855mA, the current flowing through potentiometer Rį for an RL 5KΩ and the current flowing through potentiometer R is 854μA,
The potentiometer is an instrument used for measuring the unknown voltage by comparing it with the known voltage. It can be used to determine the emf and internal resistance of the given cell and also used to compare the emf of different cells. The relative system is used by the potentiometer. The reading is more accurate in a potentiometer.
1) Rl = 1kΩ
Applying nodal analysis at V:
V/1K + V/3.3K + V-12/1K
3.3V+V+3.3V-39.6/3.3K = 0
7.6V = 39.6
V = 39.6/7.6 = 5.21 V
Il = v/Rl = 5.21/1K
Il = 5.21 mA
For Rl = 1K and Il = 5.21mA
Rl = 5 kΩ
Applying nodal analysis at V:
V/5 K + V/3.3K + V-12/1K
3.3V+5V+16.5V-198/3.3K = 0
24.8V = 198
V = 198/24.8 = 7.98 V
Tl = 7.98/5 K = 1.596 mA
Rl = 10 kΩ
Applying nodal analysis at V:
V/10K + V/3.3K + V-12/1K
3.3V+10V+33V-396/3.3K = 0
46.3V = 396
V = 396/46.3 = 8.55 V
IL = V/Rl = 8.55/10 K = 0.855mA
2) IL = 12m x 0.767K/0.767K + 10K
= 12m x 0.767/10.767
= 0.854 mA
= 854 μA
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Two blocks connected by a string are pulled across a rough horizontal surface by a force applied to one of the blocks, as shown. The acceleration of gravity is 9.8m/s^2. If each block has an acceleration of 5.2m/s^2 to the right, what is the magnitude of the applied force? Answer in units of N
The magnitude of the applied force is 14.59 N.
Newton's second law, which states that the net force exerted on an item is equal to its mass times its acceleration, can be used to address this issue.
Let's use the letters m1 and m2 to represent the masses of the left and right blocks, respectively. The following equations are therefore able to be written:
m1 * a = F - f
m2 * a = f
where F is the size of the applied force, f is the frictional force acting on the blocks, and an is the acceleration of both blocks. Because a string connects the two blocks, it should be noted that the acceleration is the same for both. The frictional force can be expressed as
f = * N,
where is the coefficient of friction and N is the normal force, can be used to express the frictional force. The weight of the blocks, which can be represented as m1 * g and m2 * g, respectively, determines the normal force acting on them.
When we solve for F and replace the frictional force expression in the first equation, we obtain:
F = m1 * a + μ * m1 * g
Inputting the values provided yields:
F = (m1 + m2) * a + μ * (m1 + m2) * g
F = (m1 + m2) * 5.2 + 0.4 * (m1 + m2) * 9.8
F = 5.2 * (m1 + m2) + 3.92 * (m1 + m2)
F = 9.12 * (m1 + m2)
We now need to determine what m1 Plus m2 equals. Although their specific masses are withheld from us, we do know that the ratio of their masses is 2:3. Let's write m for the smaller mass and 1.5m for the larger value. Next, we have:
m + 1.5m = 2.5m
1.5m/m = 3/2
So the masses are m = 2/5 and 1.5m = 6/5.
Inputting these values into the F equation yields the following results:
F = 9.12 * (2/5 + 6/5)
F = 9.12 * 8/5
F = 14.59 N
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If Earth were 9.5 times farther away from the Sun than it is now, how many times weaker would the gravitational force between the Sun and Earth be?
If Earth were 9.5 times farther away from the Sun than it is now, 95 times weaker would be the gravitational force between the Sun and Earth.
What is gravitational force ?Any two things with mass are drawn together by the gravitational force. The gravitational force is known as. The formula F = Gm1m2/r2 states that the direction of force will always point in the direction of the other mass along the line connecting the two bodies.
In contrast to gravity, which is the force of attraction between any two bodies, gravitation is the pull of any body towards the earth.
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The sound intensity 54.0 m from a wailing tornado siren is 0.170 W/m^2.
The weakest intensity likely to be heard over background noise is ≈1μW/m2. Estimate the maximum distance at which the siren can be heard.
The maximum distance at which the siren can be heard is approximately 1043.3 m, assuming there is no significant obstruction or reflection of sound waves.
What is sound intensity?The sound power per unit area is the definition of sound intensity. The measurement of sound intensity in the air near a listener's position is the typical context.
Let's call the maximum distance at which the siren = D
0.170 W/[tex]m^2[/tex] / [tex](54.0 m)^2[/tex] = I / [tex]D^2[/tex]
where I is the unknown intensity at distance D.
Solving for I, we get:
I = 0.170 [tex]W/m^2[/tex] x [tex](D/54.0 m)^2[/tex]
We know that the weakest intensity likely to be heard over background noise is ≈1μW/m2, so we can set I equal to 1 μW/[tex]m^2[/tex] and solve for D:
1 μW/[tex]m^2[/tex] = 0.170 W/[tex]m^2[/tex] x [tex](D/54.0 m)^2[/tex]
[tex]D^2[/tex] = (1 μW/[tex]m^2[/tex]) x [tex](54.0 m)^2[/tex] / 0.170 [tex]W/m^2[/tex]
[tex]D^2[/tex] = 1.086 x [tex]10^6[/tex]
D = √(1.086 x [tex]10^6 m^2[/tex])
D ≈ 1043.3 m
Thus, the maximum distance will be 1043.3 m.
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1 kg block and a 2 kg block are placed next to each other on a frictionless horizontal table. A horizontal force of 6 N is applied orthogonally to the side 1 kg block. Find the magnitude of the force acting on the 2 kg block?
Group of answer choices
4 N
1 N
3 N
2 N
Answer:
3N
Explanation:
yeah just that is it you don't need calculation to solve it
In the current divider circuit shown, if the resistors have values of R1 =607k12, R2 =292kN and R3 =216kN2, find the value of the source current I, that will produce and output current of I. =51mA. Enter your answer in units of milli-amps (mA). 11. Is R1 M R2 M R2 m
The value of the source current I, that will produce and output current of I will be = 51 mA is 219.6 mA.
To find the source current I that will produce an output current of I_out = 51 mA in the current divider circuit shown, we can use the current divider formula:
I_out = I * (R2 / (R1 + R2 + R3))
Rearranging this formula to solve for I, we get:
I = I_out * (R1 + R2 + R3) / R2 = 51 mA * (607.12 kΩ + 292 kΩ + 216.2 kΩ) / 292 kΩ = 219.6 mA
Therefore, the value of the source current I that will produce an output current of 51 mA is 219.6 mA.
Regarding the second part of the question, it is not clear what is meant by "Is R1 M R2 M R2 m". Please provide more information or clarification.
Output current refers to the current that flows out of a device or circuit and is usually measured in amperes (A) or milliamperes (mA). It is the current that is delivered to the load or external circuit connected to the output terminals of the device.
In an electronic circuit, the output current is determined by the output voltage and the impedance of the load. For example, a power supply may provide a certain voltage to a load, and the output current will depend on the resistance or impedance of the load.
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How much force will this car experience if it collides with a wall and the collision lasts for
0.05 s?
The amount of force after 0.05 seconds will be 528000 N.
What is a force?A force is an influence that can cause an object's motion to change. A force can cause a mass object to change its velocity, or accelerate. Intuitively, a force can be described as a push or a pull.
Given that a car of mass 1500kg collides with a wall. the initial and final speed of the car is -15m/s and 2.6m/s. if the collision lasts for 0.05 seconds.
The force will be calculated as:-
Mc x V₁ + F x t = Mc x V₂
Here, V₁ = -15 m /s and V₂ = 2.6 m /s.
Mc x V₁ + F x t = Mc x V₂
-( 1500 x 15 ) + F x 0.05 = 1500 x 2.6
F x 0.05 = 22500 + 3900
F = 26400 / 0.05
F = 528000 N
Therefore, the force after the collision will be 528000 N.
The complete question is given below.
A car of mass 1500kg collides with a wall. the initial and final speed of the car is -15m/s and 2.6m/s. if the collision lasts for 0.05 seconds. find the impulse caused by the collision and the average force on the car.
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A spraying pump is used to spray water from a pool to a fountain.
a) Determine the power of the pump when the work done by the pump is 800Nm at 50ms to a distance of 20m
b) Determine the mass of the pump when the water is projected at acceleration of 10m/s?
The power of the pump is its work done by time. The power used for a work done of 800 Nm in 50 seconds is 16 J/s or W. The force acting here is 40 N. Then the mass of the body is 4 kg.
What is power ?Power of an object is the rate of work done or energy used.
power = work done/ time.
It has the unit watt which is equal to J/s.
a. Given work done by the pump = 800 Nm
time = 50 s
then power = 800 Nm or J / 50 s = 16 Watt.
b. Force F = Work done/ distance
F = 800 Nm/20 m = 40 N
c. Then force = m a
given acceleration a = 10 m/s²
m = f/ a
= 40 N/10 m/s²
= 4 kg.
Therefore, mass of the pump is 4 kg.
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three capacitors of capacitance 1 micro Farad, 2 microfarad and 2 microfarad are each charged to 250 volts and then connected in series. 1) find the overall potential difference across the capacitor 2) find the charge on each capacitor and 3) find the energy stored in the combination
1) The overall potential difference across the capacitor is 1.66 V.
2) The charge on each capacitor is 1.66 C.
3) The energy stored in the combination will be 1.3778 J.
What is a capacitor?A capacitor is a device that stores electrical energy in an electric field by accumulating electric charges on two insulated surfaces. It is a two-terminal passive electronic component. Capacitance is the effect of a capacitor.
Given that three capacitors of capacitance 1 micro Farad, 2 microfarads and 2 microfarads are each charged to 250 volts and then connected in series.
Q₁ = C₁Vt
Q₁ = 1 x 5 = 5 μF
Q₂ = C₂Vt
Q₂ = 2 x 5 = 10 μF
The equivalent capacitance will be,
1 / Ct = 1 / C₁ + 1 / C₂
Ct = 2 / 3 μF
Vt = 10 / 3 ÷ 2
Vt = 1.66 V
The charge will be,
q =CV
q = 1 x 1.66
q = 1.66 C
The energy will be calculated as:-
U = 1/2 x C xV
U = 1 / 2 x 1 x 1.66²
U = 1.3778 J
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The world’s tallest lighthouse is located in Japan and is 106 m tall. A winch that provides 300 W of power is used to raise 25.0 kg of equipment to the lighthouse top at a constant velocity. How long does it take the equipment to reach the lighthouse top?
To solve this problem, we can use the formula for mechanical power:
Power = Force x Velocity
Since the equipment is being raised at a constant velocity, we can assume that the force applied by the winch is equal and opposite to the force of gravity acting on the equipment:
Force = Weight of equipment = m * g
where m is the mass of the equipment and g is the acceleration due to gravity (9.81 m/s^2).
Substituting the given values, we get:
Force = 25.0 kg * 9.81 m/s^2 = 245.25 N
Power = 300 W
Velocity = ?
We can solve for the velocity by rearranging the formula:
Velocity = Power / Force
Velocity = 300 W / 245.25 N
Velocity = 1.22 m/s
Now, we can use the formula for average speed to find the time it takes for the equipment to reach the lighthouse top:
Average speed = Total distance / Total time
Since the equipment is moving vertically, the total distance is equal to the height of the lighthouse:
Total distance = 106 m
We can solve for the total time by rearranging the formula:
Total time = Total distance / Average speed
Total time = 106 m / 1.22 m/s
Total time = 86.9 seconds (rounded to 2 decimal places)
Therefore, it takes approximately 86.9 seconds, or 1 minute and 27 seconds, for the equipment to reach the top of the lighthouse.
can someone please help me with this 50 points to whoever gets it right
if a biker travels 33 miles in 3 hours, can you guarantee that the bike speedometer must have read 11 mph at least once during the trip? can you guarantee it will read 8 mph at least once during the trip? can you guarantee it will read at least 14 mph? support your conclusions mathematically.
Can you ensure that perhaps the bicycle's speedometer must have displayed 11 mph at least once for a rider who covers 33 miles.
A speedometer is what?
Speedometer is a computer benchmark that evaluates how quickly Web applications respond. It simulates user behaviors like adding to-do items using demo web applications. The window of your browser is too small. Lets create the view port at least 850px x 650px in size to get the most accurate results. The current size is 1024 by 569 pixels.
Which speedometer works best with a Royal Enfield motorcycle?
Version 2.0 of the BRPEARl Heavy Digital Speedometer 5.5" Screen A8 automobile hud Head up Displays OBD2 Speedometer D'Mega Shop RX 100 135 RXG Instrument panel Mount Bracket An... Dig... Bullkartzone Speedo Dial for Royal Honda Cycle (W... bike rpm, tachometer, speedometer, tacho gauge
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In one experiment the electric field is measured for points at distances $r$ from a uniform line of charge that has charge per unit length $\lambda$ and length $l$, where $l \gg r$. In a second experiment the electric field is measured for points at distances $r$ from the center of a uniformly charged insulating sphere that has volume charge density $\rho$ and radius $R =$ 8.00 mm, where $r > R$. The results of the two measurements are listed in the table, but you aren't told which set of data applies to which experiment: For each set of data, draw two graphs: one for $Er^2$ versus r and one for $Er$ versus $r$. (a) Use these graphs to determine which data set, A or B, is for the uniform line of charge and which set is for the uniformly charged sphere. Explain your reasoning. (b) Use the graphs in part (a) to calculate $\lambda$ for the uniform line of charge and $\rho$ for the uniformly charged sphere.
The uniform line of charge and [tex]\rho[/tex] for the uniformly charged sphere. Using slope the value of [tex]\lambda[/tex] is [tex]\\\frac{4\pi\epsilon_0\times slope}{2}$[/tex].
For the uniform line of charge, the electric field $E$ is inversely proportional to the distance $r$, so $Er$ should be constant. For the uniformly charged sphere, the electric field $E$ is inversely proportional to the square of the distance $r$, so $Er^2$ should be constant. Therefore, we can use the graphs of $Er^2$ versus $r$ and $Er$ versus $r$ to determine which data set is for the uniform line of charge and which set is for the uniformly charged sphere.
For data set A, the graph of $Er^2$ versus $r$ is a straight line, which means that $Er^2$ is constant. Therefore, data set A is for the uniformly charged sphere. For data set B, the graph of $Er$ versus $r$ is a straight line, which means that $Er$ is constant. Therefore, data set B is for the uniform line of charge.
For the uniform line of charge, the electric field $E$ is given by
E =[tex]\frac{2\lambda}{4\pi\epsilon_0r}$,[/tex]
where $\lambda$ is the charge per unit length and $\epsilon_0$ is the permittivity of free space. Since $Er$ is constant, we can write $Er = \frac{2\lambda}{4\pi\epsilon_0}$. From the graph of $Er$ versus $r$ for data set B, we can find the slope of the straight line, which is equal to $Er$. Therefore, we can use the slope to calculate $\lambda$:
[tex]$\lambda = \frac{4\pi\epsilon_0Er}{2} = \frac{4\pi\epsilon_0\times slope}{2}$[/tex]
For the uniformly charged sphere, the electric field $E$ is given by $E = \frac{\rho r}{3\epsilon_0}$, where $\rho$ is the volume charge density. Since $Er^2$ is constant, we can write $Er^2 = \frac{\rho r^3}{3\epsilon_0}$. From the graph of $Er^2$ versus $r$ for data set A, we can find the slope of the straight line, which is equal to $Er^2$. Therefore, we can use the slope to calculate [tex]$\rho$[/tex]
[tex]$\rho = \frac{3\epsilon_0Er^2}{r^3} = \frac{3\epsilon_0\times slope}{r^3}$[/tex]
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A box initially has 335 J of kinetic energy. The final kinetic energy is 125. How much work was done to the box?
Answer:
Explanation:
The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.
Work done = 335-125=110J
Dr. Rhee wrapped a string tightly around a fixed pulley that has a moment of inertia of 0.0352 kg m2 and a radius of 12.5 cm. Then he pulls the string away from the pulley with a constant force of 5.00N. What is the speed of the string after it has unwound 2.31 m? O a. 2.09 m/s O b.4.95 m/s O c. 3.18 m/s d. 2.36 m/s O e. 1.97 m/s
The answer is closest to option e, 1.97 m/s. To solve this problem, we need to use conservation of energy. The initial potential energy of the system is converted into kinetic energy as the string unwinds.
We can find the potential energy using the equation U = Iω²/2, where I is the moment of inertia of the pulley, and ω is its angular velocity.
The potential energy of the system is given by U = Iω²/2 = (0.0352 kg m²)(ω²)/2. Initially, the potential energy is all stored in the string, so we can set U equal to the work done by the constant force to find the final kinetic energy:
U = Fd = (5.00 N)(2.31 m) = 11.55 J
Equating this to the kinetic energy, we get:
K = U = (0.0352 kg m²)(ω²)/2
Solving for ω, we get:
ω = √(2K/I) = √(2U/I) = √(2(11.55 J)/(0.0352 kg m²)) = 14.44 rad/s
Now we can find the final speed of the string by multiplying the final angular velocity by the radius of the pulley:
v = ωr = (14.44 rad/s)(0.125 m) = 1.805 m/s
Therefore, the answer is closest to option e, 1.97 m/s.
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T/F plato's apology tells the story of how sorry socrates was for having upset his fellow athenians with his persistent questioning.
The given statement " plato's apology tells the story of how sorry socrates was for having upset his fellow athenians with his persistent questioning." is False
Plato's Apology is not about how sorry Socrates was, but rather a speech he delivered during his trial in which he defended his philosophical beliefs and actions, and refused to apologize for them. Socrates argued that his questioning was necessary to improve Athens and its citizens, and that his death would only harm the city. The Apology is often seen as a key text in the development of Western philosophy, and has been interpreted in many different ways.
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what is the difference between negative velocity positive acceleration and positive velocity and negative acceleration ?
The difference between negative velocity positive acceleration and positive velocity and negative acceleration:
When an object moves in a nice course( left to proper) and the rate of exchange of speed is nice, we name it high- quality acceleration( speed is growing). while an item moves in a high quality path, the acceleration is terrible, but the price of change in haste is terrible( speed is reducing). further, the charge of exchange of speed decreases in the negative path is taken into consideration high- quality acceleration as it implies adding the haste in a high- quality route.
An object has a positive velocity when it is moving in the right direction. If an object is slowing down, its acceleration vector is pointing away from the direction in which it is moving (in this case, a negative acceleration).
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A force of 60 N is exerted on one end of a 1.0-m-long lever. The other end of the lever is attached to a rotating rod that is perpendicular to the lever. By pushing down on the end of the lever, you can rotate the rod. If the force on the lever is exerted at an angle of 3
0
∘
30 ∘
, what torque is exerted on the lever? (
sin
3
0
∘
=
0.5
;
cos
3
0
∘
=
0.87
;
tan
3
0
∘
=
0.58
)
(sin30 ∘
=0.5;cos30 ∘
=0.87;tan30 ∘
=0.58) A. 30 N B. 52 N C. 60 N D. 69 N
The required torque applied on the rotating rod that is perpendicular to the lever is calculated to be 30 N-m.
Torque is a unit of measurement for the force that can cause an item to revolve about an axis. Torque accelerates an object in an angular direction, much like force does in linear kinematics.
Applied force is given as = 60 N
Length of a lever = 1.0 m
The force on the lever is exerted at an angle of 30°.
sin 30° = 0.5
So, the torque applied on the rod = force × distance × sin30°
⇒ 60 N × 1.0 m × 0.50
⇒ 30 N-m
Thus, the torque applied on the rod is calculated to be 30 N-m.
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It can be difficult, especially for someone with partial hearing loss, to understand someone speaking rapidly in a low, soft voice.
Which of the following auditory characteristics are associated with sound waves for low, quiet voices?
correct:
-low frequency
-low amplitude
incorrect
- vestibular
Correct, low, quiet voices have sound waves with low frequency and low amplitude. Instead of hearing, the vestibular system controls balance and spatial orientation.
By comparing the two ears' responses, what aspects of the sound can be used to identify its origin?In order to determine where a sound is coming from, humans rely on two key clues. These signals include (1) the ear the sound strikes first (interaural temporal differences) and (2) the volume of the sound when it reaches each ear (known as interaural intensity differences).
What procedures are necessary for the brain to interpret sound waves as sound?Sound waves enter the outer ear and travel to the eardrum via the auditory canal. The three tiny ossicles carry the ensuing vibrations into the cochlea, where hair cells are able to pick them up.
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