Answer:
15.1 liters
Explanation:
4 gal x 4 quarts= 16 quarts
16 quarts/ 1.057quarts = 15.137 liters or 15.1 liters rounded to nearest tenth.
In the two-fragment explosion that results when a gun is fired, the bullet acquires a significantly higher speed compaired to the recoil speed of the gun. Use a physics formula or a physics principle (directly related to the observation) to justify the observation.
The bullet has a much smallar Mass, and in an explosion, the object with less mass will always achive the higher velocity due to conservation of momentum.
This can be proven simply by this equation.
[tex]M_1V_1i +M_2 V_2i = M_1V_1 + M_2 V_2.[/tex]
The only way for Momentum to be Conserved in this situation is for the lighter object to achive a higher velocity to overcome the farge mass of the other object which will unvariably have a Small Velocity.
Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant if no external forces act upon it. In a closed system, any change in momentum of one object must be balanced by an equal and opposite change in momentum of another object within the system. This principle applies to both the linear and angular momentum of a system.
The conservation of momentum has broad implications in physics, ranging from the behavior of subatomic particles to the motion of planets in our solar system. It is particularly important in understanding collisions and explosions, where the total momentum of a system is conserved even if individual objects experience significant changes in momentum.
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Complete Question:-
In the two-fragment explosion that results when a gun is fired, the bullet acquires a significantly higher speed compaired to the recoil speed of the gun. Use a physics formula or a physics principle (directly related to the observation) to justify the observation.
Using KCL and the v-i relations for resistors and capacitors, show that the voltage v(t) in the following circuit satisfies the following ODE if R= 5Ω and C-2F. Also find the capacitor voltage v (t) if is(t) = cos (t). Assume zero initial conditions. u 2 u(t) = is(t) for t > 0. dt 5
The complete solution to the ODE is given as:V(t) = (1/2C) sin(t) + KV(t) = (1/2) sin(t) + C1
The given circuit diagram can be represented in a linear circuit. Thus, using KCL (Kirchoff's Current Law) and the v-i relation for resistors and capacitors, the voltage V(t) can be found out to satisfy the following ODE.R = 5Ω and C = 2F, thus I = C * (dv/dt). Also, V = iR + Q/C, where Q is the charge stored in the capacitor. Hence, the voltage across the capacitor is given as:
V = iR + Q/CI = is(t)/2
Since initial conditions are zero, Q = 0.
Hence, the ODE of the circuit will be:
V = (1/2C) ∫ is(t)dt Or, V = (1/2C) sin(t) + K
Here, K is the constant of integration.
To find the voltage of the capacitor, we need to use the relation between current and voltage across the capacitor, given as: iC = C * dv/dt
Thus, dv/dt = iC/C = i, since C = 2FThus, v(t) = (1/C) ∫ i(t) dt Or, v(t) = (1/2) ∫ cos(t)dt Or, v(t) = (1/2) sin(t) + C1Here, C1 is the constant of integration. Thus, the voltage V(t) in the circuit is given as:V(t) = (1/2C) sin(t) + KVoltage of the capacitor is given as:
v(t) = (1/2) sin(t) + C1
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center of mass vs gravity
In most mechanics problems the gravitational field is assumed to be uniform. The center of gravity is then in exactly the same position as the center of mass. The terms center of gravity and center of mass tend to often be used interchangeably since they are often at the same location
A ski resort can manufacture enough machine made snow in 4 h to open its steepest run, whereas it would take 12 h of naturally falling snow to provide enough snow. If the resort makes snow while it is snowing naturally, how long (in h) will it take until the run can open?
The run will be able to open in 4 hours when machine-made snow is produced while it is snowing naturally.
Let the rate of production of machine-made snow be m units/hour, and the rate of snowfall be n units/hour. From the given information, we know that:
m × 4 = n × 12 => m/n = 3/1
Let the time taken for the run to open when both types of snow are produced simultaneously be t hours.
In that time, the ski resort will have produced mt units of machine-made snow and nt units of naturally falling snow.
We also know that mt + nt is equal to the amount of snow required to open the run. Therefore:
mt + nt = m × 4 => nt = m(4 - t) (1) and
mt + nt = n × t => mt = n(t - 12) (2)
Substituting the value of m/n obtained above in (1), we have:
nt = 3n(4 - t) => nt = 12n - 3nt => nt = 6n (3)
Substituting the value of mt obtained above in (2), we have:
n(t - 12) = 3nt => t = 4 hours
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Answer: 1st one: chemical to mechanical to electrical to thermal
2nd: hydroelectric, 3rd: gravity
If the pressure exerted on the floor by a box is 200kpa, find the weight of the box given that the bottom of the box has a contact area of 20cm³?
The weight of the box is approximately 0.0408 kg.
What is Pressure?
Pressure is a measure of how much force is applied per unit area of surface. It is a scalar quantity and has units of force per unit area. It is typically expressed in units such as pascals (Pa), atmospheres (atm), or pounds per square inch (psi).
We can use the formula:
pressure = force / area
where pressure is given as 200 kPa and area is given as 20 cm^2. Converting cm^2 to m^2:
20 cm^2 = 20 x 10^-4 m^2 = 0.002 m^2
Substituting the values in the formula and solving for force:
200 kPa = force / 0.002 m^2
force = 200 kPa x 0.002 m^2
force = 0.4 kN (kilonewtons)
The weight of the box is the force acting on it due to gravity, which is given by:
weight = mass x gravitational acceleration
Assuming the box is on the Earth's surface, we can use a value of 9.81 m/s^2 for gravitational acceleration. Solving for mass:
mass = weight / gravitational acceleration
mass = 0.4 kN / 9.81 m/s^2
mass = 0.0408 kg (kilograms)
Therefore, the weight of the box is approximately 0.0408 kg.
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P2. Charges q and Q are placed on the x-y plane at (0,0) and at (0, 3) m, respectively.
Where q = 50 pC and Q = -40 pC.
a. Draw the situation to solve the next step.
b. Determine the net electric flux through a closed cylindrical surface that has a diameter of 5 ma
a height of 4 m, where the axis of the cylinder is the z axis and its mid-point is at the origin.
(a). Here is a diagram of the situation:
| Q (-40 pC)
| ^
| |
--------|----------- 3 m
| |
| |
| |
| |
| |
| q (50 pC)
|_____________|___________> x = 0 m
3 m
(b). The net electric flux through the closed cylindrical surface is -100.5 N m^2/C.
We can use Gauss's Law to calculate the electric flux through the cylindrical surface.
Choose a cylindrical Gaussian surface of radius r=2.5 m and height h=4 m, centered at the origin.The electric field at any point on the cylindrical surface due to Q is given by E_Q = kQ/r^2, where k is Coulomb's constant (9 x 10^9 N m^2/C^2).The electric field at any point on the cylindrical surface due to q is given by E_q = kq/r^2.The net electric field at any point on the cylindrical surface is E_net = E_Q + E_q.Since the surface is symmetric around the z-axis, we can assume that the electric field is perpendicular to the end surfaces of the cylinder, so the electric flux through these surfaces is zero.Therefore, the net electric flux through the cylindrical surface is Φ_E = E_net * A, where A is the area of the curved surface of the cylinder.The area of the curved surface of the cylinder is A = 2πrh = 20π m^2.Substituting the values for E_Q and E_q, we get E_net = -1.60 x 10^6 N/C (negative because the electric field due to Q is in the opposite direction to that due to q).Therefore, Φ_E = (-1.60 x 10^6 N/C) * (20π m^2) = -100.5 x 10^6 N m^2/C = -100.5 N m^2/C.Therefore, the net electric flux through the closed cylindrical surface is -100.5 N m^2/C.
What is an electric flux?
Electric flux is the measure of the total electric field passing through a surface. It is a scalar quantity, and its unit is the volt meter (V m) or newton meter squared per coulomb (N m^2/C).
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1.- What is net net charge on the sweater? Why?
2.- What is the net charge on the balloon? Why?
ASAP pls and thank you!!
When students brush balloons against their wool sweaters or hair, electrons are moved from the wool or hair to the balloon. As a result, the balloon has a net negative charge, whereas the garment or hair, having shed negative charges, has a net positive charge.
What is net charge?The term "net" refers to the sum after both positive and negative costs have been deducted. So, if something has 321 positive charges and 319 negative charges, the overall charge is 321 - 319 = +2. The overall charge is 37 - 42 = -5 if it includes 37 positive charges and 42 negative charges.
Electrons are negatively charged, whereas protons are favourably charged. Atoms have an identical amount of electrons and protons and have a net charge of zero. This makes atoms always neutral.
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An object moves in a straight line along a horizontal surface. The position x of the object as a function of time t is shown by the graph. Which of the following statements are true for the object?
Answer:
An object moves in a straight line along a horizontal surface.
Answer:
A and D
Explanation:
A:the kinetic energy does decrease due to the decrement of the velocity i.e the slope is negative velocity.
it is true
B.the change of moment is not zero cause there is difference between initial and final velocity
it is false
c.also work done is not zero you can chaekc it using the formula 1/2m (vf -vi)² and choice
it is flase
D. the impulse is the applied force per time Which is mass of the object multiplied by it's the change in momentum. it is true
What are density and volume?
Simple explanation please
Answer:
Explanation:
Density is a measure of how much mass is contained in a given volume. It is the amount of matter (mass) in a given space (volume). Density is usually expressed in units of mass per unit of volume, such as kilograms per cubic meter (kg/m³) or grams per milliliter (g/mL).
Volume is the amount of space occupied by an object or substance. It is the measurement of the three-dimensional space occupied by an object, substance, or material. Volume can be measured in different units, such as liters (L), cubic meters (m³), or cubic feet (ft³), depending on the scale of the object being measured.
A 0.35-kg piece of putty is dropped from a height of 2.5 m above a flat surface. When it hits the surface, the putty comes to rest in 0.30 s. What is the average force exerted on the putty by the surface?
The average force exerted on the putty by the surface is 0 N this means that the putty experiences no net force and does not accelerate during the 0.30 s it takes to come to rest.
To answer this problem, we may apply the average force equation, which states that average force equals momentum change divided by the period during which the force occurs.
Initially, we must determine the putty's starting momentum. We may employ the momentum equation, which asserts that momentum equals mass times velocity. Because the putty is dropped from rest, its initial velocity is zero, as is its initial momentum.
The ultimate momentum of the putty must then be determined. The putty's final velocity is also zero since it comes to rest. As a result, the putty's ultimate momentum is similarly zero.
Finally, we can substitute the values we found into the equation for average force:
Average force = change in momentum/time interval
= 0 / 0.30
= 0 N
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1. Which of the following is not a force that controls the wind? a) Coriolis force b) frictional force c) electrostatic force d) gravitational force e) pressure gradient force
c) electrostatic force is not a force that controls the wind.
What is an electrostatic force?
Electrostatic force is a type of force that exists between particles with electric charges. It is also known as Coulombic force and can be attractive or repulsive depending on the sign of the charges. The strength of the electrostatic force is directly proportional to the magnitude of the charges and inversely proportional to the distance between them.
What is magnitude?
Magnitude refers to the size or amount of something, typically measured in numerical or quantitative terms. It can be used to describe various physical properties such as force, velocity, acceleration, or electric charge, among others. In physics, magnitude is often represented by a scalar quantity, which has only magnitude and no direction, as opposed to a vector quantity, which has both magnitude and direction.
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Complete question is : electrostatic force is not a force that controls the wind.
Difference between capillary action and siphoning action?
Explanation:
Capillary action and siphoning action are two different phenomena that involve the movement of fluids, but they work in different ways.
Capillary action refers to the movement of a liquid along a narrow tube or capillary due to the adhesive and cohesive properties of the liquid. This happens because the liquid molecules are attracted to the walls of the capillary, which creates a meniscus that draws the liquid up the tube. The height that the liquid rises in the capillary depends on the surface tension and the diameter of the capillary.
Siphoning action, on the other hand, is the movement of a liquid from a higher point to a lower point through a tube or hose. This happens due to the force of gravity and the difference in pressure between the two ends of the tube. The liquid flows from the higher end to the lower end because of the pressure difference, with atmospheric pressure pushing the liquid up the tube on the higher end and gravity pulling it down on the lower end.
Explanation:
Capillary action and siphoning action are both related to the movement of fluids, but they differ in their mechanisms and applications.
Capillary action refers to the ability of a liquid to flow in narrow spaces or tubes, such as capillary tubes or small pores. This is due to the cohesive forces between the liquid molecules, which cause them to adhere to the walls of the container and rise up the tube. The thinner the tube, the higher the liquid can rise. Capillary action is responsible for many natural phenomena, such as the movement of water through plants and the formation of meniscus in a test tube.
On the other hand, siphoning action refers to the transfer of a liquid from one container to another by means of a tube. This is due to the difference in pressure between the two containers, which causes the liquid to flow from the higher container to the lower container through the tube. Siphoning action can be initiated by creating a vacuum in the tube, either by sucking on it or by using a pump. Siphoning action is often used in practical applications, such as transferring fuel or other liquids from one container to another.
In summary, capillary action is the movement of a liquid within a confined space due to cohesive forces, while siphoning action is the transfer of a liquid from one container to another due to pressure differences.
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Mechanical energy → Electrical energy → Thermal energy
What is mechanical energy?
Mechanical energy is the energy possessed by an object due to its motion or position. It is the sum of kinetic energy and potential energy of an object, which can be converted to other forms of energy, such as electrical energy or thermal energy.
What is electrical energy?
Electrical energy is the energy associated with the movement of electrons through a conductor or an electrical circuit. It is the result of the movement of charged particles, such as electrons, and is commonly generated by the conversion of other forms of energy, such as mechanical, chemical, or solar energy.
What is thermal energy?
Thermal energy is the energy associated with the temperature of an object or a system. It is the result of the movement of atoms and molecules in matter, which leads to the transfer of heat from hotter to cooler objects. Thermal energy is commonly measured in units of joules or calories and is proportional to the mass and temperature of an object or a system.
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Which correctly describes a different evolutionary stage of a star like the sun?
A) it’s forms from a cold, dusty molecular cloud
B) During a yellow giant stage, it burns carbon in its core and helium in the shell surrounding the core.
C) After leaving the main sequence, its core is stable due to electron degeneracy
D) It becomes a white dwarf after exploding as a supernova
E)During a red giant stage, its core contracts and cools
Answer:
Explanation:
The correct option that describes a different evolutionary stage of a star like the sun is:
D) It becomes a white dwarf after exploding as a supernova
This is because a star like the sun does not have enough mass to undergo a supernova explosion. After it has exhausted all the fuel in its core, it will evolve into a red giant and then a planetary nebula, leaving behind a small, hot, dense remnant known as a white dwarf. Supernovae occur in much more massive stars that have cores that can collapse to form a neutron star or black hole.
5. In the diagram below, Aircraft A is flying East and maintaining a groundspeed of 340 kt (a kt = speed of 1 NM / hr). Aircraft B is flying in the same direction as aircraft A but 210 NM ahead, maintaining a ground speed of 280 kt. Aircraft A will catch Aircraft B at Point ‘X’. What distance will Aircraft B have travelled when this event occurs?
Aircraft B will have travelled 980 NM when it is caught up by Aircraft A.
We can begin by using the formula:
distance = rate × time
Let's first find the time it will take for Aircraft A to catch up with Aircraft B. Since both are flying in the same direction, the relative speed between them will be the difference in their ground speeds:
relative speed = ground speed of A - ground speed of B
= 340 kt - 280 kt
= 60 kt
The distance between the two aircraft is 210 NM. Using the relative speed, we can find the time it will take for Aircraft A to catch up to Aircraft B:
time = distance / relative speed
= 210 NM / 60 kt
= 3.5 hours
Now, we can find how far Aircraft B will have travelled in 3.5 hours at its own ground speed of 280 kt:
distance = rate × time
= 280 kt × 3.5 hours
= 980 NM
Therefore, Aircraft B will have travelled 980 NM when it is caught up by Aircraft A.
What is an aircraft?
An aircraft is a machine that is designed to be able to fly through the air. It typically has fixed or rotary wings, and is powered by engines or other propulsion systems. Aircraft come in a wide variety of shapes and sizes, from small, single-engine planes to large commercial airliners and military aircraft.
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Two identical projectiles are fired at the same time. Projectile A has a speed of 300m/s and projectile B has a speed of 600m/s. What is the ratio of the Kinetic Energy of projectile B to projectile A?
The ratio of the kinetic energy of projectile B to projectile A is 4:1.
The kinetic energy (KE) of an object is given by the formula
KE = 1/2 * m * v^2
where m is the mass of the object and v is its velocity.
Assuming the two projectiles have the same mass, we can compare their kinetic energies based solely on their velocities:
KE_B/KE_A = (1/2 * m * v_B^2)/(1/2 * m * v_A^2)
= (v_B^2/v_A^2)
Substituting the values given in the problem:
KE_B/KE_A = (600 m/s)^2 / (300 m/s)^2
= 4
Therefore, the ratio of the kinetic energy of projectile B to projectile A is 4:1. Projectile B has four times the kinetic energy of projectile A.
What is kinetic energy?
Kinetic energy is the energy an object possesses by virtue of its motion. It is a scalar quantity that depends on the mass and velocity of the object.
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fter sailing 12 mi, a sailor changed direction and increased the boat's speed by 2 mph. An additional 15 mi was sailed at the increased speed. The total sailing time was 3 h. Find the rate of the boat for the first 12 mi.
The rate of the boat for the first 12 miles is 24/13 mph.
After sailing 12 miles, a sailor changed direction and increased the boat's speed by 2 mph. An additional 15 miles was sailed at the increased speed. The total sailing time was 3 hours.
We need to find the rate of the boat for the first 12 miles.Let the rate of the boat for the first 12 miles be r mph. Therefore, the speed of the boat after the change of direction is (r + 2) mph.
Distance covered in the first 12 miles = 12 miles
Time taken for the first 12 miles = 12/r
Distance covered in the next 15 miles = 15 miles
Time taken for the next 15 miles = 15/(r + 2)
Total time taken = 3 hours
Therefore,12/r + 15/(r + 2) = 3
Multiply the above equation by r(r + 2), we get:
12(r + 2) + 15r = 3r(r + 2)
Simplify and solve for r:
r = 24/13 mph
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5. In the diagram below, Aircraft A is flying East and maintaining a groundspeed of 340 kt (a kt = speed of 1 NM / hr). Aircraft B is flying in the same direction as aircraft A but 210 NM ahead, maintaining a ground speed of 280 kt. Aircraft A will catch Aircraft B at Point ‘X’. What distance will Aircraft B have travelled when this event occurs?
For the event to occur, Aircraft B will have travelled a distance of 980 NM.
How to calculate distance?Since Aircraft A is flying East, we can assume that the positive direction is to the East and negative direction is to the West. Let's assume that the position of Aircraft A is x and position of Aircraft B is x + 210 NM.
Let t be the time it takes for Aircraft A to catch up with Aircraft B. At that moment, both aircraft will be at the same position, so:
distance traveled by Aircraft A = distance traveled by Aircraft B
Ground speed x time = Ground speed x time + 210
Using the given ground speeds, we can set up the equation as:
340t = 280t + 210
60t = 210
t = 3.5 hours
Therefore, Aircraft B will have traveled a distance of:
distance = ground speed x time
distance = 280 kt x 3.5 hr
distance = 980 NM
So, Aircraft B will have traveled 980 NM when Aircraft A catches up with it at Point X.
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My favorite sports team lost the game. Can I sue the opposing team for emotional trauma?
Answer:
No, you cannot sue the opposing team for emotional trauma resulting from your favorite sports team's loss. Sports are competitive events, and it is expected that one team will win and the other will lose. It is not a legal basis for a lawsuit.
Adult brains are not capable of neurogenesiss . True False
Answer:
False. Adult brains are capable of neurogenesis, which is the process of generating new neurons (nerve cells) in the brain. Although it was previously believed that neurogenesis only occurred during early development, research has shown that certain regions of the brain, such as the hippocampus, continue to produce new neurons throughout adulthood. However, the rate of neurogenesis in adults is much lower than in developing brains
EX :SOMEONE FATHER TODAY YOUR FATHER DOES,T KNOW ABOUT TECH OR ANY SAMRT APPS BUT HE KNOW BETTER N HIS GENRATON
A 120-kN truck has an engine that transmits a power of 380 kW to all the wheels. If the wheels do not slip on the ground, determine the angle of the largest incline the truck can climb at a constant speed of 72 km/h.
To determine the angle of the largest incline the truck can climb at a constant speed of 72 km/h, we need to use the formula for power, which is P = Fv, where P is the power, F is the force, and v is the velocity.
What is the equation for the maximum incline angle as ?Since the velocity is constant, the force required to maintain this speed up an incline is equal to the force of gravity acting on the truck, which is given by Fg = mg, where m is the mass of the truck and g is the acceleration due to gravity.
Thus, we can write the equation for the maximum incline angle as:
sinθ = Fg/F
where θ is the angle of the incline. Substituting the given values, we get:
sinθ = (mg)/Pv
sinθ = (120000 kg)(9.81 m/s²)
sinθ =( 0.157)/(380000 W)(20 m/s)
θ = 9.04 degrees
Therefore, the angle of the largest incline the truck can climb at a constant speed of 72 km/h is approximately 9.04 degrees.
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The maximum angle of incline the truck can climb at a constant speed of 72 km/h without slipping is approximately 18.3 degrees.
calculation of the question :-
First, we need to calculate the force required to maintain a constant speed of 72 km/h on an incline. We can use the following formula:
Force = weight * sin(theta) + rolling resistance + air resistance
where weight is the weight of the truck, theta is the angle of the incline, rolling resistance is the force required to overcome the friction between the wheels and the ground, and air resistance is the force required to overcome air resistance.
Since the wheels do not slip on the ground, the rolling resistance is equal to the weight of the truck multiplied by the coefficient of rolling resistance, which is typically around 0.01. Air resistance is typically negligible at lower speeds, so we can ignore it in this case.
Let's assume the weight of the truck is 120 kN and the coefficient of rolling resistance is 0.01. We can now calculate the force required to maintain a constant speed of 72 km/h on an incline:
Force = 120 kN * sin(theta) + 0.01 * 120 kN
Next, we need to determine the power required to produce this force. We can use the following formula:
Power = force * speed
where speed is the speed of the truck in meters per second. Since the speed of the truck is 72 km/h, or 20 m/s, we can calculate the power required:
Power = (120 kN * sin(theta) + 0.01 * 120 kN) * 20 m/s
Now we can use the given engine power of 380 kW to determine the maximum angle of incline:
380 kW = (120 kN * sin(theta) + 0.01 * 120 kN) * 20 m/s
Simplifying this equation, we get:
sin(theta) = (380 kW / (120 kN * 20 m/s)) - 0.01
sin(theta) = 0.3167
Taking the inverse sine of both sides, we get:
theta = sin^-1(0.3167) = 18.3 degrees
Therefore, the maximum angle of incline the truck can climb at a constant speed of 72 km/h without slipping is approximately 18.3 degrees.
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The definition of the unit of current, the Ampere,is based on A. The force per unit length on a conductor in a uniform magnetic field B. The force per unit length on parallel current carrying conductors C. The charge per unit time delivered by a cell of e.m.f 1.0 V D. The charge passing a point per unit time in electrical current
Answer: D
Explanation:
a motor uses kn of force to power a vehicle that has a top speed of m/s. what is the power delivered by the motor? round answers to one decimal place.
A motor uses kn of force to power a vehicle that has a top speed of m/s. The power delivered by the motor is 9.8 kW (kilowatts).
To compute the power delivered by the motor, use the following formula:
P = Fv
Where:
P is the power delivered by the motor
F is the force exerted by the motor
v is the velocity at which the motor delivers the force
First, convert the force from kN to N by multiplying it by 1000 kN = 1000 N.
Now we can substitute the values in the formula:
P = 1000 N × m/sP = 1000 Nm/s
To convert Newton-meter to watts, divide it by the conversion factor 1 W = 1 J/s.
So:P = 1000 Nm/s / 1 WP = 1000 W
To convert watts to kilowatts, divide it by 1000. So:
P = 1000 W / 1000P = 1 kW
The power delivered by the motor is 1 kW.
Rounding it to one decimal place:
P = 1.0 kW
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which of the following would have the strongest magnetic field. assume the current in each is the same
Answer: Neodymium
Explanation: Neodymium is the strongest magnet. It is an alloy made from iron and boron. is the strongest magnet.
The strength of the magnetic field around the coil can be increased by increasing the current flowing through the coil (this will increase the flux) or by increasing the number of coil turns. which will also increase the flux Φ.
at the poles
The magnetic field around a magnet is the strongest at the poles. The maximum number of magnetic field lines pass through the poles.
A rock on a string is whirled fast enough to move in a vertical circle as shown. Gravity is acting downward.What is the direction of the rock's acceler- ation at the position shown?
At the position shown in the diagram, the rock's acceleration is pointing towards the centre of the circle. This means that the acceleration is directed downwards, in the opposite direction of gravity. The acceleration is a vector, so it can be represented as "vertical", pointing directly downwards.
At the position shown, the direction of the rock's acceleration is downwards. This is because the force acting on the rock is gravity, which is pulling the rock towards the center of the circle. Thus, the direction of the acceleration is always towards the center of the circle in vertical circles.
The motion of the rock is a combination of uniform circular motion and free fall. When the rock is at the topmost point of the circle, its velocity is zero, and it begins to fall under the influence of gravity. At this point, the acceleration of the rock is solely due to gravity and is equal to g (acceleration due to gravity).As the rock moves down the circle, the force of gravity and the tension force acting on the string combine to provide a net force acting towards the center of the circle.
This provides the centripetal acceleration that keeps the rock moving in a circle. At the bottommost point of the circle, the tension force in the string becomes zero, and the acceleration of the rock is solely due to gravity, but this time it acts in the direction of the tension force (i.e., towards the center of the circle).
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if the mass of a cart is quickly loaded to have twice the mass while a propelling force remains constant, the cart's acceleration
The mass of a cart is quickly loaded to have twice the mass while a propelling force remains constant, the cart's acceleration is halved due to the inverse proportionality of mass and acceleration.
When the mass of a cart is quickly loaded to have twice the mass while a propelling force remains constant, the cart's acceleration is halved. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is because force equals mass times acceleration (F=ma). When the mass of the cart is doubled, the net force on the cart remains the same, but the mass increases, causing the acceleration to decrease by half. This is due to the fact that the same force must now accelerate twice the mass, resulting in a lower acceleration. This is known as inverse proportionality; as one quantity doubles, the other quantity is halved.
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Can someone check my answers? If I’m incorrect can you correct me? Thank you. Image below.
Refer to the attached image.
Overall: Parts (a) and (c) need to be corrected.
a 504 g mass oscillates with an amplitude of 12.0 cm on a spring whose spring constant is 20.0 n/m .
The period of oscillation is approximately 0.998 seconds.
StepsWe can use the following formula to find the period of oscillation:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the spring constant.
Substituting the given values, we get:
T = 2π√(0.504 kg / 20.0 N/m)
T = 2π√(0.0252 kg/m)
T = 2π * 0.1589 s
T = 0.998 s (rounded to three significant figures)
Therefore, the period of oscillation is approximately 0.998 seconds.
The force needed to stretch or compress a spring by a specific amount is known as the spring constant (k), which serves as a gauge for a spring's stiffness. In the SI system, the spring constant is measured in Newtons per meter (N/m).
For example, if a spring requires a force of 10 N to stretch it by 0.5 meters, then the spring constant is:
k = F/x = 10 N / 0.5 m = 20 N/m
In many computations involving elastic systems, such as the oscillation of a mass on a spring or the compression of a spring in a mechanical system, the spring constant, a crucial spring parameter, is taken into account.
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A body freely falling under the action of gravity passes two points 10 metres apart vertically In 0.2s. From what height, above the higher point did it start to fall?
Answer:
Explanation:
We can use the equation for free fall motion to solve this problem:
h = (1/2)gt^2
where:
h = height from which the body started to fall (what we want to find)
g = acceleration due to gravity (9.8 m/s^2)
t = time taken to fall 10 meters (0.2 s)
First, we need to find the velocity of the body when it passes the lower point. Since the body is freely falling, it will have the same velocity as an object thrown vertically downward from rest at the height from which it started to fall (h). We can use the equation for final velocity in free fall to find this velocity:
vf^2 = vi^2 + 2gh
where:
vf = final velocity (which is the velocity when the body passes the lower point)
vi = initial velocity (which is zero)
g = acceleration due to gravity (9.8 m/s^2)
h = height from which the body started to fall (what we want to find)
Rearranging the equation and substituting the known values, we get:
vf = sqrt(2gh)
vf = sqrt(2 × 9.8 m/s^2 × h)
vf = sqrt(19.6h) m/s
Now we can use this velocity to find the time taken by the body to travel the 10-meter distance between the two points:
vf = gt
t = vf/g = sqrt(19.6h)/9.8 s
Finally, we can substitute this value of t into the equation for height and solve for h:
h = (1/2)gt^2 = (1/2) × 9.8 m/s^2 × (sqrt(19.6h)/9.8 s)^2
h = (1/2) × h
h = 5 meters
Therefore, the body started to fall from a height of 5 meters above the higher point.