A 20.0 kg cart is moving with a velocity of 7.30 m/s down a level hallway. A constant force of -11.0 N acts on the cart and its velocity becomes 3.50 m/s. a) What is the change in kinetic energy of the cart? b) How much work was done on the cart? c) How far did the cart move while the force acted?
My thoughts: KE = 1/2mv^2. The mass would be 20.0 kg. How would you find the change in kinetic energy?
a) (1/2) M [V2^2 - V1^2]
b) Negative work is done slowing it down. Same result as (a), if there was no friction. If there was friction, you have to know how far it moved to compute the work done.
c) Assuming no friction,
Work done = (force)*(distance) = kinetic energy change
Solve for the distance
To find the change in kinetic energy (ΔKE) of the cart, you can use the formula:
ΔKE = KE(final velocity) - KE(initial velocity)
Given that the cart's initial velocity (v1) is 7.30 m/s and the final velocity (v2) is 3.50 m/s, you can calculate the initial and final kinetic energies as follows:
KE(initial) = 1/2 * m * v1^2
KE(final) = 1/2 * m * v2^2
Substituting the given values into the equations:
KE(initial) = 0.5 * 20.0 kg * (7.30 m/s)^2
KE(final) = 0.5 * 20.0 kg * (3.50 m/s)^2
Now, you can calculate the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy:
ΔKE = KE(final) - KE(initial)
Simplifying the equations:
ΔKE = (0.5 * 20.0 kg * (3.50 m/s)^2) - (0.5 * 20.0 kg * (7.30 m/s)^2)
Once you solve this equation, you will find the change in kinetic energy of the cart (a).
Is there anything else I can assist you with?
To find the change in kinetic energy of the cart, you can subtract the final kinetic energy from the initial kinetic energy.
a) First, calculate the initial kinetic energy using the formula KE = 1/2mv^2, where m is the mass and v is the velocity.
Plugging in the values:
Initial kinetic energy = 1/2 * 20.0 kg * (7.30 m/s)^2
b) Next, calculate the final kinetic energy using the same formula, but with the new velocity.
Final kinetic energy = 1/2 * 20.0 kg * (3.50 m/s)^2
c) Finally, to find the change in kinetic energy, subtract the final kinetic energy from the initial kinetic energy.
The formula would be:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
This will give you the answer for part (a) of the question.