A frictionless cart with a mass of 3.60 kg is rolling across a horizontal surface. A force of 5.20 N [W] acts onthe cart over a displacement of 12.0m [W]. If the final speed of the cart is 7.50 m/s, what was its initialkinetic energy?a. 67.2J c. 77.6 Jb. 38.9J d. 10.1 J
Question
A frictionless cart with a mass of 3.60 kg is rolling across a horizontal surface. A force of 5.20 N [W] acts onthe cart over a displacement of 12.0m [W]. If the final speed of the cart is 7.50 m/s, what was its initialkinetic energy?a. 67.2J c. 77.6 Jb. 38.9J d. 10.1 J
Solution
To solve this problem, we first need to find the work done on the cart. The work done on an object is given by the formula:
Work = Force x Distance
Here, the force is 5.20 N and the distance is 12.0 m. So, the work done on the cart is:
Work = 5.20 N x 12.0 m = 62.4 J
This work done on the cart is equal to the change in kinetic energy of the cart. The final kinetic energy of the cart is given by the formula:
Kinetic Energy = 0.5 x mass x (speed)^2
The final kinetic energy of the cart is:
Kinetic Energy = 0.5 x 3.60 kg x (7.50 m/s)^2 = 101.25 J
Since the work done on the cart is equal to the change in kinetic energy, the initial kinetic energy of the cart is:
Initial Kinetic Energy = Final Kinetic Energy - Work Done
Initial Kinetic Energy = 101.25 J - 62.4 J = 38.85 J
So, the initial kinetic energy of the cart was approximately 38.9 J, which corresponds to option b.
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