A mass of 8 kg is traveling at a constant 10.4 m/s when a 38 N force, F, starts to act in the opposite direction, stopping the object after it has traveled. How much work was done by the force, F, in stopping the object?
Question
A mass of 8 kg is traveling at a constant 10.4 m/s when a 38 N force, F, starts to act in the opposite direction, stopping the object after it has traveled. How much work was done by the force, F, in stopping the object?
Solution
To solve this problem, we need to use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the initial kinetic energy of the object. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
KE_initial = 1/2 * 8 kg * (10.4 m/s)^2 = 430.08 Joules
Step 2: Since the object is stopped, the final kinetic energy is 0.
KE_final = 0 Joules
Step 3: The work done on the object is equal to the change in its kinetic energy.
Work = KE_final - KE_initial = 0 Joules - 430.08 Joules = -430.08 Joules
The negative sign indicates that the work was done against the motion of the object. So, the work done by the force, F, in stopping the object is 430.08 Joules.
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