A crate of mass 50 kilograms is being pushed across a rough surface at a steady 8.0 metres per second. The crate is then released and comes to a stop in 10 seconds. What is the average rate at which the frictional force on the crate removes kinetic energy from it?
Let’s call the mass of the crate 50 kilograms 𝑚. And we’ll call the crate’s constant speed of 8.0 metres per second 𝑣. The time it takes the crate to stop 10 seconds we’ll call 𝑡. We’ll call the rate at which the frictional force on the crate removes kinetic energy from it capital 𝑅 sub E, the rate at which energy is removed.
Let’s draw a diagram of this scenario. We have a crate of mass 𝑚, moving along a horizontal surface at speed 𝑣. The frictional force 𝐹 sub f between the mass and the fore pulls energy away from the mass as it slides to a stop. We want to find the rate at which the kinetic energy of the crate is lost as it comes to a stop.
To start, let’s recall the equation for the kinetic energy of an object. An object’s kinetic energy equals one-half its mass times its speed squared. We can calculate the kinetic energy of the crate right before it starts to slow down. That kinetic energy is half its mass of 50 kilograms times its speed of 8.0 metres per second squared. Multiplying these values together, we find that the crate’s initial and maximum kinetic energy is 1600 joules. The rate at which that energy is lost will equal the total energy of the crate 1600 joules divided by the time over which that energy is depleted.
So we can write 𝑅 sub E is equal to KE divided by 𝑡, the time it takes the crate to come to a stop. This equals 1600 joules divided by 10 seconds. On average then, kinetic energy is lost from the crate at a rate of 160 joules every second. This is the average rate of kinetic energy loss of the crate as it slows.