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