10_1425_web_Lec_13_KineticEnergy

10_1425_web_Lec_13_KineticEnergy - Kinetic Energy and...

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Kinetic Energy and Energy Conservation Physics 1425 Lecture 13 Michael Fowler, UVa
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Moving Things Have Energy Energy is the ability to do work: to deliver a force that acts through a distance. Placing a weight gently on a nail does nothing. Dropping the weight on the nail can drive the nail into the wood. If the weight is moving when it hits the nail, it has the ability to do work driving the nail in. This is its kinetic energy. A 5kg
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How Much Work Does the Moving Weight Do? After contact with the nail, the forces between the weight and the nail are equal and opposite. Suppose the nail is driven in a total distance x 0 . In going through a small distance Δ x , the work done on the nail Δ W = F Δ x . Meanwhile, for the weight - F = ma , the weight has slowed down : - F = m Δ v / Δ t . Therefore Δ W = F Δ x = - m Δ v Δ x / Δ t . Now for small Δ x , we can take Δ x / Δ t = v , so Δ W = - mv Δ v , and A Δ x 5kg x 0 -F F 0 0 0 2 1 0 2 0 x v W dW mvdv mv = = −= ∫∫ Weight hits nail with speed v 0
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Where Did the Weight’s Energy Come From? We’ve seen that if the weight hits the nail and comes rapidly to rest, it loses energy ½ mv 0 2 . This is its kinetic energy K at speed v 0 . Let’s suppose it gained that energy by being dropped from rest at a height h . At uniform acceleration g , v 0 2 = 2 gh .
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10_1425_web_Lec_13_KineticEnergy - Kinetic Energy and...

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