Let me set up the parameters for the experiments. The bullet is 20 grams. The wo

Question

Let me set up the parameters for the experiments. The bullet is 20 grams. The wood block is 400 grams. It is 10 cm high and 20 cm wide. The thickness will not be necessary. The center of mass of the block travels a distance of 1 meter after the collision. The bullet enters the block 5 cm from the center in case 2. Let's assume that it takes 10 J of energy to penetrate the block of wood by 1 mm. Here are the approximations. Assume that the bullet ends up 5 cm from the center of mass of the block in case 2 when considering the rotational motion of the block. Assume that the collision is instantaneous as well. Assume that there is no air resistance. What is the difference between the two cases other than the fact that the block is rotating in the second case? Answer using numbers. Watch your units. Draw a diagram to keep track of all your numbers. Calculate the angular velocity difference. Calculate the energy loss difference Calculate the penetration depth difference.

Explanation / Answer

considering first case -

torque = change in angular momentum

as applied torque is zero there won't be any change in angular velocity so angular velocity will be zero.

gain in potential energy = 0.420*9.8*1 = 4.416 joule'

if the speed of the bullet was same in both the cases so loss in kinetic energy = 4.416 joule

so energy loss in penetration + gain in potential energy = kinetic energy of the bullet

considering second case -

intial angular velocity = 0

final = w

gain in potential energy = 4.416 joule

as supplied torque would change the angular velocity so kinetic energy loss must go in three sections -

gain in PE + gain in rotational KE + penetration

so penetration will be more in second case

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