A bullet (mass- 0.220 kg) moving horizontally at 530 m/s penetrates a 3.50 kg wo

Question

A bullet (mass- 0.220 kg) moving horizontally at 530 m/s penetrates a 3.50 kg wood block resting on a frictionless table Consider three different scenarios: a) After emerging from the block, the bullet has been slowed down to 318 m/s. What is the final speed of the block? m/s b) Repeat the above question, only now assume that the bullet bounces back at 318 m/s. What is the final speed of the block? m/s c) Repeat the above question, only now figure that the bullet sticks to the block. What is the mass of the (block+bullet)? What is the final speed of the block? kg m/s. In all of these cases, if you add up the KE for both objects after the impact, you get less than the total KE before. Just to emphasize this, for each case, construct an energy table determine how much kinetic energy gets turned into thermal energy: a) Vblock Vbullet KEblock KEbullet Thermal | 0 J total Before After b) Vblock Vbullet Before After 0 m/s c) Vblock Vbullet Before After 0 m/s 0 m/s 0 J 0 J KEblock0J KE bullet Thermal OJQb? total Qa? KEbullet Thermal OJQc? total

Explanation / Answer

m = mass of bullet = 0.22 kg

M = mass of block = 3.50 kg

vi = initial velocity of bullet = 530 m/s

Vi = initial velocity of block = 0 m/s

vf = final velocity of bullet = 318 m/s

Vf = final velocity of block = ?

using conservation of momentum

m vi + M Vi = m vf + M Vf

(0.22) (530) + (3.50) (0) = (0.22) (318) + (3.50) Vf

Vf = 13.33 m/s

b)

m = mass of bullet = 0.22 kg

M = mass of block = 3.50 kg

vi = initial velocity of bullet = 530 m/s

Vi = initial velocity of block = 0 m/s

vf = final velocity of bullet = - 318 m/s

Vf = final velocity of block = ?

using conservation of momentum

m vi + M Vi = m vf + M Vf

(0.22) (530) + (3.50) (0) = (0.22) (- 318) + (3.50) Vf

Vf = 53.33 m/s

c)

mass of the combination = m + M = 0.22 + 3.5 = 3.72 kg

V = final speed

using conservation of momentum

m vi + M Vi = (m + M) V

(0.22) (530) + (3.50) (0) = 3.72 V

V = 31.3 m/s

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