The ballistic pendulum is a device to measure the speed of a projectile. A block

Question

The ballistic pendulum is a device to measure the speed of a projectile. A block, B, is suspended by a string of length L and is initially at rest. The projectile, A, moves to the right before it collides head-on with the block. The projectile is embedded in the block and the two swing up as one unit. The maximum height h is measured to be 0.2 m and the masses of the projectile and the block are mA = 2 g and mB = 400 g. We want to determine the initial speed vA of the projectile and will neglect drag forces.



(a) What is true for the collision between the projectile and the block:
(i) momentum is conserved (ii) kinetic energy is conserved (iii) mass is conserved
[1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii)
(b) Which conservation law/principle applies to the projectile and block swinging up together?
(i) Wnet = K2 - K1 (ii) U1 + K1 = U2 + K2 (iii) U1 + K1 = U2 + K2 - Wfr
[1] only (i) [2] only (ii) [3] only (iii) [4] (i) and (ii) [5] (i) and (iii)
(c) Calculate the speed of the block with projectile after the collision
[1] vA = 2 m/s [2] vA = 200 m/s [3] vA = 400 m/s
[4] vA = 402 m/s [5] none of these
(d) Calculate the speed of the projectile before the collision.
[1] vA = 2 m/s [2] vA = 200 m/s [3] vA = 400 m/s
[4] vA = 402 m/s [5] none of these

Explanation / Answer

a) momentum and mass are both conserved so:
[4] (i) and (iii)

b) energy is conserved in the swing (and we neglect drag):
[2] only (ii)

c) U1 + K1 = U2 + K2
U1 and K2 are zero so
K1 = U2
(0.5)mv^2 = mgh
m's cancel
(0.5)v^2 = (9.8)(0.2m)
v = 1.98m/s

[1] 2m/s

d) mAvA = (mA+mB)v'
(2g)vA = (402g)(2m/s)
vA = 398m/s

[3] vA = 400m/s

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