A ballistic pendulum is a device that is used to measure the speed at which a pr

Question

A ballistic pendulum is a device that is used to measure the speed at which a projectile leaves the barrel of a gun. The diagram below depicts how it works: a bullet of known mass, m, is fired into a block of much larger mass, M, which is initially at rest. The larger mass is the bob on a pendulum. The bullet embeds in the block and after the collision the two masses (now stuck together) swing the pendulum upwards to a maximum height/angle before coming to rest. (a) Let’s say the bullet has a mass of 12 grams and the block has a mass of 10 kg (note we have a bullet measured in grams and the block in kilograms).

The bullet is fired and leaves the barrel with a muzzle speed of 200 m/s. If the pendulum arm has a length of 50 cm, find the following: (a) the type of collision (i.e. elastic or inelastic); (b) the total momentum just before the collision; (b) the total momentum just after the collision; (c) the speed of the (bullet + block) together just after the collision at the bottom of the pendulum’s swing; (d) the tensile force endured by the pendulum arm; Hint: the pendulum swings in a circular arc so draw a force diagram and think ‘centripetal forces’.

(e) Also, find the change in the system’s total KE from before the collision to just after the collision. (f) How much work did the block’s friction do on the bullet during the process of slowing the bullet? If the bullet was found to have wedged into the block a distance of 8 cm, how much resistive/frictional force did the block’s material impart on the bullet? (g) To what height does the (block + bullet) reach above the lowest point in the pendulum swing? (h) to what maximum angle does the (block + bullet) reach before coming to rest?

Explanation / Answer

here,

M1 = mass of the bullet = 12 g = 0.012 kg
V1 = initial speed of the bullet = 200 m/sec.

M2 = mass of the blob = 10 kg
V2 = initial speed of the blob = 0

L = 0.5 m

A) The collision will inelastic as KEi is transferred to Blob and they are moving together

B)

Momentum befroe Collsion :
Pi = M1*V1 + M2*V2
Pi = M1*V1
Pi = 0.012 *200
Pi = 2.4 kg.m/s

Momentum After collision :
Pf = (m1+m2)*V
Pf = (0.012 +10)V
Pf = 10.012*V

C)
Pi = Pf
2.4 = 10.012*V2
V = 24.02 m/s

D)

T - M2*g = (M1+M2)*v^2/r

T - 10*9.8 = 10.012 * 24.02^2 / 0.5

T = (10.012 * 24.02^2 / 0.5) - 98

T = 11455.05 N

T = 11.45 KN

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.