A pendulum can be used to calculate the speed of a bullet that comes out of a gu

Question

A pendulum can be used to calculate the speed of a bullet that comes out of a gun. A bullet shot from the left will embed itself in a block of wood suspended by two strings. After this totally inelastic collision the block (and bullet) will swing to the right reaching a height y.

Consider a 10.4 g bullet fired into a ballistic pendulum of mass 4.000 kg. If the block rises to a height of 4.50 cm

(a) What was the initial speed of the bullet? hint: Deal with the swing first, then the collision.

(b) What percentage of the bullet’s initial kinetic energy was lost in the actual collision?

Explanation / Answer

a)Change in potential Energy when it is at height of 4.5cm = (M+m)gh = 4.01*9.8*0.045 = 1.77 J

So this must be equal to the kinetic energy of the(block + bullet) just after the collision. So,

KE = (p2/2m) = 1.77

=> p = sqrt(2*4.01*1.77) = 3.77 kg.m/s

Since in the collision the momentum is conserved before and after it. So the momentum just before the collision must be equal to 3.77 Kg.m/s.(where v is the velocity before the collision.)

So 0.0104*v = 3.77

or v = 362.277 m/s

b) Kinetic energy before the collision = p2/2m = 3.772/(2*0.0104) = 683.3125 J

loss in kinetic energy = 679.5425.

so % loss = 100*679.5425/683.3125 = 99.45%.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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