depicts the following scenario. In a ballistic pendulum, an object of mass m is

Question

depicts the following scenario. In a ballistic pendulum, an object of mass m is fired with an initial speed v_i at the bob of a pendulum. The bob has a mass M, and is suspended by a rod of negligible mass. After the collision, the object and the bob stick together and swing through an arc, eventually gaining a height h. Now we will consider some slightly different related scenarios to Example 9-12. Suppose a bullet of mass m = 7.05 kg is fired into a ballistic pendulum whose bob has a mass of M = 0.700 kg. If the bob rises to a height of 0.148 m, what was the initial speed of the bullet? What was the speed of the bullet-bob combination immediately after the collision took place? Express your answer using three significant figures. Refer back to example 9-12. A bullet with a mass of m = 8.10 g and an initial speed of v_i = 320 m/s is fired into a ballistic pendulum. What mass must the bob have if the bullet-bob combination is to rise to a maximum height of 0.125 m after the collision? Express your answer using two significant figures.

Explanation / Answer

part A

Given that

mass of bullet m=7.05 kg

mass of the bob M=0.7 kg

height h=0.148 m

now we find the initial velocity of the bullet

initial velocity u={m/M+m}(2gh)^1/2

={7.05/7.05+0.7}(2*9.8*0.148)^1/2

=12/7.75

=1.55 m/s

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now we find the finial velocity of bullet-bob combation

finial velocity Vf=(2*9.8*0.148)^1/2=1.7 m/s

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Part C

Given that

mass of bullet m=0.0081 kg

initial speed u=320 m/s

maximum height h=0.125

0.0081*320=(0.0081+M)(2*9.8*0.125)61/2

2.592/1.57=0.0081+M

mass of the bob M=1.651-0.0081=1.6429 kg =1642.9 grams

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