Question

n 38 g rifle bullet traveling at 410 m/s buries itself in a 4.2 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the maximum vertical displacement of the pendulum (height).(g = 9.8 m/s2)

Answer 1

68cm

Step-by-step explanation:

You can solve this problem by using the momentum conservation and energy conservation. By using the conservation of the momentum you get

`p_f=p_i\\mv_1+Mv_2=(m+M)v`

m: mass of the bullet

M: mass of the pendulum

v1: velocity of the bullet = 410m/s

v2: velocity of the pendulum =0m/s

v: velocity of both bullet ad pendulum joint

By replacing you can find v:

`(0.038kg)(410m/s)+0=(0.038kg+4.2kg)v\\\\v=3.67(m)/(s)`

this value of v is used as the velocity of the total kinetic energy of the block of pendulum and bullet. This energy equals the potential energy for the maximum height reached by the block:

`E_(fp)=E_(ki)\\\\(m+M)gh=(1)/(2)mv^2`

g: 9.8/s^2

h: height

By doing h the subject of the equation and replacing you obtain:

`(0.038kg+4.2kg)(9.8m/s^2)h=(1)/(2)(0.038kg+4.2kg)(3.67m/s)^2\\\\h=0.68m`

hence, the heigth is 68cm