Question

A block that has a mass M = 500 g is hanging at rest on a light string. A projectile with a mass m = 15 g moving horizontally with a velocity of 255 m/s strikes M and sticks in it. The block and its projectile swing up. How high does the center of mass rise?

Answer 1

2.8m

Step-by-step explanation:

Convert to metric:

500g = 0.5 kg

15g = 0.015 kg

Assuming elastics collision, we could use the law of momentum conservation to calculate the speed of black and projectile post-collision V:

mv = (M + m)V

`V = (mv)/(m+M) = (0.015*255)/(0.5 + 0.015) = 7.43 m/s`

This would make the system moves up, which convert its kinetic energy to potential energy. By the law of energy conservation when the mass reaches its highest point (aka speed = 0)

`E_k = E_p`

`0.5(M+m)V^2 = (M+m)gh`

`h = (V^2)/(2g) = (7.43^2)/(2*9.81) = 2.8m`