Question

To test out your new foam dart blaster, you hang a small cube, size 5cm on a side with mass 0.3 kg, from your ceiling. You then fire a 36.8 gram foam dart at the bottom of it with a speed of 16.2 m/s, and the dart sticks to the cube. Calculate the height in m that the block will reach relative to where it started.

Answer 1

Gravitational acceleration = g = 9.81 m/s2

Mass of the cube = M = 0.3 kg

Mass of the foam dart = m = 36.8 g = 0.0368 kg

Speed of the dart when it hits the cube = u = 16.2 m/s

Speed of the dart and cube after the collision = v

By conservation of linear momentum,

mu = (m+MU

(0.0368 )(16.2) = (0.0368 + 0.3) ບ

v = 1.77 m/s

Height the cube will reach = H

The kinetic energy of the cube and the dart after the collision is converted into the potential energy of the cube and dart as they go up.

-= mgH

5=gH

(1.77) - (9.81)H

H = 0.16 m

Height that the block will reach relative to where it started = 0.16 m