Question

To test out your new foam dart blaster, you hang a small cube, size 5cm on a side with mass 0.2 kg, from your ceiling. You then fire a 43.7 gram foam dart at the bottom of it with a speed of 18.1 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 = 0.2 kg

Mass of the foam dart = m = 43.7 g = 0.0437 kg

Speed of the foam dart when it hits the cube = u = 18.1 m/s

The foam dart sticks to the cube therefore the speed of the foam dart and the cube after the collision is same.

Speed of the foam dart and the cube after the collision = v

By conservation of linear momentum,

mu = (m + M)v

(0.0437)(18.1) = (0.0437 + 0.2)v

v = 3.25 m/s

Height gained by the block = h

By conservation of energy the kinetic energy of the cube and the foam dart after the collision is converted into the potential energy as it rises upwards.

h = 0.538 m

Height the block will reach relative to where it started = 0.538 m