Question

A 236 g cart moves on a horizontal, frictionless surface with a constant speed of 26.9 cm/s. A 66.1 g piece of modeling clay is dropped vertically onto the cart. If the clay sticks to the cart, find the final speed of the system. Answer in units of cm/s.

Answer 1

The final speed of the system is 21 cm/s.

Step-by-step explanation:

Given:

Mass of the cart (M) = 236 g

Initial velocity of the cart (U) = 26.9 cm/s

Mass of the clay (m) = 66.1 g

Initial velocity of the clay (u) = 0 cm/s (At rest initially)

Let the final velocity of the system be 'v'.

Now, total initial momentum is given as:

Initial momentum = Initial momentum of cart + Initial momentum of clay

`P_i=MU+mu\\\\P_i=236* 26.9+0=6348.4\ g\cdot cm/s`

Final momentum of the system is given as:

Final momentum = Total mass × Final velocity

`P_f=(M+m)v\\\\P_f=(236+66.1)v\\\\P_f=302.1v`

Now, from conservation of total momentum, final momentum is equal to initial momentum. So,

`P_f=P_i\\\\302.1v=6348.4\\\\v=(6348.4)/(302.1)=21\ cm/s`

Therefore, the final speed of the system is 21 cm/s.