Question

A playground ride consists of a disk of mass M =32 kg and radius R-1.7 m mounted on a low-friction axle (see figure below). A child of mass m =24 kg runs at speed V Ξ2.7 m/s on a line tangential to the disk and jumps onto the outer edge of the disk.Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact. (Assume the child is initially moving in the positive direction. Indicate the direction with the sign of your answer.)

Answer 1

The change in linear momentum of the system consisting of the child plus the disk is 129.6 kg·m/s in the positive direction.

Step-by-step explanation:

To calculate the change in linear momentum of the system consisting of the child plus the disk, we need to find the initial and final momentums. Initially, the child is running at a speed of 2.7 m/s and has a mass of 24 kg. The linear momentum of the child before impact is given by:

P_initial = mass_initial × velocity_initial

P_initial = 24 kg × 2.7 m/s = 64.8 kg·m/s (in the positive direction)

The disk has a mass of 32 kg and is initially at rest. Therefore, its initial linear momentum is 0 kg·m/s.

After the child jumps onto the disk, both the child and the disk move together. The final linear momentum of the system is:

P_final = P_initial + P_added

P_final = 64.8 kg·m/s + 24 kg × 2.7 m/s

P_final = 64.8 kg·m/s + 64.8 kg·m/s = 129.6 kg·m/s (in the positive direction)

Therefore, the change in linear momentum of the system is:

Change in momentum = P_final - P_initial

Change in momentum = 129.6 kg·m/s - 0 kg·m/s = 129.6 kg·m/s (in the positive direction)