Set 3 Problem number 27

• Problem

• Solution

Problem

A rubber band does 85 J of work as it launches a mass of 8.9 kg.

• By how much does the elastic PE of the system change, and if no energy is dissipated what will be the KE change of the mass?
• Assuming that no other forces act on the mass, if the mass started from rest, what velocity will attain?

Solution

As the rubber band does positive work on the mass the elastic PE of the rubber band decreases, so as the rubber band does 85 J of work its elastic PE decreases by 85 J.

• If no energy is dissipated, then the KE change of the mass will equal the PE loss of 85 J.
• If its velocity before the change was 0 then its original KE was 0.

• If no other forces act on during the PE change, the 85 J change in the object's KE will give it a KE of 85 J.

• A mass of 8.9 kg with a KE of 85 J will have .5 mv^2 = KE, so its velocity is

• v = `sqrt(2 KE / m) = `sqrt(2 * 85 J / 8.9 kg) = 4.37 m/s.