Set 3 Problem number 27

• Problem

• Solution

Problem

Assuming that no energy is dissipated in the process and that no other forces act on the object, what velocity will mass of 5 kg attain, starting from rest, as a rubber band does 86 J of work on it? What will be the PE and KE changes of the system during this process?

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 86 J of work its elastic PE decreases by 86 J.

• If no energy is dissipated, then the KE change of the mass will equal the PE loss of 86 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 86 J change in the object's KE will give it a KE of 86 J.

• A mass of 5 kg with a KE of 86 J will have .5 mv^2 = KE, so its velocity is

• v = `sqrt(2 KE / m) = `sqrt(2 * 86 J / 5 kg) = 5.86 m/s.