Set 3 Problem number 27

• Problem

• Solution

Problem

What velocity will be attained by the mass of 6.2 kg if, starting from rest, a rubber band does 31 Joules of work on it?

Assume that no other forces act on the object. By how much do the PE and the KE of the system change in the 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 31 J of work its elastic PE decreases by 31 J.

• If no energy is dissipated, then the KE change of the mass will equal the PE loss of 31 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 31 J change in the object's KE will give it a KE of 31 J.

• A mass of 6.2 kg with a KE of 31 J will have .5 mv^2 = KE, so its velocity is

• v = `sqrt(2 KE / m) = `sqrt(2 * 31 J / 6.2 kg) = 3.16 m/s.