The Great Sandini is a 60-kg circus performer who is shot from a cannon (actually a spring gun). You don’t find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1100 N/m that he will compress with a force of 4400 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 40 N during the 4.0 m he moves in the barrel. At what speed will he emerge from the end of the barrel, 2.5 m above his initial rest position?

Solution 53P Step 1 of 4: A person of mass m= 60 kg is at rest on a ‘x’ meters compressed spring with force F spring4400 N and force constant k=1100 N/m. We need to calculate the speed at a height 2.5m from the end of barrel, with which the person flies when he moves through the barrel with friction force fri= 40 N for d= 4m as shown in the figure below, Step 2 of 4: Given data, Mass, m=60 kg Force constant,k =1100 N/m Force on spring F spring4400 N Height , h =2.5 m Frictional force, F = 40 N fri Distance, d= 4m To find, Compression, x= Speed of person, v= First we need to calculate the compression distance x, Using F = k x spring Substituting F spring=4400 N and k =1100 N/m and solving for x 4400 N = (1100 N/m) x x = 4m Therefore, the spring is compressed 4m.