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 1300 N/m that he will compress with a force of 6500 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 50 N during the 5.0 mm he moves in the barrel. Required:
At what speed will he emerge from the end of the barrel, 2.5 mabove his initial rest position?

22m/s

Explanation:

Mass, m=60 kg

Force constant, k=1300N/m

Restoring force, Fx=6500 N

Average friction force, f=50 N

Length of barrel, l=5m

y=2.5 m

Initial velocity, u=0

Substitute the values

m

Work done due to friction force

We have

Substitute the values

Initial kinetic energy, Ki=0

Initial gravitational energy, \

Initial elastic potential energy

Final elastic energy,

Final kinetic energy,

Final gravitational energy,

Final gravitational energy,

Using work-energy theorem

Substitute the values

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s