Question

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?

Answer 1

Answer:

V=15.46m/s

Explanation:

By making an energy balance:

Initial energy:  $\frac{K*X^2}{2}$   where K=1100N/m  and X=4m

Final energy: $\frac{m*V^2}{2} + m*g*h$   where m=60kg and h=2.5m

Work done by friction force: -Ff*X   where Ff = 40N and X=4m

The balance will be:

$\frac{m*V^2}{2} + m*g*h-\frac{K*X^2}{2}=-Ff*X$  Solving for V:

$V=\sqrt{\frac{-Ff*X+K*X^2/2-m*g*h}{m/2} }=15.46m/s$  using g=9.8m/s^2