Spring gun physics?

Question

The spring of a spring gun has force constant k = 400 N/m and negligible mass. The spring is compressed 6.00 cm and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal.

(a) Calculate the speed with which the ball leaves the barrel if you can ignore friction.

(b) Calculate the speed of the ball as it leaves the barrel if a constant resisting force of 6.00 N acts on the ball as it moves along the barrel

(c) For the situation in part (b), at what position along the barrel does the ball have the greatest speed? (In this case, the maximum speed does not occur at the end of the barrel.)

(d) What is that greatest speed?

Answer 1

The 2 great Laws of Kinematics are F = ma and you can't push on a rope. Everything else drops out with a little bit of Calculus and Horsesense.

In part (a) (if you ignore friction) the spring has a potential energy of kx²/2 = 0.72 J. Since all of this energy will be imparted to the ball, the ball will have a kinetic energy of
mv²/2 = 0.72J and, since it's mass is .03 kg, it will have a velocity of
√48 = 6.928 m/s.

Now *you* get off yer dead αss and figure out which equations apply to the other cases given. You only get to learn this stuff once, and I had my turn 40+ years ago ☺


Doug