A spring-based toy gun is used to shoot a ball of mass M straight up. The ball is not attached to the spring. The ball is pushed downward into the spring so that the spring is compressed to a distance S below its relaxation point. After the release, the ball reaches a maximum height 3S, measured from its relaxation position, see Fig. 1(b). (a) Find the constant of the spring. (b) Find the equilibrium point of the ball when it is on the compressed spring with no forces other than gravity and the spring acting on it. Clearly indicate the point you are using as the origin of your coordinate system and which direction is positive. system and which direction is positive. (c) Now the ball is glued to the spring so that it oscillates up and down instead of flying off the spring. The spring is again compressed to the same distance S below its of relaxation. Write an equation for the position of the ball as a function of time after it is released. Indicate clearly which point you are using as the origin of your coordinate system and which direction is positive (if it changes).
A spring-based toy gun is used to shoot a ball of mass M straight up.
The ball is not attached to the spring. The ball is pushed downward into the spring so that the spring is compressed to
a distance S below its relaxation point. After the release, the ball reaches a maximum height 3S,
measured from its relaxation position, see Fig. 1(b). (a) Find the constant of the spring. (b) Find
the equilibrium point of the ball when it is on the compressed spring with no forces other than gravity and the
spring acting on it. Clearly indicate the point you are using as the origin of your coordinate system and which direction is positive.
system and which direction is positive. (c) Now the ball is glued to the spring so that it oscillates up and down
instead of flying off the spring. The spring is again compressed to the same distance S below its
of relaxation. Write an equation for the position of the ball as a function of time after it is released. Indicate
clearly which point you are using as the origin of your coordinate system and which direction is positive
(if it changes).
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