Question

1. 2. A spring-loaded toy gun is used to shoot a ball of mass M straight up in the air. The ball is not attached to the spring. The ball is pushed down onto the spring so that the spring is compressed a distance S below its unstretched point. After release, the ball reaches a maximum height 35, measured from the unstretched position of the spring (see diagram below). Maximum Height Spring unstretched Spring compressed Mass released from west will Find the spring constant of the spring. [10 Marks] Find the equilibrium point of the ball when it is sitting on the spring with no forces other than the force due to gravity of the ball acting on the spring. Clearly indicate the point you are using as the origin of your coordinate system and what direction is positive. [7 Marks] Now, the ball is glued onto the spring so that it oscillates up and down rather than flying off the spring. The spring is again compressed the same distance S below its unstretched point. Write an equation for the position of the ball as a function of time after it is released. Clearly indicate the point you are using as the origin of your coordinate system and what direction is positive. [8 Marks)

Answer 1

Upward direction is positive and downward is negative.

35 Let the spring constante =k , mass of ball am Inloal compression of springs using Energy conservation Як (s”- та - мд (35) - Ак(s} = m3 (45) |к --- Что 1 % а let spring compress by a, distance to ost» Episълим о v 1 mg = kro 5 - () - 15 Of ball glired and the spring. It becomes spring mass to system. Now spring is impressing + Фоугол азется у Фуѕ bлт 44 маълим condation no. Equitbrium Is - м — что y=ssinut Position de