7 A small, hollow, plastic ball, of mass \(m \mathrm {~kg}\) is at rest at a point \(O\) on a polished horizontal surface. The ball is attached to two identical springs. The other ends of the springs are attached to the points \(P\) and \(Q\) which are 1.8 metres apart on a straight line through \(O\).
The ball is struck so that it moves away from \(O\), towards \(P\) with a speed of \(0.75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
As the ball moves, its displacement from \(O\) is \(x\) metres at time \(t\) seconds after the motion starts.
The force that each of the springs applies to the ball is \(12.5 m x\) newtons towards \(O\).
The ball is to be modelled as a particle. The surface is assumed to be smooth and it is assumed that the forces applied to the ball by the springs are the only horizontal forces acting on the ball.
7
- Find the minimum distance of the ball from \(P\), in the subsequent motion.
7
- In practice the minimum distance predicted by the model is incorrect.
Is the minimum distance predicted by the model likely to be too big or too small?
Explain your answer with reference to the model.
[0pt]
[2 marks]