A ball of mass 0.20 kg is attached to one end of a string and whirled around in a horizontal circle of radius 0.80 m at a constant speed of 4.0 m/s. The tension in the string provides the resultant force that keeps the ball moving along this circular path. (a) State the directio…

Answer: ((a)) The resultant force acts at right angles to the ball's velocity, directed towards the centre of the circle. ((b)) The resultant force is always at right angles to the ball's velocity, so it has no component along the direction of motion. A force acting perpendicular to the velocity changes only the direction of motion, not the speed, so the ball's speed stays constant while its direction co… ((c)) The force needed increases. On a smaller circle, the direction of the ball's motion must change more rapidly to keep it on the tighter curved path at the same speed, so a greater force is needed to produce this faster change in direction. ((d)) The ball moves off in a straight line, at a constant speed, in the direction it was travelling at the instant the string broke (a tangent to the circle at that point). This is because, once the string breaks, no resultant force acts on the ball, so by Newton's first law it conti…. Part (a): Direction of the resultant force For the ball to keep moving on a circular path, the resultant force on it must act at right angles to its velocity, directed towards the centre of the circle. This is provided here by the tension…

IGCSE Physics 0625: Circular Motion, Centripetal Force and Newton's First Law

A ball of mass $0.20\text{ kg}$ is attached to one end of a string and whirled around in a horizontal circle of radius $0.80\text{ m}$ at a constant speed of $4.0\text{ m/s}$ . The tension in the string provides the resultant force that keeps the ball moving along this circular path.

(a) State the direction of the resultant force acting on the ball at any instant, relative to the ball's velocity at that instant. [1]

(b) Explain, in terms of the resultant force described in (a), why the ball's speed stays constant even though a resultant force is continuously acting on it. [2]

(c) The string is then shortened so that the ball moves at the same constant speed of $4.0\text{ m/s}$ , but now on a circle of smaller radius. State and explain what happens to the size of the force needed to keep the ball moving on this smaller circle, compared with the original circle. [2]

(d) While the ball is moving on the circular path, the string suddenly breaks. Describe the subsequent motion of the ball immediately after the string breaks, and explain your answer in terms of the forces now acting on it (ignore gravity and air resistance). [2]

Part (a): Direction of the resultant force

For the ball to keep moving on a circular path, the resultant force on it must act at right angles to its velocity, directed towards the centre of the circle. This is provided here by the tension in the string.

Part (b): Why the speed stays constant

A resultant force can be split into a component along the direction of motion (which would speed the object up or slow it down) and a component at right angles to the direction of motion (which changes only the direction of motion).

Because the resultant force on the ball is entirely at right angles to its velocity at every instant, it has no component along the direction of motion. It therefore cannot speed the ball up or slow it down. It can only keep changing the direction in which the ball is travelling. This is why the ball moves at a constant speed while continuously changing direction as it goes around the circle.

Part (c): Effect of a smaller radius

When the string is shortened, the ball moves on a circle of smaller radius but at the same speed of $4.0\text{ m/s}$ .

On a smaller circle, the ball’s path curves more sharply, so its direction of motion must change more rapidly to keep it on this tighter path at the same speed. Changing the direction of motion more quickly, for the same speed, requires a bigger force. So the force needed to keep the ball moving on the smaller circle is greater than the force needed on the original, larger circle.

Part (d): The string breaks

The instant the string breaks, it can no longer provide a force on the ball. Ignoring gravity and air resistance, there is then no resultant force acting on the ball at all.

By Newton’s first law, an object with no resultant force acting on it continues moving at a constant velocity. That is, at a constant speed, in a straight line. So immediately after the string breaks, the ball flies off in a straight line at constant speed, in whatever direction it happened to be moving at that instant (a tangent to the circle at the point where the break occurred). It does not continue to curve around the circle, and it does not stop.

Final answers

(a) The resultant force acts at right angles to the velocity, towards the centre of the circle
(b) A force at right angles to the velocity changes only the direction, not the speed, so speed stays constant
(c) The force needed increases for the smaller radius, since the direction must change more rapidly at the same speed
(d) The ball moves off in a straight line at constant speed (a tangent to the circle), since no resultant force acts on it once the string breaks