Edexcel A-Level Physics: Further Mechanics

A small ball is attached to one end of a light inextensible string. The other end is held fixed and the ball is whirled in a vertical circle of constant radius at a steady speed. As the ball travels round the loop, the tension in the string changes even though its speed is roughly constant.

Explain how and why the tension in the string varies as the ball moves round the vertical circle, and hence explain why the string is most likely to snap when the ball is at the lowest point of the circle. In your answer you should refer to the centripetal force requirement and to the weight of the ball at the top and bottom of the loop.

(6 marks)

A conical pendulum consists of a small bob attached to the end of a light inextensible string. The bob moves in a horizontal circle at constant speed while the string traces out a cone, making a constant angle of 35° with the vertical.

Quantity	Value
Mass of bob, $m$m	0.25 kg
Length of string, $L$L	1.20 m
Angle of string to vertical, $\theta$θ	35°
Gravitational field strength, $g$g	9.81 m s⁻²

(a) Calculate the tension in the string. (2 marks)

(b) Calculate the centripetal force acting on the bob. (2 marks)

(c) Calculate the angular speed of the bob and the time for one complete revolution. (2 marks)

On a smooth horizontal air table, puck A of mass 0.40 kg slides at 5.0 m s⁻¹ and strikes a stationary puck B of mass 0.60 kg. After the collision puck A moves off at 2.0 m s⁻¹ at an angle of 30° above its original direction. Puck B moves off below the original direction. The original direction of A is taken as the positive $x$x-axis.

	Mass / kg	Speed before / m s⁻¹	Speed after / m s⁻¹	Direction after
Puck A	0.40	5.0	2.0	30° above $x$x-axis
Puck B	0.60	0	?	below $x$x-axis

(a) By conserving momentum in two perpendicular directions, calculate the speed of puck B after the collision. (3 marks)

(b) Determine whether the collision is elastic, showing your reasoning with a calculation. (2 marks)

A small coin rests on a flat horizontal turntable a distance 0.12 m from the central axis. The turntable is gradually made to spin faster. The coin stays in place until, at a certain rotation rate, it begins to slide outwards. The coefficient of static friction between the coin and the turntable surface is 0.30. Take $g = 9.81$g=9.81 m s⁻².

(a) Explain which force provides the centripetal force on the coin, and calculate the maximum angular speed at which the coin can rotate without slipping. (3 marks)

(b) The coin is moved to a new position twice as far from the axis (0.24 m). State and explain the new maximum angular speed before it slips. (2 marks)

A squash ball of mass 0.15 kg travelling at 12 m s⁻¹ strikes a smooth vertical wall. It hits the wall at an angle of 30° to the wall surface and rebounds at the same angle with unchanged speed, so only the component of its velocity perpendicular to the wall is reversed.

Calculate the magnitude of the impulse the wall exerts on the ball, and state its direction. (4 marks)

An object moves at constant speed in a horizontal circle.

(a) Define the angular velocity of the object, and state its SI unit. (2 marks)

(b) Explain why the centripetal force acting on the object does no work, even though the object is constantly accelerating. (1 mark)