Edexcel A-Level Physics: Mechanics

A skydiver of total mass 85 kg steps out of a stationary helicopter and falls vertically. After a long free fall she opens her parachute. The motion can be divided into three stages: (i) immediately after she leaves the helicopter, (ii) shortly before she opens the parachute, and (iii) the moment just after the parachute opens.

Describe and explain, in terms of the forces acting and Newton's laws, how the velocity and acceleration of the skydiver change throughout the fall, from the instant she leaves the helicopter until she finally descends at a steady (terminal) velocity on the parachute. In your answer you should refer to her weight, the drag (air resistance), and the two terminal velocities that occur.

(6 marks)

A block of mass 4.0 kg rests on a smooth (frictionless) slope inclined at 30° to the horizontal. A light inextensible string runs from the block, up the slope and over a frictionless pulley at the top, to a freely hanging mass of 6.0 kg. The system is released from rest, and the 6.0 kg mass descends, pulling the 4.0 kg block up the slope.

Quantity	Value
Mass on slope, $m_1$m1​	4.0 kg
Angle of slope, $\theta$θ	30°
Hanging mass, $m_2$m2​	6.0 kg
Gravitational field strength, $g$g	9.81 m s⁻²

(a) Calculate the resultant force that accelerates the connected system. (2 marks)

(b) Hence calculate the acceleration of the system. (2 marks)

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

A light-rail tram starts from rest and pulls away from a stop. A data logger records its velocity at 5-second intervals:

Time / s	0	5	10	15	20	25
Velocity / m s⁻¹	0	6.0	12.0	18.0	18.0	18.0

(a) Use the data to show that the tram's acceleration is uniform during the first 15 s, and state its value. (2 marks)

(b) Describe the motion of the tram between 15 s and 25 s. (1 mark)

(c) Determine the total distance travelled by the tram in the 25 s shown. (2 marks)

A small manoeuvring spacecraft of mass 900 kg is at rest relative to a space station, drifting in deep space where external forces are negligible. To move away, it fires a short thruster burst that ejects 1.5 kg of exhaust gas at a speed of 3000 m s⁻¹ relative to the station. The burst lasts 0.30 s.

(a) Calculate the recoil speed of the spacecraft immediately after the burst. (3 marks)

(b) Estimate the average force the thruster exerts on the spacecraft during the burst, and state the law that links this to the force on the gas. (2 marks)

An electric pump raises water from a well and delivers it to a storage tank a vertical height of 12 m above the water surface. The pump lifts 0.45 m³ of water every minute and draws an electrical input power of 1500 W. The density of water is 1000 kg m⁻³ and $g = 9.81 \ \text{m s}^{-2}$g=9.81 m s−2. The water leaves the pipe slowly, so its kinetic energy may be neglected.

(a) Calculate the useful output power of the pump (the rate at which it gives the water gravitational potential energy). (2 marks)

(b) Hence calculate the efficiency of the pump. (2 marks)

Newton's second law is often quoted in the form $F = ma$F=ma, but its more general statement is in terms of momentum.

(a) State Newton's second law in terms of momentum, and show how the familiar equation $F = ma$F=ma follows from it when the mass is constant. (2 marks)

(b) State what is meant by the impulse of a force, and give its SI unit. (1 mark)