A 2 kg mass is lifted vertically through a height of 3 meters.
a) Calculate the gravitational potential energy gained by the mass. [2 marks]
b) If this took 4 seconds, calculate the minimum power needed. [2 marks]
gravitational field strength = 9.81 N/kg
a) Using E = mgh [1 mark]
E = 2 × 9.81 × 3 = 58.86 J [1 mark]
b) Using P = E/t [1 mark]
P = 58.86/4 = 14.715 W [1 mark]
A spring has a spring constant of 20 N/m. Calculate the elastic potential energy stored when it is extended by 0.15 meters.
Using E = ½ke² [1 mark]
E = ½ × 20 × 0.15² [1 mark]
E = 0.225 J [1 mark]
A car of mass 1200 kg is traveling at 20 m/s.
a) Calculate its kinetic energy [2 marks]
b) The car brakes and comes to a stop in 40 meters. Calculate the force of the brakes. [2 marks]
a) Using E = ½mv² [1 mark]
E = ½ × 1200 × 20² = 240,000 J [1 mark]
b) Using Work done = Force × distance [1 mark]
240,000 = F × 40, F = 6000 N [1 mark]
An electric heater transfers 5000 J of energy to some water. If the efficiency of the heater is 85%, calculate:
a) The energy wasted [2 marks]
b) The total energy input [1 mark]
Total input = 5000/0.85 = 5882.35 J [1 mark]
Energy wasted = 5882.35 - 5000 [1 mark]
= 882.35 J [1 mark]
A student lifts a 5 kg mass through a height of 2 meters in 3 seconds.
a) Calculate the work done against gravity [2 marks]
b) Calculate the power output [2 marks]
gravitational field strength = 9.81 N/kg
a) Work done = mgh [1 mark]
= 5 × 9.81 × 2 = 98.1 J [1 mark]
b) Power = work done/time [1 mark]
= 98.1/3 = 32.7 W [1 mark]
A kettle has a power rating of 2000 W. It is used to heat 0.5 kg of water from 20°C to 100°C.
Specific heat capacity of water = 4200 J/kg°C
Calculate:
a) The energy transferred to the water [2 marks]
b) The minimum time taken [2 marks]
a) E = mcΔθ [1 mark]
= 0.5 × 4200 × 80 = 168,000 J [1 mark]
b) Time = energy/power [1 mark]
= 168,000/2000 = 84 seconds [1 mark]
A ball of mass 0.5 kg falls from a height of 10 m and bounces to a height of 8 m.
Calculate:
a) The initial gravitational potential energy [1 mark]
b) The final gravitational potential energy [1 mark]
c) The energy lost [1 mark]
d) The efficiency of the bounce [1 mark]
gravitational field strength = 9.81 N/kg
a) Initial GPE = 0.5 × 9.81 × 10 = 49.05 J [1 mark]
b) Final GPE = 0.5 × 9.81 × 8 = 39.24 J [1 mark]
c) Energy lost = 49.05 - 39.24 = 9.81 J [1 mark]
d) Efficiency = 39.24/49.05 = 0.80 or 80% [1 mark]
A cyclist of mass 70 kg is traveling at 5 m/s. They stop pedaling and come to rest after 20 seconds.
Calculate:
a) The initial kinetic energy [2 marks]
b) The average power of the resistive forces [1 mark]
a) KE = ½mv² = 0.5 × 70 × 5² = 875 J [2 marks]
b) Power = 875/20 = 43.75 W [1 mark]
A motor lifts a mass of 12 kg through a height of 5 meters in 10 seconds.
The efficiency of the motor is 75%.
Calculate:
a) The useful power output [2 marks]
b) The total power input [2 marks]
gravitational field strength = 9.81 N/kg
a) Work done = mgh = 12 × 9.81 × 5 = 588.6 J [1 mark]
Power output = 588.6/10 = 58.86 W [1 mark]
b) Total power input = 58.86/0.75 [1 mark]
= 78.48 W [1 mark]
A pendulum swings from a height of 0.3 meters to a height of 0.25 meters.
The mass of the pendulum bob is 0.2 kg.
Calculate:
a) The energy lost in one swing [2 marks]
b) The percentage of energy lost [2 marks]
gravitational field strength = 9.81 N/kg
a) Initial GPE = 0.2 × 9.81 × 0.3 = 0.5886 J
Final GPE = 0.2 × 9.81 × 0.25 = 0.4905 J
Energy lost = 0.5886 - 0.4905 = 0.0981 J [2 marks]
b) Percentage energy lost = (0.0981/0.5886) × 100 = 16.7% [2 marks]