Exercises on Energy and Power

  1. A wagon is pulled 1.2 km along a horizontal road with the force 160 N directed along the road. The speed of the wagon is kept constant.

a)Calculate the work done.

b)Determine the friction force.

  1. Marie lifts her suitcase, 18 kg, from the platform up onto a train, 75 cm above the platform. Then she carries it to her seat and puts it on a rack 2.0 m above the floor.
    Calculate the mechanical work that she does, if her mass is 52 kg.
  2. A car approaches a long uphill slope with the speed 90 km/h. The driver disengages the engine and lets the car roll up the slope. How far up will the car go, if we can neglect all friction and air resistance?
  3. A small stone with mass 10 g is dropped from a tower that is 12 m high. The stone has no initial speed.

a)Calculate the initial potential energy of the stone in relation to the ground.

b)What is the kinetic energy right before the stone hits the ground?

  1. A car with mass 1.5 tons drives on the high way and its speed is increased from 70km/h to 110 km/h. Determine how much the kinetic energy increases.
  2. A cart with mass 4.8 kg stands still on a horizontal table. It is pulled with the force 1.2 N and the frictional force can be neglected. Calculate the speed of the cart when it has rolled 1.5 m.
  3. a)Calculate the kinetic energy of a train with mass 490 tons that moves with the speed 36 km/h.

b)Calculate the necessary braking force that is needed to stop the train in 120 m.

  1. a)A lift (Am elevator) with mass 600 kg moves upwards 10 m in 12 s.
    Determine the power that is necessary to perform this lifting.

b)The lift has the efficiency 83 %. Determine the electric power that has to be provided during the lifting.

  1. A machine can develop the power 370 W. Calculate the work that this machine can do during an hour.
  2. A car drives with the constant speed 90 km/h. The engine then develops the power 45 hp (horsepower). Calculate the driving force if 1 hp = 735 W.
  3. An engine has the output of 3.6 kW to a crane. Calculate the time necessary to lift 900kg 10 m straight upwards.
  4. In a waterfall 1500 m3 of water falls every minute. The falling height is 7.5 m.

a)Calculate the power of the falling water.

b)The water drives a turbine that can convert 90 % of the energy of the falling water to electricity. Calculate the output electric power of the turbine.

  1. A litre of petrol (Am. a liter of gasoline) contains the energy 31 MJ and a litre costs 13.00 SEK. What does it the cost to accelerate from 0 km/h to 110 km/h on a horizontal road? Assume that the car has the mass 1500 kg and that the efficiency of the engine is 30 %.
  2. (MVG) A dynamometer is pulled out so it shows 6.0 N. Determine the work needed to pull it out an additional 4.0 cm so it shows 8.0 N?

Answers to exercises on energy and power

  1. a) 0.19 MJb) 160 N
  2. ((52 + 18) · 9.82 · 0.75 + 18 · 9.82 · 2.0) J. Answer: 0.87 kJ
  3. a) 1.2 J b) 1.2 J
  4. 0.42 MJ
  5. 0.87 m/s
  6. a) 25 MJ b) 0.20 MN
  7. a) P = W/t = mgh/t gives 4.9 kW b) 5.9 kW
  8. 1.3 MJ
  9. 25 s
  10. a) 1.8 MW b) 1.7 MW
  11. 0.98 SEK.
  12. The strain(or potential) energy of a spring = , where k = spring constant.
    F = k·L gives  L1 = 12 cm and L2 = (L1 + 4) cm =16 cm.
    k = F/L gives k = 50 N/m. Ep = 0.64 J – 0.36 J =0.28 J
    The work needed is the same as the change of the strain energy. Ans. 0.28 J