Kinetic energy

Kinetic energy is energy of motion. It increases with both mass and speed. Speed is squared in the equation while the mass is not. Because the speed is squared, even low mass objects (such a 1 kg meteorite) can have enormous kinetic energies when their speed is high. Ordinary objects such as balls and arrows have kinetic energies between 1 and 100 joules at typical speeds. More massive objects, such as cars, have kinetic energies up to a million joules.

Typical kinetic energies of moving objects

mass
(kg) / speed
(m/s) / speed
(mph) / kinetic energy (J)
baseball / 0.15 / 9 / 20.1 / 6.1
arrow / 0.01 / 100 / 224 / 50
bowling ball / 8 / 8 / 17.9 / 256
sprinter / 75 / 10 / 22.4 / 3,750
car at 30 mph / 1,500 / 13.4 / 30 / 135,000
car at 60 mph / 1,500 / 26.8 / 60 / 540,000
car at 90 mph / 1,500 / 40.2 / 90 / 1,214,000
small meteorite / 1 / 20,000 / 44,740 / 200,000,000

Note: with calculators you may need to think about the order of operations. With some calculators the value of the speed v should be squared before multiplying by the mass and the factor of one-half.

Example: Calculate the kinetic energy of a 3 kg ball moving at 5 m/s.

Applying new knowledge

Before calculating the kinetic energy in problems 1 – 6 below, use the examples in the table above to get an estimate. Record your initial estimate and see how close you can come to the calculated value. This will help you develop a ‘feel’ for the quantities involved.

  1. Calculate the kinetic energy of a .010 kg paper airplane moving at 10 m/s. Estimate: _____

answer: 0.50 joules

  1. Calculate the kinetic energy of a 12 kg dog running at a speed of 5 m/s. Estimate: _____

answer: 150 J

  1. Calculate the kinetic energy of a .065 kilogram sparrow flying at 12 m/s. Estimate: _____

(1g = 0.001 kg)

answer: 4.7 J

  1. Calculate the kinetic energy of a group of 5 pebbles, each with a mass of .050 kilograms. The pebbles are moving at 25 m/s.

answer: 78 J Estimate: _____

  1. Calculate the kinetic energy of a sports car with a mass of 1,200 kg traveling at a speed of

80.0 mph. (HINT: 1 mph = 0.45 m/s)

answer: 7.8 * 105 J Estimate: _____

  1. Calculate the kinetic energy of a falling rock with a mass of 22 kg and a speed of 9.0 m/s.

answer: 890 J Estimate: _____

  1. An object has 100 J of kinetic energy. If the object’s mass doubles, what is its kinetic energy?

A. 50 J B. 100 J C. 200J D. 400 J

  1. An object has 100 J of kinetic energy. If the velocity of the object doubles, what is its kinetic energy?

A. 50 J B. 100 J C. 200J D. 400 J

  1. Which has more kinetic energy: a 1.0 kg ball moving at 10 m/s or a 10 kg ball moving at

1.0 m/s?

answer: The 1.0 kg ball (50 joules of Ek versus 5 joules)

  1. How fast is a 2.0 kg object moving if its kinetic energy is 100 J?

answer: 10 m/s

  1. What is the speed of a 400 kg motorcycle (and rider) if its kinetic energy is 125,000 joules?

answer: 25 m/s

  1. A 350 kg horse and 50.0 kg rider are riding together at a speed of 19.0 m/s. Keeping the kinetic energy the same, what would be the speed of a 100 kg rider on the same horse?

answer: 17.9 m/s

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