This page covers the following topics:
1. Gravitational potential energy
2. Elastic potential energy
3. Kinetic energy
Gravitational potential energy refers to the energy possessed by an object due to its position above the ground. It can be calculated by multiplying the mass of an object, gravitational field strength and height the object has been lifted to. Gravitational field strength on the surface of the Earth is commonly approximated to be 9.81 m/s².
Elastic potential energy is the energy stored in elastic objects when they are stretched or compressed. This occurs when a force is applied to an object, which causes it to change shape. When the object returns to its original shape, the stored elastic potential energy is released.
Kinetic energy is the energy an object has due to its motion and thus its speed. It can be calculated using E = 1/2 × mass × velocity² and is given in joules, J. A moving vehicle can be stopped only when work is done on it which is equivalent to the kinetic energy the vehicle possesses.
Kate drops a 275 g volleyball towards the ground. Given that when the ball is 0.5 m above the ground the change in gravitational potential energy is 2.7 J, calculate the height above the ground at which the ball is dropped from. Use g = 9.81 N/kg.
E = mgh
2.7 J = 0.275 kg × 9.81 N/kg × change in height
change in height = 2.7 J/(0.275 kg × 9.81 N/kg) = 1.00 m (3 s. f.)
height above the ground initially = 0.5 m + 1.00 m = 1.5 m
Calculate the gravitational potential energy stored in a tennis ball of mass 60 g that is held 1.4 m above the ground. Use g = 9.81 N/kg.
E = mgh
E = 0.06 kg × 9.81 N/kg × 1.4 m = 0.82 J
A biker is driving his bike of mass 10 kg at a speed of 7.2 m/s. Given that the kinetic energy of the bike and biker is 1763 J, calculate the mass of the biker.
E = 0.5mv²
Let m be the biker's mass.
1763 J = 0.5 × (m + 10 kg) × (7.2 m/s)²
m = (2 × 1763) ÷ 7.2² − 10 = 58 kg
Given that the mass of a runner is 62 kg and that she is running at a speed of 11 m/s, find the kinetic energy of the runner.
E = 0.5mv²
E = 0.5 × 62 kg × (11 m/s)² = 3751 J
Find the spring constant for a spring that requires 12 J to be compressed by 1 cm.
1 cm = 0.01 m
E = kx²/2
12 = k × 0.01² ÷ 2
k = 240000 N/m
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