This page covers the following topics:
1. Gravitational potential energy
2. Elastic strain energy
3. Kinetic energy
4. Rotational 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.
All the work done in stretching or compressing an elastic object is stored as elastic strain energy, which is equivalent to the elastic potential energy. The elastic strain energy in J can be calculated using E = 1/2 × F × x, where F is the force that is causing the stretching or compressing of the object in N, and x is the extension in m. This energy is equivalent to the area under a force-extension graph.
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.
Rotational kinetic energy is a part of the total kinetic energy of an object and it is defined as the kinetic energy possessed by an object due to its rotational motion. The moment of inertia of an object is a measure of how difficult it is to alter its rotational speed and can be calculated using I = mr², where m is the mass of the object and r is the distance from the axis of rotation.
A flywheel is a very heavy wheel that takes a lot of force to spin around and to stop from spinning, meaning that it has a high angular momentum and moment of inertia. When the flywheel is spinning at a great speed, it tends to keep spinning; thus, resulting in storage of energy in the form of kinetic energy due to its movement. This energy can then be used in another point in the system. Flywheels are usually used to smooth torque and speed, and for storing energy in vehicles, as well as in machines used for production processes.
A vinyl record placed in a record player is spinning at an angular speed of 3.5 rad/s. Given that the radius of the record is 30 cm and its mass is 180 g, calculate the rotational kinetic energy of the record.
I = mr²
I = 0.18 kg × (0.3 m)² = 0.0162 kgm²
E = 0.5Iω²
E = 0.5 × 0.0162 kgm² × (3.5 rad/s)² = 0.0992 J (3 s. f.)
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 spring is stretched by 10 cm using a force of 10 N. Calculate the elastic strain energy stored in the spring.
E = (1/2)Fx
E = (1/2) × 10 N × 0.1 m = 0.5 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
End of page