e-Consult | Revision Qns

1.

A ball is dropped from a height of 20m onto a horizontal, spring-loaded surface. The spring is initially compressed by 10cm. Assuming no energy is lost to air resistance, calculate the potential energy of the ball just before it hits the ground and the maximum potential energy of the spring after it has compressed.

Potential Energy (PE) before impact:

PE = mgh, where:

m = mass of the ball (assume 0.5 kg)

g = acceleration due to gravity (9.8 m/s²)

h = height (20m)

PE = 0.5 kg * 9.8 m/s² * 20 m = 98 J

Maximum Potential Energy of the Spring:

The potential energy stored in a spring is given by:

PE_spring = (1/2)kx², where:

k = spring constant (assume 200 N/m)

x = compression (0.1 m)

PE_spring = (1/2) * 200 N/m * (0.1 m)² = 1 J

Therefore, the potential energy of the ball before impact is 98 J and the maximum potential energy of the spring after compression is 1 J.

2.

A student is investigating the energy stored in a spring. They stretch the spring by 0.1 m from its original length. Calculate the amount of elastic potential energy stored in the spring, assuming the spring constant (k) is 200 N/m. Show your working.

The formula for elastic potential energy (U) stored in a spring is:

U = (1/2) * k * x²

Where:

U = Elastic potential energy (in Joules)

k = Spring constant (in N/m)

x = Displacement from the equilibrium position (in meters)

Substituting the given values:

U = (1/2) * 200 N/m * (0.1 m)²

U = (1/2) * 200 N/m * 0.01 m²

U = 1 J

Therefore, the amount of elastic potential energy stored in the spring is 1 Joule.

3.

Describe how energy is transferred in a simple electric motor. Explain the role of the magnetic field and the commutator in the process.

In a simple electric motor, energy is transferred from electrical energy to kinetic energy. The process involves the interaction of magnetic fields and electric currents. The motor consists of a coil of wire (the armature) and magnets. When an electric current flows through the coil, it creates a magnetic field around the coil.

The interaction between the magnetic field of the coil and the magnetic field of the permanent magnets causes the coil to experience a force. This force is due to the principle of electromagnetism – moving charges in a magnetic field experience a force. This force causes the coil to rotate. The direction of the force is determined by Fleming's Left-Hand Rule.

However, the direction of the current in the coil would reverse if the coil rotated a full 360 degrees. To ensure continuous rotation, a commutator is used. The commutator is a segmented ring that reverses the direction of the current in the coil every half rotation. This ensures that the magnetic force continues to act in the same direction, maintaining continuous rotation.

The magnetic field provided by the permanent magnets is crucial. It provides a constant magnetic field that interacts with the magnetic field of the coil. Without the magnetic field, there would be no force on the coil, and it would not rotate. The electrical energy is converted into mechanical energy through the continuous rotation of the coil driven by the magnetic forces. The efficiency of the motor is affected by factors such as the strength of the magnetic field, the number of turns in the coil, and the resistance of the coil.

1.7.1 Energy (3)