smc-3692-80-Newton’s Three Laws

PHYSICS, M6 2019 HSC 31

A student suspends an electric ceiling fan from a spring balance.

The fan is switched on, reaching a maximum rotational velocity after ten seconds.

Explain the changes that would be observed on the spring balance in the first 15 seconds after the fan is switched on. (4 marks)

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The student predicted that the current through the fan's motor would vary as shown on the graph.

Assess the accuracy of the student's prediction. (4 marks)

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a. As the fan rotates it exerts a downwards force on air molecules.

By Newton’s Third Law, an equal and opposite force is exerted on the fan by the air. This counteracts the fan’s weight, decreasing the net downwards force acting on the fan.

For the first ten seconds:

→ The fan’s rotation speed increases.

→ The force on the fan due to the air increases.

→ The force observed on the spring balance decreases.

After ten seconds:

→ The force acting on the fan due to the air remains constant.

→ The recorded force on the spring balance remains constant.

b. Between 0-10 seconds:

The student’s prediction of an increasing current is incorrect.

→ Initially, the current through the motor is at a maximum as the fan’s motor is stationary and it experiences no change in magnetic flux (no back EMF induced).

→ As the fan speeds up, the rate of change of flux through the motor increases.

→ An increasing EMF is induced in the motor (Faraday’s Law).

→ This is back EMF which acts to oppose the current.

→ a decrease in current occurs during the first 10 seconds.

Between 10-15 seconds:

The student’s prediction of a constant current is correct.

→ The motor is rotating at a constant speed.

→ The magnitude of induced back EMF remains constant.

→ the current through the motor remains constant.

Show Worked Solution

a. As the fan rotates it exerts a downwards force on air molecules.

By Newton’s Third Law, an equal and opposite force is exerted on the fan by the air. This counteracts the fan’s weight, decreasing the net downwards force acting on the fan.

For the first ten seconds:

→ The fan’s rotation speed increases.

→ The force on the fan due to the air increases.

→ The force observed on the spring balance decreases.

After ten seconds:

→ The force acting on the fan due to the air remains constant.

→ The recorded force on the spring balance remains constant.

♦ Mean mark (a) 48%.

b. Between 0-10 seconds:

The student’s prediction of an increasing current is incorrect.

→ Initially, the current through the motor is at a maximum as the fan’s motor is stationary and it experiences no change in magnetic flux (no back EMF induced).

→ As the fan speeds up, the rate of change of flux through the motor increases.

→ An increasing EMF is induced in the motor (Faraday’s Law).

→ This is back EMF which acts to oppose the current.

→ a decrease in current occurs during the first 10 seconds.

Between 10-15 seconds:

The student’s prediction of a constant current is correct.

→ The motor is rotating at a constant speed.

→ The magnitude of induced back EMF remains constant.

→ the current through the motor remains constant.

♦ Mean mark (b) 39%.

PHYSICS, M6 2020 HSC 32

A rope connects a mass on a horizontal surface to a pulley attached to an electric motor as shown.

Explain the factors that limit the speed at which the mass can be pulled along the horizontal surface. Use mathematical models to support your answer. (7 marks)

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The factors limiting the speed of the mass along horizontal surface can be divided into two main parts: Factors involving friction between the mass and the table and factors involving the force output of the motor and pulley.

Friction between the mass and table:

→ The mass will experience a friction force of `F_(f)=mu N`. Since the mass has no vertical acceleration, `N=mg\ \ =>\ \ F_(f)=mu mg.`

→ So, the speed at which the mass can be pulled is limited by the coefficient of kinetic friction between the mass and the table `mu` and the magnitude of the mass `m`.

Force produced by the motor:

→ The torque produced by the motor is given by `tau=NIAB sin theta`

→ The torque of the motor and hence maximum speed at which the mass can be pulled is limited by the number of turns `N` of the coil in the motor, the current passing through the coils `I`, the area of the coils `A` and the magnetic field strength of the stator magnets `B`.

→ Via the pulley, the torque generated by the motor generates a force which pulls the mass. As `Tau =rF sin theta`, a smaller pulley radius means that a larger force can be used to pull the mass.

→ So, the speed at which the mass can be pulled is limited by pulley radius.

Answers could also contain:

→ Back emf in the motor limiting its maximum speed.

→ The efficiency of the motor.

Show Worked Solution

The factors limiting the speed of the mass along horizontal surface can be divided into two main parts; 1-Factors involving friction between the mass and the table and 2-Factors involving the force output of the motor and pulley.

Friction between the mass and table

→ The mass will experience a friction force of `F_(f)=mu N`. Since the mass has no vertical acceleration, `N=mg\ \ =>\ \ F_(f)=mu mg.`

→ the speed at which the mass can be pulled is limited by the coefficient of kinetic friction between the mass and the table `mu` and the magnitude of the mass `m`.

Force output of the motor and pulley

→ The power of the motor depends on its torque and the pulley radius `(tau=rF sin theta).`

→ The torque produced by the motor is given by `tau=NIAB sin theta`

→ The force of the motor and hence maximum speed at which the mass can be pulled is also limited by the number of turns of the coil in the motor, the current passing through the coils, the area of the coils and the magnetic field strength of the stator magnets.

Answers could also contain:

→ Back emf in the motor limiting its maximum speed.

→ The efficiency of the motor.

Mean mark 58%.

PHYSICS, M5 2021 HSC 14 MC

Which of the following statements correctly describes the gravitational interaction between the Earth and the Moon?

The Earth accelerates towards the Moon.
The net force acting on the Earth is zero.
The Moon and Earth experience equal and opposite accelerations.
The force acting on the Moon is smaller than the force acting on the Earth.

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`A`

Show Worked Solution

According to Newton’s Third Law, the earth and moon experience equal forces in opposite directions. This causes them to accelerate towards each other.

`=>A`

♦ Mean mark 19%.