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PHYSICS, M5 2017 HSC 22a

A torque is applied to a nut, using a wrench, as shown.
 
   
 
Suggest TWO ways that the applied torque could be increased.   (2 marks)

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The applied torque can be increased by:

  • Increasing the magnitude of the applied force.
  • Increasing the distance between the nut and the point of applied force.
Show Worked Solution

The applied torque can be increased by:

  • Increasing the magnitude of the applied force.
  • Increasing the distance between the nut and the point of applied force.

PHYSICS, M6 2024 HSC 21

To tighten a nut, a force of 75 N is applied to a spanner at an angle, as shown.
 

  1. Calculate the magnitude of the torque produced by the applied force.   (2 marks)

  2. Explain TWO ways in which torque can be increased in a simple DC motor.   (4 marks)

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a.    \(8.7\ \text{Nm  (2 sig.fig)}\)  

b.    Torque \((\tau=nIAB)\) in a simple DC motor can be increased as follows:

  • Increasing the current through the motor by increasing the voltage of the power source. This will increase the force on each arm of the motor due to the motor effect and increase the overall torque of the motor.
  • Increasing the number of coils in the DC motor. This will increase the torque as each individual coil will experience a force due to the motor effect. The forces on each coil will add together to increase the overall force on each arm of the motor increasing the torque of the motor.
  • Other answers could have included: increasing the area of the coil, increasing the strength of the external magnetic field by using electromagnets or adding a radial magnetic field as it increases the average torque applied to the motor.

Show Worked Solution

a.     \(\tau\) \(=Fr\sin\theta\)
    \(=75 \times 0.18 \times \sin 40\)
    \(=8.7\ \text{Nm  (2 sig.fig)}\)  

 

b.    Torque \((\tau=nIAB)\) in a simple DC motor can be increased as follows:

  • Increasing the current through the motor by increasing the voltage of the power source. This will increase the force on each arm of the motor due to the motor effect and increase the overall torque of the motor.
  • Increasing the number of coils in the DC motor. This will increase the torque as each individual coil will experience a force due to the motor effect. The forces on each coil will add together to increase the overall force on each arm of the motor increasing the torque of the motor.
  • Other answers could have included: increasing the area of the coil, increasing the strength of the external magnetic field by using electromagnets or adding a radial magnetic field as it increases the average torque applied to the motor.

PHYSICS, M5 2023 HSC 17 MC

A mass attached to a lightweight, rigid arm hanging from point \(O\), oscillates freely between \(X\) and \(Z\).
 

Which statement best describes the torque acting on the arm as it oscillates?

  1. It is constant in magnitude and direction.
  2. It is zero at \(Y\) and a maximum at \(X\) and \(Z\).
  3. It is zero at \(X\) and \(Z\) and a maximum at \(Y\).
  4. It is constant in magnitude but its direction changes.
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\(B\)

Show Worked Solution
  • In the scenario above, the only force acting the on the oscillating arm is the force due to gravity which acts vertically downwards.
  • The torque can be calculated by  \(\tau=rF\sin\theta\)
  • The angle between the arm and force of gravity at \(Y\) is \(180^{\circ}\) as they are parallel, therefore  \(\tau=\)0 \(\text{Nm}\).
  • At \(X\) and \(Z\), the magnitude of the force of gravity perpendicular to the arm is a maximum, thus the magnitude of the torque at \(X\) and \(Z\) is a maximum.
     

\(\Rightarrow B\)

♦ Mean mark 50%.

PHYSICS, M5 EQ-Bank 4 MC

A torque is applied to a nut, using a wrench.
 

Which change will increase the magnitude of applied torque?

  1. Increasing the angle between the applied force and the wrench
  2. Decreasing the angle between the applied force and the wrench
  3. Increasing the distance between the nut and the point of application of the force
  4. Decreasing the distance between the nut and the point of application of the force
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`C`

Show Worked Solution
  • `tau = rF sin theta`
  • Increasing the distance (`r`) between the point of application of the force and the nut will increase applied torque.

`=>C`

PHYSICS, M5 2019 HSC 26

A student carried out an experiment to investigate the relationship between the torque produced by a force and the angle at which the force is applied. A 400 N force was applied to the same position on the handle of a spanner at different angles, as shown.
 

A high-precision device measured the torque applied to the bolt.

The data from the experiment is graphed below.
 

The student concluded that the torque `(tau)` was proportional to the angle `(theta)` and proposed the model

`tau=ktheta`

where  `k` = 1.7 Nm/degree.

  1. Justify the validity of the student's model using information from the graph.   (3 marks)
  1. What happens to the accuracy of this model's predictions as the angle increases beyond 25°? Justify your answer with reference to a different model.   (3 marks)
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a.   The graph shows a linear relationship.

  • Constructing a line of best fit on the student’s graph shows the the gradient is approximately`=(34-17)/(20-10) =1.7`.
  • These findings are consistent with the student’s model of `tau=1.7 theta`
  • Therefore, the model is valid.

b.   Model accuracy:

  • The accuracy of this model decreases as the angle increases beyond 25°.
  • Torque produced by a force is more accurately described by `tau=rF sin theta.`
  • At small angles, `sin theta ~~ theta`, so the model is accurate. However at larger angles, `sin theta lt theta`, so the student’s model will predict values of torque greater than those predicted by `tau=rF sin theta`.
Show Worked Solution

a.   The graph shows a linear relationship.

  • Constructing a line of best fit on the student’s graph shows the the gradient is approximately`=(34-17)/(20-10) =1.7`.
  • These findings are consistent with the student’s model of `tau=1.7 theta`
  • Therefore, the model is valid.

b.   Model accuracy:

  • The accuracy of this model decreases as the angle increases beyond 25°.
  • Torque produced by a force is more accurately described by `tau=rF sin theta.`
  • At small angles, `sin theta ~~ theta`, so the model is accurate. However at larger angles, `sin theta lt theta`, so the student’s model will predict values of torque greater than those predicted by `tau=rF sin theta`.