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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, M6 2017 HSC 22

  1. A torque is applied to a nut, using a wrench, as shown.
     

     
    Suggest TWO ways that the applied torque could be increased.   (2 marks)
  1. A coil consisting of 15 turns is placed in a uniform 0.2 T magnetic field between two magnets. A current of 7.0 amperes flows in the direction shown.
     

Calculate the magnitude and direction of the torque produced by the side `BC` of the 15-turn coil.   (3 marks)

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a.   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.
 

b.   0.05 Nm into the page

Show Worked Solution

a.   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.
 

b.   `F_(BC)` `=BIl sin theta`
    `=0.2 xx7xx0.08 xx sin 90^(@)`
    `=0.112  text{N}`

 
`text{Total force (15 turns)}  =0.112 xx15=1.68\ text{N}`

`:.tau` `=rF sin theta`
  `=1.68 xx0.03 xx sin90^(@)`
  `=0.05  text{Nm into the page}`

Mean mark (b) 58%.

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`

⇒ The model is valid.
 

b.   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`

⇒ The model is valid.
 

b.   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