SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

PHYSICS, M6 2023 HSC 31

A roller coaster uses a braking system represented by the diagrams.
 

When the roller coaster car reaches the end of the ride, the two rows of permanent magnets on the car pass on either side of a thick aluminium conductor called a braking fin.

The graph shows the acceleration of the roller coaster reaching the braking fin at two different speeds.
 


Explain the similarities and differences between these two sets of data.  (5 marks)

Show Answers Only

Similarities:

→ Both graphs have similar shapes that show a peak in negative acceleration at approximately 0.8 seconds.

→ The negative acceleration curves become almost identical in the 3 – 4 second range, which is consistent with both roller coaster cars coming to a stop at the same time.

→ As the braking fin passes through the two rows of permanent magnets, the braking fin experiences a change which results in an EMF being induced in the braking fin (Faraday’s Law).

→ This EMF results in the formation of eddy currents which flow to reduce the change in flux that created it (Lenz’s Law) and therefore act to reduce the relative motion between the permanent magnets and braking fin.

→ In this way, the roller coaster car experiences a negative acceleration in both data sets.

→ After maximum negative acceleration, both cars experience a reduction in the effects of the magnetic braking. This is due to the speed of the cars slowing down and hence reducing the change in flux which in turn reduces the magnitude of the eddy currents in the braking fin. 

→ The KE of the roller coaster cars is continuously being converted into electrical resistive heating through the formation of the eddy currents.
 

Differences: 

→ The cart with \(u\) = 12 ms\(^{-1}\) experiences a greater magnitude of (negative) acceleration as the braking fin experiences a greater rate of change of flux than the \(u\) = 10 ms\(^{-1}\) case.

→ This leads to a greater induced EMF across the breaking fin and therefore stronger eddy currents are produced.

→ As the repulsive force is proportional to the strength of the eddy currents, the 12 ms\(^{-1}\) cart will experience a greater repulsive force and greater negative acceleration.

Show Worked Solution

Similarities:

→ Both graphs have similar shapes that show a peak in negative acceleration at approximately 0.8 seconds.

→ The negative acceleration curves become almost identical in the 3 – 4 second range, which is consistent with both roller coaster cars coming to a stop at the same time.

→ As the braking fin passes through the two rows of permanent magnets, the braking fin experiences a change which results in an EMF being induced in the braking fin (Faraday’s Law).

→ This EMF results in the formation of eddy currents which flow to reduce the change in flux that created it (Lenz’s Law) and therefore act to reduce the relative motion between the permanent magnets and braking fin.

→ In this way, the roller coaster car experiences a negative acceleration in both data sets.

→ After maximum negative acceleration, both cars experience a reduction in the effects of the magnetic braking. This is due to the speed of the cars slowing down and hence reducing the change in flux which in turn reduces the magnitude of the eddy currents in the braking fin. 

→ The KE of the roller coaster cars is continuously being converted into electrical resistive heating through the formation of the eddy currents.
 

Differences: 

→ The cart with \(u\) = 12 ms\(^{-1}\) experiences a greater magnitude of (negative) acceleration as the braking fin experiences a greater rate of change of flux than the \(u\) = 10 ms\(^{-1}\) case.

→ This leads to a greater induced EMF across the breaking fin and therefore stronger eddy currents are produced.

→ As the repulsive force is proportional to the strength of the eddy currents, the 12 ms\(^{-1}\) cart will experience a greater repulsive force and greater negative acceleration.

PHYSICS, M6 2017 HSC 28

Contrast the design of transformers and magnetic braking systems in terms of the effects that eddy currents have in these devices.   (6 marks)

Show Answers Only

Transformers:

→ A transformer involves primary and secondary coils wound around a laminated iron core.

→ When an AC current is applied to the primary coil, changes in magnetic flux induce a current in the secondary coil.

→ Eddy currents have undesirable effects in transformers as the iron core is a conductor.

→ So, there is induction of unwanted eddy currents which leads to energy losses in the form of heat.

→ Lamination of the iron core minimises these eddy currents and subsequent energy loss.
 

Magnetic Braking Systems:

→ In contrast, eddy currents are beneficial in magnetic braking systems.

→ Magnetic breaking involves using eddy currents to produce a force that stops a moving vehicle by converting kinetic energy into heat energy.

→ In order to maximise induced eddy currents, and thus the breaking effect, magnetic breaks are designed with large sheets or discs of conductive material such as copper.

Show Worked Solution

Transformers:

→ A transformer involves primary and secondary coils wound around a laminated iron core.

→ When an AC current is applied to the primary coil, changes in magnetic flux induce a current in the secondary coil.

→ Eddy currents have undesirable effects in transformers as the iron core is a conductor.

→ So, there is induction of unwanted eddy currents which leads to energy losses in the form of heat.

→ Lamination of the iron core minimises these eddy currents and subsequent energy loss.
 

Magnetic Braking Systems:

→ In contrast, eddy currents are beneficial in magnetic braking systems.

→ Magnetic breaking involves using eddy currents to produce a force that stops a moving vehicle by converting kinetic energy into heat energy.

→ In order to maximise induced eddy currents, and thus the breaking effect, magnetic breaks are designed with large sheets or discs of conductive material such as copper.


♦♦♦ Mean mark 49%.

PHYSICS, M6 2022 HSC 32

One type of stationary exercise bike uses a pair of strong, movable magnets placed on opposite sides of a thick, aluminium flywheel to provide a torque to make it harder to pedal.
 


 

  1. Explain the principle by which these magnets make it harder to pedal.  (3 marks)
  1. The bike rider wants to increase the opposing torque on the flywheel. Justify an adjustment that could be made to the magnets to achieve this.  (3 marks)
Show Answers Only

a.    Magnetic breaking is a consequence of Lenz’s Law.

→ The changing magnetic flux through the wheel, as a result of its rotation, causes eddy currents to be induced (Faraday’s Law).

→ According to Lenz’s Law, these eddy currents produce a force which opposes the rotation of the wheel, making it more difficult to pedal.
 

b.   Adjustment to increase opposing torque:

→ Moving the magnets closer to the outer edge of the flywheel will increase the opposing torque on it. As the linear speed of the wheel is greater near the edge, the rate of change of flux passing through it will increase.

→ This increases the magnitude of induced emf as  `epsilon=-N(Delta theta)/(Delta t).`

→ Consequently, the opposing force and torque will increase.

→ Moving the magnets closer to the edge of the flywheel also increases the distance between the point of application of the opposing force and the axis of rotation of the wheel. As  `tau=rF`  this further increases opposing torque.

Show Worked Solution

a.    Magnetic breaking is a consequence of Lenz’s Law.

→ The changing magnetic flux through the wheel, as a result of its rotation, causes eddy currents to be induced (Faraday’s Law).

→ According to Lenz’s Law, these eddy currents produce a force which opposes the rotation of the wheel, making it more difficult to pedal.
 

b.   Adjustment to increase opposing torque:

→ Moving the magnets closer to the outer edge of the flywheel will increase the opposing torque on it. As the linear speed of the wheel is greater near the edge, the rate of change of flux passing through it will increase.

→ This increases the magnitude of induced emf as  `epsilon=-N(Delta theta)/(Delta t).`

→ Consequently, the opposing force and torque will increase.

→ Moving the magnets closer to the edge of the flywheel also increases the distance between the point of application of the opposing force and the axis of rotation of the wheel. As  `tau=rF`  this further increases opposing torque.