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Objects
in the following situations are performing circular motion:
i)
a car moving on a banked road at the designated speed of the road, |
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Since the car is moving at the designated speed,
there is no friction along the inclination. |
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As the circular motion is horizontal, the centripetal
force is horizontal. This is provided by the horizontal component of the
normal reaction R with the road. |
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The appropriate set of equations is |
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ii)
an aeroplane is moving in a curved horizontal path in air.
Draw diagrams to
show the forces acting on the car and the aeroplane. For each case, explain
the origin of the net force. |
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The lift is generated by the difference in
pressure above and below the wing. |
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The horizontal centripetal force is provided
by the horizontal component of the lift N. |
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The appropriate set of equations is |
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| b. |
Explain
why a bicycle in a bend must tilt. Derive an expression for the angle of
tilt that the bicycle makes with the vertical. |
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The diagram shows all the forces acting on
the bicycle. The centripetal force is provided merely by the static friction
f. The set of equations for the forces is |
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If the bicycle does not tilt, there would be
a net anti-clockwise moment about G. |
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For motion without toppling, the angle of tilt
is given by setting the total moment about G to zero: |
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| c. |
Explain
why a car turning round a bend will also tilt but in a direction opposite
to the bicycle in (b). |
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As the car is moving in a circular path, the
centripetal force is provided by the frictions in both tyres. |
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The total moment of the car taking about G
must be zero: |
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The suspension spring on the right is compressed
more. Thus, the car tilts to the right as it turns left as shown. |
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Tilting of a car in a bend is different from
the tilting of a bicycle. That a car tilts is because the force acting
on the wheels are different. |
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