Download Question 22 - RobboPhysics

UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
A cyclist is travelling on a road through a dip, as shown in the diagram below. The combined mass of
the cyclist and his bicycle is 85 kg.
He is travelling at 5.0 ms-1 at point A. The shape of the road at the bottom of the dip is approximately
circular. A is 1.0 m higher than B. He stops pedalling at A. Air resistance and other frictional forces
are very small. Little kinetic energy is associated with the rotation of the wheels.
Question 1.
Calculate the speed of the bicycle at the point B. Show your working.
Question 2.
When the bicycle is at B, which one of the following statements best describes the size of the upward
force of the road on the bicycle? Give reasons for your choice.
A. It is equal to the combined weight of the bicycle and rider.
B. It is greater than the combined weight of the bicycle and rider.
C. It is less than the combined weight of the bicycle and rider.
D. There is insufficient information to decide.
When a glider turns during flight, its wings are tilted to aid the turn.
Question 3.
Assuming the glider maintains a constant altitude (height) and speed during a circular turn, show the
forces responsible for achieving this.
Question 4.
If the wings make an angle of 600 with the vertical and the glider has a total mass of 300 kg, determine
the magnitude of the net force responsible for turning the glider.
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
A car on a flat circular track is travelling in a circle, as shown below. The car must not travel too fast or
the sideways frictional force will not be large enough to keep the car on the road.
The maximum sideways frictional force that the road-tyre combination can produce for the car in the
diagram is 2000 N. The car has a mass of 1000 kg. The track has a radius of 100 m.
Question 5.
Calculate the maximum speed that the car can have and stay on the road.
Include the unit in your answer.
A cyclist is travelling at a constant speed of 7.0 ms-1 round a curve in a horizontal road. The centre of
mass of the cyclist and her bicycle moves in a circle which has a radius of 8.0 m. The mass of the
cyclist and her bicycle is 90 kg.
Question 6.
What is the magnitude of the net force which causes the cyclist and her bicycle to move in circular
motion?
Question 7.
Show all the external forces acting on the bicycle and rider as she rides round the curve, and indicate
their directions clearly. (Ignore air resistance, and treat the bicycle and rider as one object.)
Hence show how these forces combine to produce the net force calculated in Question 6.
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
An energy-efficient vehicle of mass 410 kg moving at a constant speed of 19.1 m s-1 turns a banked
corner. The vehicle travels around the corner in a horizontal circular arc of radius 50.0 m. The grid
below shows the force of gravity on the vehicle and the normal reaction of the surface on the vehicle.
The force of friction between the tyres and the road is not shown. The vectors are drawn to scale.
Question 8.
Draw a vector which represents the net force on the vehicle.
Question 9.
What is the magnitude of the friction acting along the slope between the tyres and the road?
A car of mass 1.2 x 103 kg is moving in a horizontal circle with constant speed of 20 ms-1 around a
circular banked track of radius 80 m as shown in the diagram above.
Question 10.
Draw and label an arrow to show the direction of the net force on the car.
Question 11.
What is the magnitude of the net force on the car?
When the road surface is wet, such a banked track is much safer than a level track would be. In terms
of the forces acting on the car, explain why this is so.
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
In the game of totem-tennis a tennis ball is attached by a light string to the top of a pole. The ball is
struck with a bat so that it swings around the pole. The string does not stretch.
Question 12.
On a simple diagram, show the directions of the individual forces which act on the ball. Label each
force with its name.
In the case shown above, the ball travels in a horizontal circle at a constant speed. The string is at a
constant angle of 300 to the vertical. The length of the string is 1.5 m and the mass of the tennis ball is
0.060 kg.
Question 13.
Calculate the vertical component of the tension in the string.
Question 14.
Calculate the horizontal component of the tension in the string.
Question 15.
Calculate the magnitude of the acceleration of the ball.
In another case, the ball does not travel at a constant speed, and the angle of the string varies up and
down as shown below.
At the highest point P the ball is 1.10 m above the ground, and at the lowest point Q it is 0.70 m above
the ground. The speed of the ball is 4.0 ms-1 at P.
Question 16.
Calculate its speed at Q. Include your working with reasons.
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
Information for questions 17 - 19
The diagram, below, shows an object, suspended from railing attached to the ceiling of a moving van
which is negotiating a left hand turn at high speed. The object is connected to a rope, and has a mass of'
7.0 kg. The inside of the van is 2.0 m high; the railing is 30 cm from the ceiling of the van. The length
of the rope is 1.5 m and is 62 degrees to the vertical.
Question 17.
If the van is cornering at a constant speed, what is the value of the centripetal force.
Question 18.
Calculate the tension in the rope. Show your working out and include a diagram.
Question 19.
When the van reaches point A, the rope breaks. In which direction, as viewed from above, is the object
most likely to move?
The following information refers to Questions 22-24
Students, on a physics excursion to the Melbourne Show, take a. fun ride on one of the more
spectacular rides. Thrillseekers are rolled backwards and forwards in a vertical loop going higher and
higher until the passenger cage momentarily stops at position "A". The cage can then complete the
vertical circle without further energy being supplied by the machinery.
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
For questions 22 to 24, assume that the velocity at the highest point of the vertical circle is zero.
Question 22
When do the occupants experience the greatest amount of acceleration?
A
B
C
D
E
At the top (position A )
Going down (position B)
At the bottom (position Q
Going up (position D)
The amount of acceleration does not change, only its direction
Question 23
What is the speed of the carriage at the lowest point (position C) of the vertical circle?
Question 24
What is the apparent weight, experienced by a 60kg occupant, at the lowest point of the vertical circle?
In athletics, a hammer consists of a steel ball of mass 5.0 kg, attached to a wire of negligible mass.
Before releasing the hammer, an athlete rotates, swinging the ball in a circle by holding the end of the
wire. Figure below illustrates the situation.
Question 25
Assume that the ball is moving in a horizontal circle of radius 1.6 m, with a speed of 20 m s-1.
What is the tension in the wire?
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UNIT 4. Revision Questions (‘92-’95) MOTION. PART A:CIRCULAR MOTION
Figure below shows a view from above the thrower and hammer at the instant of release. The arrow
shows the direction of rotation of the athlete and hammer.
Question 26
Which one of the diagrams A. to E. in Figure below, best shows the path of the ball after release?
The racing motorcyclist shown in Figure (a) travels at a constant speed of 108 km h-1 (30 m s-1) around
a horizontal curved track of radius 120 m. Part of the curved track is shown, from above, in Figure (b).
Mass of motorcyclist = 85 kg
Mass of motorcycle = 200 kg
(a)
(b)
Question 27
What is the magnitude of the acceleration of the motorcyclist?
Question 28
How long does it take for the motorcyclist to travel from point X to point Y on the curve shown in
Figure (b)?
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