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THE UNIVERSITY OF SYDNEY
PHYS 1002
PHYSICS 1 (FUNDAMENTALS)
JUNE 2010
Time allowed: THREE Hours
MARKS FOR QUESTIONS ARE AS INDICATED
TOTAL: 90 MARKS
INSTRUCTIONS
**- All questions are to be answered.
- Use a separate answer book for section A and section B.
- All answers should include explanations in terms of physical principles.**
DATA
Density of fresh water at 20 °C and 1 atm =^ 1.000^ ^103 kg.m^3
Density of sea water at 20 °C and 1 atm =^ 1.024^ 10 kg.m^3 ^3
Atmospheric air pressure P =^ 1.013^ 10 Pa^5
Free fall acceleration at Earth's surface g =^ 9.80 m.s^2
Speed of light in vacuum c =^ 3.00^ 10 m.s^8 ^1
SECTION A
Question 1
A large beaker full of water is placed on weighing scales and the weight of beaker plus water is noted.
(a) A rock suspended from a cord is then lowered into the water, and held fully immersed but not touching the bottom. (The water which overflows is drained on to the floor away from the weighing scales.) Explain briefly, why the reading on the weighing scales does not change when the rock is lowered into the water.
(b) The rock is now lowered so that it rests on the bottom of the beaker. Will the reading on the weighing scales increase, decrease, or stay the same? Explain your answer.
Question 3
Christopher and Jayne were sitting on laboratory chairs, facing each other, initially at rest on a horizontal floor. Christopher had a larger mass than Jayne. They pushed against each other. (Assume that the chairs can move across the floor without friction)
(a) While they were pushing each other, who experienced the greater magnitude of pushing force? Briefly explain your answer.
(b) At some time t after they finished pushing each other, who will have travelled further from their initial position? Briefly explain your answer.
(c) After they finished pushing each other, whose momentum was larger in magnitude? Briefly explain your answer.
Question 4
(a) A beetle sits near the edge of a stationary horizontal turntable. Draw a free-body diagram showing the forces acting on the beetle. What is the net force?
(b) Later the turntable is spinning at a constant angular velocity around a vertical axis. Draw the free-body diagram for the forces acting on the beetle. Make sure that the direction towards the centre of the turntable is clear.
(c) A centripetal force is acting on the beetle. What is providing this centripetal force?
(d) The turntable begins to spin faster. Which direction should the beetle move to minimise the chance of slipping? Briefly explain your answer with reference to appropriate physical principles.
SECTION B (Please use a separate book for this section.)
Question 7
A geologist has a rock sample and wishes to identify it. The rock has a mass of 0.870 kg. The rock is suspended from a spring balance and a cord and fully immersed in pure water with the rock not touching the bottom. The spring balance shows a tension T in the cord of 6.62 N.
(a) Draw a diagram showing the forces on the rock while it is fully immersed in the water.
(b) Write an equation relating (in symbols) the forces acting on the rock.
(c) Find the volume of the rock. Show your reasoning.
(d) Referring to the densities listed below, determine what the rock is made from. Show your reasoning.
Densities:
Pure water: 1.00 10 3 kg.m
Gypsum: 2.30 10 3 kg.m
Quartz: 2.65 103 kg.m- Siderite: 3.90 103 kg.m- Barite: 4.48 103 kg.m-
Question 8
A tennis player hits a ball with a speed v directed horizontally from a point which is2.50m
above the ground as shown in the diagram. The ball travels down the court and just clears a tennis net which is (^) 0.90min height and (^) 15.0m from the point where the ball was hit.
Assume that air resistance and the size of the tennis ball can be neglected.
(a) Show that the ball just passes over the net 0.57 seconds after it was hit by the tennis player. Hint: At the time that the ball passes the net it has fallen from its initial height to the height of the net.
(b) Calculate the value of the initial speed v.
(c) Calculate the velocity of the ball at its position on top of the net as shown in the diagram above.
There is a target area of the court that extends a distance of 7.0mbehind the net as shown in the diagram.
(d) Calculate the position at which the ball lands and indicate if the ball lands within the target area.
Question 10
A (^) 2.0mlong uniform pole has a mass of (^) 2.0kg.A bucket of mass (^) 4.0kg is hung a distance
of 0.20m from the left-hand end of the pole as shown in the diagram. A bucket of mass
9.0kg is hung a distance of 0.50mfrom the right-hand end of the pole.
Henry picks up the pole at a point X, which is a distance x from the left end of the pole.
(a) Write an expression in terms of distance x for the torque around point X arising from each of the following: (i) the weight of the bucket near the left-hand end of the pole; (ii) the weight of the bucket near the right-hand end of the pole; (iii) the weight of the pole; (iv) the force exerted by the person lifting the pole and buckets.
(b) Write an expression for the net torque resulting from the individual torques in part (a).
(c) Using your results, determine at what distance x should Henry pick up the pole and have it balance.
Question 11
If a diver bobs up and down on the end of a diving board, the motion can be modelled as that of a mass oscillating on a spring.
A light and flexible diving board deflects by 0.225mfrom the horizontal when Robert, a
68.0kg^ diver, stands on its end as shown in the diagram.
(a) Calculate the effective spring constant for the diving board.
Robert then jumps a little and lands back on the end of the board, depressing it by an extra 0.105m after which the board moves up and down so the end of the board and Robert moves
as a simple harmonic oscillator.
(b) Calculate the period of the oscillation.
(c) Sketch a graph of the position of the end of the diving board against time for two complete cycles of oscillation. Take upwards as the positive vertical direction. On your graph also show the position of the undeflected board and the position of maximum deflection downwards. Show numerical values on the time and position axes.
The amplitude of the oscillation of the diving board increases if Robert drives the motion of the board with his legs at the right frequency.
(d) Calculate the frequency of the driving force exerted by Robert’s legs to give the largest amplitude of vibration. Briefly justify your answer.
