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EXAMINATION PAPER CONTAINS STUDENT’S ANSWERS
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The Handbook of Mathematics, Physics and Astronomy Data is provided
KEELE UNIVERSITY
EXAMINATIONS, 2009/
Level I
Thursday 21st^ January 2010, 9:30–11:
PHYSICS/ASTROPHYSICS
PHY-
MECHANICS, GRAVITY and RELATIVITY
Candidates should attempt ALL of PARTS A and B, and TWO questions from PART C. PARTS A and B should be answered on the exam paper; PART C should be answered in the examination booklet which should be attached to the exam paper at the end of the exam with a treasury tag. PART A yields 16% of the marks, PART B yields 24%, PART C yields 60%. You are advised to divide your time in roughly these proportions. Figures in brackets [ ] denote the marks allocated to the various parts of each question.
Please do not write in the box below
A C1 Total B C C C
NOT TO BE REMOVED FROM THE EXAMINATION HALL
/Cont’d
PART A Tick the box by the answer you judge to be correct (marks are not deducted for incorrect answers)
A1 The units of force are equivalent to:
kg m s−^2 kg m s−^1 kg m^2 s−^2 kg m^2 s [1]
A2 A particle moving with distance x = 2t^2 has a velocity of:
8 t 4 t^2 4 t 4 [1]
A3 A 1-kg hammer strikes a 10-g nail exerting a force of 80 N. The nail exerts a force on the hammer of: 0.8 N 8 N 80 N 100 N [1]
A4 The kinetic energy of a particle is changing. Which of the following statements must be false? a is constant a is decreasing F is zero dx dt is decreasing [1]
A5 Particle A has the same kinetic energy as particle B, but has twice the mass. Com- pared to the speed of B, its speed is: 2
2 1/2 [1]
A6 The force acting on a body is equivalent to:
dE/dx E × x m^2 v dp/dx [1]
A7 A 2-kg mass, travelling at 2 m s–1, collides with a stationary mass of 1-kg. Assuming no loss of kinetic energy in the collision, the total kinetic energy of the masses after the collision is: 2 J 3 J 4 J 6 J [1]
A8 A machine is propelled by a force of 200 N which causes it to travel a distance of 5 m, in the same direction as the force, in 2 s. The average power is: 500 W 1000 W 1200 W 2000 W [1]
/Cont’d
PART B Answer all EIGHT questions
B1 A car accelerates away from a traffic light, then coasts for a while, slowing gradually, and then applies the brakes to come to a halt at another traffic light. Sketch graphs of the car’s acceleration, speed and distance travelled. [3]
B2 A force of F = 3t is applied to a particle for a time 0 < t < 5 s. What is the change in momentum? [3]
B3 A circular wheel, 2 m in radius, winds in a chain which pulls a coal truck up an incline. If the torque of the wheel is 3000 N m, what is the tension in the chain? [3]
B4 Define the quantity torque. [3]
/Cont’d
B5 A 4-m long rod of negligible mass is rotated about its center. Fixed to each end of the rod are 3-kg masses. What is the moment of inertia? [3]
B6 What is the gravitational potential 1000 km away from a mass of 10^22 kg? [3]
B7 State the fundamental postulates of Special Relativity. [3]
B8 What is the total energy of an electron travelling at 0.8c? [3]
/Cont’d
C3 By equating gravitational attraction with the centripetal force show that a body in a circular orbit at a radius r from a planet of mass M must have a speed v given by v^2 = GM r. (^) [10]
If a space station orbits 100 km above the Earth find the total energy needed to be given to a 100-kg payload to land it on the space station. [Earth’s radius is 6380 km; its mass is 6.0 × 1024 kg; ignore the Earth’s rotation.] [10] If the space station fires thrusters, accelerating it in the same direction it is travelling, what changes in its orbit will result? [5] If the space station then reverses the thrusters, and fires them against the direction in which it is travelling, describe what would happen. [5]
C4 Using the Lorentz transforms, prove that a time interval of τ , as measured in its own frame S, appears to last for a time interval of γτ when viewed from a moving frame S′. [12] Cosmic-ray muons are created 5 km above the Earth’s surface and travel down- wards at a speed of 0.995c. These particles are unstable and decay with a typical lifetime of 2.2 × 10 −^6 s. How far does a muon typically travel, as seen from the muon’s frame? Will a typical muon travel far enough to reach the Earth’s surface? Justify and explain your answers. [10] A detector stops 100 cosmic-ray muons. Given that the rest-mass of the muon is 1.88 × 10 −^28 kg, what is the energy absorbed by the detector? [8]
