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KEELE UNIVERSITY
LEVEL 1 EXAMINATIONS, 2008
(PRINCIPAL COURSE)
Wednesday 16th January, 13:00–15:
ASTROPHYSICS/PHYSICS
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 on separate sheets which should be attached to the exam paper using a treasury tag. PART A yields 16% of the marks, PART B yields 24% and PART C yields 60%.
Figures in brackets [ ] denote the marks allocated to the various parts of each question. Tables of physical and mathematical data may be obtained from the invigilator.
Registration Number......................................
A C1 Total B C C C
PART A Tick the box by the answer you judge to be correct (marks are not deducted for incorrect answers).
A1 The units of momentum are equivalent to:
m^2 s−^2 kg m s−^1 kg m s kg m^2 s [1]
A2 A 1-kg mass travelling at 2 m s−^1 collides with a stationary 5-kg mass and sticks to it. After the collision the momentum of the combined mass is (in SI units): 2 6 3 1 [1]
A3 Work is calculated from:
dE/dt
∫ F dt P dm
∫ F dx [1]
A4 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]
A5 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]
A6 A particle which starts from rest and moves with acceleration of a = 3t^2 has a velocity of: t^3 6 t 6 t^2 2 t^3 [1]
A7 A man pulls a sledge over level ground by a rope which makes an angle of 30◦^ to the horizontal. The tension (force) in the rope is 30 N. In pulling the sledge over 8 m the work done is: 120 J 208 J 227 J 240 J [1]
A8 A flywheel revolves at 6π rad s−^1. The number of revolutions per second is:
1 2 3 6 [1]
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 3000-kg coal truck is held on a 20◦^ incline by a chain. What is the minimum breaking strain the chain would need? [Take g = 9.8 m s−^2 ] [3]
B4 Newton’s 2nd law can be written F = dp/dt or F = ma. Write down statements equivalent to both of these for the quantity torque instead of force. [3]
B5 A 0.3-kg mass is swung in a circle using a 2-m piece of string. If it circles once per second, what is the angular momentum of the mass? [3]
B6 What is the escape velocity from the surface of a planet of mass 10^25 kg and radius 8000 km? [3]
B7 At what speed would an electron have the same energy as a proton does at rest? [3]
B8 The Sun emits radiation at 3.9× 1026 W. By how much does the Sun’s mass decrease in a second? [3]
C3. When orbiting a body of mass√ M at a distance r the speed is given by v = GM/r. Using this, find a relation between r and the orbital period P. [6] A geostationary satellite orbits the Earth in the same time the Earth rotates once. What is the radius of its orbit? [The Earth’s mass is 6 × 1024 kg.] [8] An enemy projectile is launched from Earth’s surface to collide with the satellite. If the mass of the missile is 10 kg, what is the minimum energy needed to achieve this? [Earth’s radius is 6380 km.] [8] If a replacement satellite has a mass of 50 kg, what is the energy needed to place a new satellite in that orbit? [8]
C4. Consider a beam, 10 m long as measured in its own frame S. A super-fast train passes by at 0.3c (in the direction of the beam’s length); observations from the train are referred to as the frame S′. By considering the events of observing (simultaneously in S′) the two ends of the beam, show that the beam appears to be Lorentz contracted by a factor γ as seen from the train. [10] Now suppose that two clocks, which are synchronised as judged from S, are placed at either end of the beam. An observer in the train watches the two events of the second hand of each clock passing the minute mark. What does he measure the spatial distance between these two events to be? [10] Now consider two consecutive ticks, 1 s apart in S, of the same clock. What is spatial and temporal separation of these events as seen from S′? [10]
