Download 1 - University of Surrey

UNIVERSITY OF SURREY
SCHOOL OF ELECTRONICS AND PHYSICAL SCIENCES
DEPARTMENT OF PHYSICS
BSc and MPhys Programmes in Physics
LEVEL HE1
PAPER 1
PRINCIPLES OF PHYSICS
Time allowed: 2 hours
SECTION A: Answer ALL questions
SECTION B: Answer TWO questions
Examiner:
Dr S J Sweeney
The only University approved calculators are Casio Models FX115MS,
FX115W or FX115S for September 1998 entry onwards.
The numbers at the end of each section of a question give an
approximate indication of the marks available.
SECTION A: ANSWER ALL QUESTIONS
1.
Calculate the determinant:
1 1 2
4 2 3
1 2 4
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
2.
Two objects of mass 2kg and 1kg respectively, move along the y-axis with the
same speed vy. What is the centre-of-mass velocity for this two-body system?
(a) 3vy
(b) vy
(c) 0
(d) -vy
(e) -3vy
3.
Three forces of (3 iˆ + ĵ - k̂ ) N, ( iˆ - 4 ĵ ) N and k̂ N act on an object. The unit
vector in the direction of the resultant force is:
(a) (4 iˆ -3 ĵ ) N
(b)
11 + 9 +1 N
(c) (3 iˆ -4 ĵ - k̂ ) N
(d)
(e)
1 ˆ
(4 i -3 ĵ ) N
5
1
(3 iˆ -4 ĵ - k̂ ) N
26
4.
Which of the following statements about the vector product a  b is incorrect?
(a) The magnitude of a  b is equal to the area of the parallelogram formed by
the vectors a and b .
(b) a  b is a vector which is perpendicular to both a and b .
(c) If a and b are parallel vectors, the vector product is zero.
(d) The magnitude of a  b is equal to ab cos where  is the smallest angle
between a and b .
(e) a  b = - b  a .
5.
A voltage of 1V is measured across the terminals of a 1F capacitor and the
charge stored by the capacitor, Q, is related to the voltage, V, and capacitance,
C, by Q  CV . To the nearest order of magnitude, how many electrons are
stored in the capacitor (assume the electronic charge, e = 1.6x10-19C)?
(a) 1
(b) 10-19
(c) 0
(d) 1019
(e) 1038
6.
An object moves from iˆ m to ( iˆ + ĵ - k̂ ) m whilst being acted upon by a force
( iˆ + ĵ + k̂ ) N. What is the work done by the force on the object?
(a) 0 J
(b) 2 J
(c) ( iˆ + ĵ ) J
(d) 1 J
(e)
7.
5 J
If a nucleus is represented by an object the size of a tennis ball, indicate the
distance between two tennis balls that would best correspond to the distance
between two nuclei in a crystal. Assume size of nucleus is 10-15m and typical
spacing of nuclei in a crystal is 10-10m.
8.
(a)
0.1 cm
(b)
10 m
(c)
10 km
(d)
1000 km
(e)
106 km
Three forces, F1, F2 and F3 satisfy the two equations, F1 + F2 = F3
and F1 + F2 = F3. Which one of the following statements is true?
(a) F1, F2 and F3 form a triangle of forces.
(b) The two equations are always true for any forces, F1, F2 and F3.
(c) F1 and F2 must be anti-parallel.
(d) The two equations can never be simultaneously satisfied.
(e) F1 and F2 must be parallel.
9.
A particle of charge, q, travelling with a velocity, v = vx iˆ ms-1, enters a
magnetic field, B = Bx iˆ + By ĵ + Bz k̂ T. Which of the following is the correct
expression for the force acting on the particle?
(a) q (-vxBz ĵ + vxBy k̂ ) N
(b) q (vxBy ĵ + vxBz k̂ ) N
(c) qvxBx N
(d) 0
(e) None of the above.
10.
An ancient agricultural measure of the mass of hay is the Truss. If
1 Truss = 60lb and a Truss of hay has a volume of 17.7 ft3, what is the density
of hay in SI units (you may assume that 1lb = 0.454kg and 1ft = 30.48cm)?
(a) 0.056 Truss/ft3
(b) 5.4 kg/m3
(c) 1 kg/m3
(d) 3.39 lb/ft3
(e) 54.3 kg/m3
11.
The energy, E, of a photon is given by, E = hf, where f is the photon frequency
and h is the Planck constant. What are the dimensions of h?
(a) [M][L]2[T]-3
(b) [M][L]2[T]-1
(c) h is dimensionless.
(d) [M][L][T]-3
(e) [M][L][T]-1
12.
Which of the following is a valid vector equation?
(a) (a  b)  c = d
(b) (a  b)  c = d
(c) (a  b) c = d
(d) (a  b)  c = d
(e) (a  b)  c = d
13.
A mass of 1kg slides along a horizontal surface at a constant speed. Given that
the coefficient of kinetic friction between the object and the surface, k = 0.5,
what is the magnitude of the frictional force acting on the object in terms of the
acceleration due to gravity, g.
(a) 0
(b) g
(c) -g
(d) 0.5g
(e) 2g
14.
An ice-skater spins on her axis with her arms outstretched. She then brings her
arms towards her body closer to the axis of rotation. What can be said about her
angular speed, , her moment of inertia, I, her angular momentum, L, and her
rotational kinetic energy, Krot?
(a)  increases, I decreases, L remains constant, Krot increases.
(b)  increases, I decreases, L increases, Krot remains constant.
(c)  decreases, I increases, L remains constant, Krot increases.
(d)  increases, I decreases, L remains constant, Krot remains constant.
(e)  decreases, I increases, L increases, Krot increases.
15.
A particle has a velocity given by v = (3t2 iˆ + k̂ ) ms-1. Given that, at t = 1s, the
particle was at (2 iˆ + ĵ ) m, the position of the particle as a function of time, is
(a)
t3+t m
(b)
t3 iˆ + t k̂ m
(c)
(t3+2) iˆ + ĵ + t k̂ m
(d)
(t3+1) iˆ m
(e)
(t3+1) iˆ + ĵ + (t-1) k̂ m
30 Marks
SECTION B: ANSWER TWO QUESTIONS
1.
(a) Write down the differential equations which relate the velocity, v, and
acceleration, a, of an object to its position, r.
2 marks
(b) Prove that, in the case of constant acceleration, the position of an object is
given by
r = ro + vot + ½ at2.
Explain the meaning of each term in this equation.
6 marks
(c) A tennis player serves a standard tennis ball (diameter = 6.65cm) at 24ms -1, the
ball leaving the racket horizontally at a height of 2.2m (to the ball centre).
(i)
Develop a vector expression for the position of the ball as a function of
time.
(ii)
Assuming that air resistance may be neglected, by how much does the
centre of the ball clear the net which is 12m away and has a height of
90cm? (Assume that g=9.8ms-1).
(iii)
Neglecting air resistance, what is the minimum horizontal speed that the
tennis ball must be served at to just clear the net?
(iv)
Briefly describe the effect air resistance will have on the calculation in
part (iii).
12 marks
2.
(a)
State and explain what is meant by Galilean transformations. Under what
circumstances are such transformations valid?
4 marks
(b)
Explain how viewing a system from the centre-of-mass frame of reference
can aid the analysis of two-body collisions.
4 marks
(c)
At t = 0, a 1kg mass is located at position iˆ m and has a velocity of
2 ĵ ms-1. At the same time, a 2kg mass is located at position ĵ m and has a
velocity of ( iˆ + ĵ ) ms-1.
(i)
Calculate the position of the centre-of-mass for this two-body
system.
(ii)
Calculate the centre-of-mass velocity.
(iii)
Calculate the velocity of the 1kg mass as viewed from the frame of
the 2kg mass.
6 marks
(d)
These two masses collide at position ( iˆ +2 ĵ ) m and join to form a
composite object of mass 3kg.
(i)
What type of collision is this? What can be said about the final
kinetic energy of this system after the collision?
(ii)
What is the final velocity of the composite?
(iii)
Calculate the fraction of the kinetic energy that has been dissipated
to the surroundings in the collision.
6 marks
3.
(a)
A simple wheel may be considered to be a thin disc of uniform thickness. If
the wheel has a radius of 25cm and rotates at 120 revolutions per minute,
determine the period of revolution, angular velocity and the speed of a
particle on the outer rim.
Given that the moment of inertia of a wheel of radius, r, and mass, m, is
½ mr2, determine the angular momentum of the wheel if its density is
10gcm-3 and it has a thickness of 2cm.
8 marks
(b)
A stationary wheel of mass, m, and radius, r, is released at the top of a
slope, at which point, the wheel begins to rotate.
(i)
Briefly explain what causes the wheel to start rotating.
(ii)
If the speed at the centre line of the wheel is v, derive an expression
for the total kinetic energy of the wheel in terms of v and m.
6 marks
(c)
Consider the wheels shown below. The two wheels have the same radius
and same total mass. The shaded area corresponds to high density material,
whilst the un-shaded area corresponds to low density material. Thus, wheel
A has high density material concentrated towards its centre whilst wheel B
has high density material concentrated to its perimeter. If these two wheels
are released together at the top of a slope, which wheel, if any, will roll
down the slope fastest? Justify your answer.
Wheel A
Wheel B
6 marks