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
Work crossed out will not be marked.
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:
0 1 1
1 0 0
0 1 1
(a) -2
(b) -1
(c) 0
(d) 1
(e) 2
2.
One object of mass 0.5kg moves along the x-axis with speed -2vx. Another
object of mass 1.5kg moves along the x-axis with speed +
centre-of-mass velocity for this system?
8
(a) - vx
3
4
(b) - vx
3
(c) -vx
(d) 0
(e) vx
2
vx. What is the
3
3.
Three forces of (2 iˆ - ĵ +3 k̂ ) N, (- iˆ + ĵ - k̂ ) N and (+ iˆ - ĵ + k̂ ) N act on an
object. The unit vector in the direction of the resultant force is:
(a) (2 iˆ - ĵ +3 k̂ ) N
(b)
14 N
(c)
14 (2 iˆ - ĵ +3 k̂ ) N
(d)
1
14
(2 iˆ - ĵ +3 k̂ ) N
(e) 0 N
4.
A sledge of mass m slides with constant velocity down a hill of angle  with
respect to the horizontal. Which one of the following expressions correctly
relates the magnitude of the frictional force, fk, to the coefficient of kinetic
friction, k ?
(a) f k   k mg
(b) f k   k mg cos
(c) f k   k mg sin 
(d) f k  0
(f) The coefficient of kinetic friction is not appropriate for this problem.
5.
Measurements of the water level at the end of a long lake show that the lake
rises and falls with a definite period in a similar way to tides on a seashore. The
tidal period, T, for an elliptical lake may be written as
T
1 .7 L
gh n
where L is the length of the lake, h is the depth of the lake and g is the
acceleration due to gravity. Using dimensional analysis or otherwise, what is
the value of n ?
(a) -
1
2
(b) 0
(c)
1
2
(d) 1
(e) 2
6.
A submarine travels 50km in one hour travelling at constant speed in a straight
line. The density of water, , is 1g/cm3. Assuming that the drag coefficient, c,
of the submarine is 0.5, its effective cross-sectional area, A, is 20m2 and that the
1
Drag force, D, may be written as, D  cAv 2 , the closest estimate for D is
2
(a) 106 N
(b) 0.01 N
(c) 1000 N
(d) 10-6 N
(e) 100 N
7.
In a television set, an electron is accelerated through a voltage of 1000V as it
travels from the emission cathode to the screen (anode). The kinetic energy of
the electron as it hits the screen surface is
(a) 1.6 x 10-16 J
(b) 1.6 x 10-19 J
(c) 1.6 x 1016 J
(d) 1.6 x 1019 J
(e) 1.6 J
8.
A fictitious planet called Zog has a mass of 106 splot and a density of
10 splot/blob3. If 1 blob = 50 km, and assuming that Zog is spherical, what is
the radius of Zog ?
(a) 3100 m
(b) 1.44 x 106 m
(c) 1440 m
(d) 5.8 x 10-4 m
(e) 3.10 x 106 m
9.
What is the vector product a  b where a = ( iˆ + ĵ +2 k̂ ) and b = ( iˆ +2 ĵ + k̂ ) ?
(a) -3 iˆ - ĵ - k̂
(b) -3 iˆ - ĵ + k̂
(c) -3 iˆ + ĵ - k̂
(d) 0
(e) -3 iˆ + ĵ + k̂
10.
A car has an acceleration given by a = 2t iˆ -3t2 ĵ +5 k̂ ms-2. What is the velocity
of the car as a function of time given that at t = 2s, v = iˆ + ĵ + k̂ ms-1 ?
(a) (t2+3) iˆ +(t3-9) ĵ +(9-5t) k̂ ms-1
(b) (t2-3) iˆ +(9-t3) ĵ +(5t-9) k̂ ms-1
(c) -t3+t2+5t ms-1
(d) t2 iˆ -t3 ĵ +5t k̂ ms-1
(e) 2t iˆ -3t2 ĵ +5 k̂ ms-1
11.
A force of 3 iˆ - ĵ N acts on an object and causes a displacement of ĵ - k̂ m. The
work done by the force on the object is
(a)
10 J
(b) 0 J
(c) 3 iˆ - k̂ J
(d) –1 J
(e) 2 J
12.
A helicopter rotor consists of four blades, each of mass m = 10 kg and length
l = 4 m. The rotational energy of each blade is given by E 
1 2
I where  is
2
the angular velocity and I is the moment of inertia of a blade given by
1
I  ml 2 . Calculate the rotational energy of the rotor when it is spinning at 1
3
revolution per second.
(a) 4211 J
(b) 108 J
(c) 1053 J
(d) 27 J
(e) 8422 J
13.
Starting from the smallest multiplicative factor and ending with the largest,
which of the following is in the correct order
(a) femto, atto, pico, nano, micro, milli, kilo, mega, tera, giga
(b) atto, femto, pico, nano, micro, milli, kilo, mega, giga, tera
(c) tera, giga, mega, kilo, milli, micro, nano, pico, femto, atto
(d) pico, nano, atto, femto, micro, milli, kilo, mega, giga, tera
(e) tera, femto, pico, nano, micro, milli, kilo, mega, giga, atto
14.
Which of the following is a true statement for two bodies making an inelastic
collision ?
(a) Only momentum is conserved.
(b) Kinetic energy and momentum are conserved.
(c) Neither total energy nor momentum are conserved.
(d) Total energy is not conserved.
(e) Total energy and momentum are conserved but kinetic energy is not.
15.
Which of the following are the correct dimensions of power ?
(a) [M][L]2[T]-2
(b) it is dimensionless
(c) [M][L][T]-3
(d) [M][L]2[T]-3
(e) [M][L]3[T]-3
30 Marks
SECTION B: ANSWER TWO QUESTIONS
1.
(a) Figure 1 shows the variation of the speed of an object moving in a straight line
as a function of time, v(t). Using the information given in the figure, determine
a suitable expression for v(t). Hence or otherwise determine an expression for
the displacement of the object as a function of time, r(t), assuming that its
initial position is 0 m. For both expressions, define each of the terms used and
show your working.
6 marks
v
gradient = a
vo
t
Figure 1 (Question 1a)
(b) At t=0, a ball is shot from level ground into the air. After a time tb the ball has
reached a height of 80m and its velocity is v = 8 iˆ +30 ĵ ms-1 where iˆ and ĵ are
unit vectors in the horizontal and vertical directions respectively. Assuming that
the acceleration due to gravity is 10ms-2 and neglecting air resistance, answer
the following questions.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
What is the horizontal speed of the ball at t=0 ?
What is the velocity of the ball at t=0 ?
Calculate tb.
How long does it take for the ball to reach its maximum height ?
What is the total horizontal distance travelled by the ball when it strikes the
ground again ?
What is the speed of the ball and its angle with the horizontal at the instance
it strikes the ground ?
14 marks
2.
(a)
What do you understand by moment of inertia ? State two ways by which a
rotating object could be redesigned to increase its moment of inertia without
increasing the volume of the object.
6 marks
(b)
The angular momentum L of an object at position r with respect to an
origin O is, L = r x p , where p is its linear momentum. Show that the rate
of change of angular momentum is equal to the applied torque.
4 marks
(c)
A DVD can be thought of as a solid disc of thickness 1.2mm and diameter
120mm. Given that the maximum possible speed at a point on the disc is
4ms-1, determine the period of revolution of the disc and its angular
velocity.
Given that the moment of inertia of a uniform disc of radius l and mass M is
1 2
Ml , calculate the angular momentum of the solid disc if its density is
2
1.1gcm-3.
10 marks
3.
A ball (ball 1) of mass m strikes a stationary ball (ball 2) of equal mass
with a glancing collision. Ball 2 recoils and ball 1 is deflected from its
original path.
(a)
State the physical quantities you would expect to be conserved in this
collision, assuming the collision is elastic.
3 marks
(b)
-1
-1
If the initial and final speeds of ball 1 are 5ms and 4ms respectively,
calculate the recoil speed of ball 2.
4 marks
(c)
Show that after the collision, the two balls move along paths which are
at right angles to each other.
6 marks
(d)
Calculate the centre-of-mass velocity of the two ball system using
appropriate unit vectors. Hence determine the velocity of each ball,
prior to collision, as observed from the centre-of-mass frame of
reference.
5 marks
(e)
What evidence might there be that the collision is not perfectly elastic?
2 marks