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Phys 112: Mechanics Question Paper
Phys 112: Mechanics
Course:Bachelor Of Education In Physics
Institution: Chuka University question papers
Exam Year:2012
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CHUKA UNIVERSITY
COLLEGE
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF SCIENCE (GENERAL), BACHELOR OF SCIENCE
(COMPUTER SCIENCE) AND BACHELOR OF EDUCATION (ARTS)
PHYS 112: MECHANICS
STREAM: B.SC. (GEN.), B.SC (COMP.SCI) & TIME: 2 HOURS
B.ED (ARTS) Y1S1
DAY/DATE: THURSDAY 9/12/2010 11.30 A.M. – 1.30 P.M
INSTRUCTIONS:
- Question ONE is compulsory and carries 40 marks.
- Other questions carry 15 marks.
- Answer question one and any other TWO.
Q.1 (a) Given below are some statements. Decide whether they are true or false
giving reasons for your choice.
(i) A car covers the first half of its distance between two places at a
speed of 40 km/hr and the second half at 60 km/hr. The average
speed of the car is then 50 km/hr. [2 marks]
(ii) It is possible to sometimes have a single isolated force.
[2 marks]
(iii) The total energy of a body in motion is equal to the work it can do
in being brought to rest. [2 marks]
(iv) The outside “horses” on a merry go round get more acceleration
than the inside ones. [2 marks]
(iv) A quick collision between two bodies is more violent than a slow
collision even when the initial and the final velocities are identical.
[2 marks]
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(b) Three vectors are given as follows:
A
= i – 3j
B
= 2i + 4j
C
= 2i + j – 4j
(i) Show that
A
x
B
= -B
x
A
[3 marks]
(ii) Find
A
.
B (
x
C
)
[3 marks]
(c) (i) State the work-energy principle. [1½ marks]
(ii) A coin of mass 3.2g is dropped vertically to a floor a distance
of 11m. Determine the speed of the coin just before it hits the
floor. [3 marks]
(d) (i) Distinguish between elastic and inelastic collision. [1½ marks]
(ii) A particle of mass = 70g is initially at rest. Another particle of
mass M2
= 35g moving with a velocity of 1.9ms
-1
collides with M
2
elastically. What are the velocities of the two particles after the
collision? [4 marks]
(e) From the top of a tower of height 50m, a ball is thrown vertically upward
with a certain velocity. It hits the ground 10s after it is thrown up. With
what velocity is that ball projected? [4 marks]
(f) A car of mass 1200Kg falls vertically a distance of 24m starting from rest.
What is the work done by the force of gravity on the car? Use the workenergy theorem to find the final velocity of the car just before it hits the
ground. (Treat the car as pointlike). [6 marks]
(6) A train has to negotiate a curve of radius 300m. By how much will the
outer rails be raised with respect to the inner rail for a speed of 54km h
-1?
The distance between the rail is 1.5m. (Take g = 10ms
-1
). [4 marks]
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Q.2 (a) Two forces are given by
1 F
= 2j + 3k and
2
F
= - 4j - 5j. Calculate the
resultant force and the angle between the forces. [4 marks]
(b) A particle has shifted along some trajectory in the plane xy from point 1
whose radius vector
1
r
= i + 2j to point 2 with the radius vector
2
r
= 2i - 3j.
During that time the practice experienced the action of certain forces, one
of which
F
= 3i + 4j. Find the work performed by the force
F
.
(Here
1
r
,
2
r
and
F
are given in SI units) [3 marks]
(c) A string of length 1m is fixed at one end and carries a mass of 100g at the
other end. This string makes 2 revolutions per second around a vertical
axis passing through its second end.
Calculate
(i) Angle of inclination of the string with the vertical. [4 marks]
(ii) The tension in the string. [2 marks]
(iii) The linear velocity of the mass. [2 marks]
Q.3 (a) State the principle of conservation of linear momentum. [2 marks]
(b) Two masses M1 and M
2, where M
1
= 2.0kg, moving at 80i m/s collided
with a mass M2
= 6.0kg moving in the same direction at 2.0i m/s. If the
collision is elastic, determines the velocities of each of the two masses
after the collision. [7 marks]
(c) A bullet of mass 10g moving vertically upwards with a speed V (500 m/s)
as shown embeds itself
Wooden
Block
V
Bullet
M
In a wooden block of mass 2kg., to what maximum height does the block
rise above its initial position? [6 marks]
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Q.4 (a) (i) Define centripetal acceleration. [2 marks]
(ii) A rotating object increases its speed from rest to 25 rad s
-1
in 10s.
Find the linear acceleration of a point 0.25m from the axis of
rotation. [2 marks]
(b) A cricket ball of mass 150g is moving with a velocity of 12ms
-1
and is hit
by a bat so that the bull is turned back with a velocity of 20ms
-1
. The
force of the blow acts for 0.01s. Find the average force exerted on the ball
by the bat. [5 marks]
(c) The driver of a train A, moving with a uniform speed of 144 kh hr
-1
sight
another train B, 1km ahead of him. The train B is moving with a uniform
speed of 108 km hr
-1
. The driver of train A immediately applies brakes
producing a constant retardation and just manages to avoid a collision.
(i) What is the retardation of train A?
(ii) For how long is this retardation produced? [6 marks]
Q.5 (a) (i) State the law of universal gravitation. [2 marks]
(ii) What is the magnitude of gravitational force between a 70-kg man
and a 70-kg woman separated by a distance of 10? Treat both
masses as particles. [3 marks]
(b) An artificial satellite is describing an equatorial orbit at 1600 km above the
surface on the earth.
(i) Calculate its orbital speed and the period of revolution.
[5 marks]
(ii) If the satellite is traveling in the same direction as the rotation of
the earth (i.e. from west to east). Calculate the vertically overhead
to an observer at a fixed point on the equator.
(Radius of earth = 6400km). [5 marks]
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