THE COPPERBELT UNIVERSITY
PHYSICS DEPARTMENT
SCHOOL OF MATHEMATICS AND NATURAL SCIENCES
DEFERRED TEST 1
COURSE: PH 110 APRIL 2021
ANSWER ALL QUESTIONS TIME: TWO (2) HOURS
QUESTION ONE
(a) Convert the following:
i. 100 mg into kg [2]
ii. 0.005 N into cgs system [2]
iii. 0.1 cm2 into m2 [2]
iv. 0.1 liters into cm3 [2]
v. 2.5 x 10-10 m into μm [2]
(b) State two (2) advantages of using the method of Estimations and Order of
Magnitude in calculations. [2]
(c) State two (2) disadvantages of using the method of Estimations and Order of
Magnitude in calculations. [2]
(d) Given the vectors A = 5𝑖 ̂ +3𝑗 ̂ + 2𝑘 ̂and B = -4𝑖 ̂ +4𝑗 ̂ + 7𝑘. Find the angle between
vectors A and B [5]
(e) A car initially at point X moves at constant velocity for 0.5 km eastward for 10
minutes to reach point Y and after point Y it suddenly changes to a constant
velocity to move another 2 km eastward for 5 minutes to reach point Z.
(i) Calculate the average velocity in SI units for the scenario [3]
(ii) Calculate acceleration of the car from X to Z. [3]
1
QUESTION TWO
(a) Given that the three vectors A = 2𝑖̂ +3𝑗 - 2𝑘, B = -4𝑖 +3𝑗 + 7𝑘 and C = -𝑖 ̂+ 4𝑗 + 9𝑘
act at one point in space. Find:
(i) The resultant vector [6]
(ii) The magnitude of the resultant vector [4]
(iii) The unit vector of the resultant [4]
(iv) The direction of the resultant with respect to the x-axis [4]
(b) Given the vectors A = 2𝑖 ̂ +3𝑗 ̂ - 2𝑘, B = -4𝑖 ̂ +3𝑗 ̂ + 7𝑘 and C = -𝑖 ̂ +4𝑗 ̂ + 9𝑘.
Find the scalar triple product A.(B x C) [7]
QUESTION THREE
(a) A projectile is fired downwards with an initial velocity of 30 m/s at 30o angle to
the vertical (as shown) and hits the ground after 10 s. Use g = 9.82 m/s2
Calculate:
(i) The final velocity on impact [4]
(ii) The height from which the projectile was fired [4]
(iii) The range of the projectile [3]
(iv) The x-component of the acceleration [2]
(b) A projectile is fired upward (vertically). It takes 30 seconds to come back to its
starting point. Calculate:
(i) The maximum possible height reached [4]
(ii) The initial velocity [3]
(iii) The velocity halfway upwards [3]
(iv) Give one reason why in practice the time of ascent may be different from time
of descent in projectile motions [2]
2
SOLUTION-QUESTION ONE
(a)
i. 1g = 1kg/1000 = 10-3 kg; 1mg = 1kg/1,000,000 = 10-6 kg; 100mg => 10-4 kg [2]
ii. 0.005 N = 0.005 kg.m/s2 = 0.005 (1000)g(100)cm/s2 = 100 g.cm/s2 [2]
iii. 1cm = 10-2m; 1cm2 = 10-4m2; 0.1cm2 = 10-4m2 x 10-1cm2 = 10-5 m2 [2]
iv. 1 L = 1000cm3; 0.1 L = 100 cm3 [2]
v. 2.5 x 10-10 m = 2.5 x 10-6 x10-4 m = 2.5 x 10-4 μm [2]
(b) - Estimates serve as a partial check if the exact calculations are correct.
- Calculations can be carried out where limited information is available
- Can be used where it is difficult or impossible to get an exact answer in a
calculation [2]
(c) - It does not give precise answers
- Values close to each other cannot easily be estimated apart [2]
(d) Given the vectors A = 5𝑖 ̂ +3𝑗 ̂ + 2𝑘 ̂and B = -4𝑖 ̂ +4𝑗 ̂ + 7𝑘. Find the angle between
vectors A and B [5]
A.B = |A||B|cosθ; cosθ = A.B/|A||B|; θ = cos-1 (A.B/|A||B|)
But, A.B =5(-4) + 3(4) + 2(7) = -20 + 12 + 14 = 6;
|A|= √52 + 32 + 22 = √38
|B|= √(−4)2 + 42 + 72 = √81
Also √38x√81 = 𝟓𝟓. 𝟒𝟖
Hence θ = cos-1 (6/55.48); θ = cos-1 (0.108147); θ = cos-1 (0.108147) = 83.79o
(e) A car initially at point X moves at constant velocity for 0.5 km eastward for 10
minutes to reach point Y and after point Y it suddenly changes to a constant
velocity to move another 2 km eastward for 5 minutes to reach point Z.
(i) average velocity:
500𝑚
𝑢 = 0.5𝑘𝑚/10 min = = 0.833 𝑚/𝑠
600𝑠
2000𝑚
𝑣 = 2𝑘𝑚/5 min = = 6.667 𝑚/𝑠
300𝑠
Average velocity = (v+u)/2 = (6.667 + 0.833)/2 = 7.5 m/s [3]
(ii) acceleration from X to Z:
Acceleration = (v-u)/t; Acceleration = (6.667-0.833)/900= 6.48 x 10-3 m/s2; [3]
3
SOLUTION - QUESTION TWO
(a) vectors A = 2𝑖̂ +3𝑗 - 2𝑘, B = -4𝑖 +3𝑗 + 7𝑘 and C = -𝑖 ̂+ 4𝑗 + 9𝑘
(i) The resultant vector R:
R = A + B + C = (2-4-1) 𝑖 + (3+3+4) 𝑗 + (-2+7+9) = -3𝑖 +10𝑗 + 14𝑘 [6]
(ii) magnitude of R: 𝑅 = √(−3)2 + 102 + 142 = √305 = 17.46 [4]
𝑹 −3i +10j + 14k
(iii) Unit vector of R: 𝑅̂ = = [4]
𝑅 17.46
(iv) direction of R: Tan(θ) = 10/3 = 3.333; θ = Tan-1(3.333)= 73.3o [4]
(b) Find the scalar triple product A.(B x C) :
2 3 −2
(B x C)= |−4 3 7 | = 2(3x9 − 7x4) − 3(−4x9 + 1x7) − 2(−4x4 + 1x3)
−1 4 9
= −2 + 87 + 26 = 111 [7]
SOLUTION - QUESTION THREE
(a) A projectile is fired downwards with an initial velocity of 30 m/s at 30o angle to
the vertical (as shown) and hits the ground after 10 s. Use g = 9.82 m/s2
(i) The final velocity on impact
𝑢𝑦 = 30 cos(30) = 25.981𝑚/𝑠; 𝑢𝑥 = 30 sin(30) = 15𝑚/𝑠;
𝑣𝑦 = 𝑢𝑦 + 𝑎𝑦 𝑡 = 25.981 + 9.82(10) = 124.181𝑚/𝑠
𝑣𝑥 = 𝑢𝑥 + 𝑎𝑥 𝑡 = 15 + 0(10) = 15𝑚/𝑠
𝑣 = √𝑣𝑦 2 + 𝑣𝑥 2 = √124.1812 + 152 = 125.08 𝑚/𝑠 [4]
(ii) The height from which the projectile was fired
𝑣𝑦 2 −𝑢𝑦 2
𝑣𝑦 2 = 𝑢𝑦 2 + 2𝑎𝑦 𝑆𝑦 ; 𝑆𝑦 = = (124.1812 − 25.9812 )/2(9.82)
2𝑎𝑦
= (15420.928 − 675.012)/19.64 = 14745.916/19.64 = 750.81 𝑚 [4]
(iii) The range of the projectile
4
(𝑣𝑥 +𝑢𝑥 )𝑡 2𝑣𝑥 𝑡
𝑆𝑥 = = = 𝑣𝑥 𝑡 = 15(10) = 150 𝑚 [3]
2 2
(iv) x-component of the acceleration = 0 m/s2 due to constant velocity [2]
(b) A projectile is fired upward (vertically). It takes 30 seconds to come back to its
starting point. Calculate:
(i) The maximum possible height reached:
Time taken to go up is 30/2= 15 s; 𝑣𝑦 = 𝑢𝑦 + 𝑎𝑦 𝑡 => 0 = 𝑢𝑦 − 9.82(15)
𝑢𝑦 = 9.82(15) =
(𝑣+𝑢)𝑡 (0+𝑢)15 15𝑢 9.82(15)(15)
𝑆𝑦 = = = = = [4]
2 2 2 2
(ii) The initial velocity
𝑢𝑦 = 9.82(15) = [3]
(iii) The velocity halfway upwards
𝑢𝑦 9.82(15)
𝑣= = = [3]
2 2
(iv) Give one reason why in practice the time of ascent may be different from time
of descent in projectile motions: Air resistance [2]
5
Page 1 of 2
The Copperbelt University (CBU)
School of Mathematics and Natural Sciences
PH 110 Test 1 – Deferred September 2020 Online
Name: __________________________ Id Number:_____________
Group: ______________________________
Use gravitational acceleration g = 9.82 m/s2 where not specified.
ANSWER ALL QUESTIONS
1. In a freefall vertical motion where the time of ascent is equal to the time of descent, use
equations to show that the initial velocity at firing upwards is equal to the final velocity at
landing. [10 marks]
2. Explain why your weight may be different when you are in Kitwe compared to when you are
in Gwembe valley even when your mass is the same. [10 marks]
3. Explain with the use of equations why a pistol fired from the clouds 10 km away is capable
of killing a person on the ground compared to when it is fired horizontally over same
distance. [10 marks]
4. A 1000 kg elevator is rising and its speed is increasing at 8 m/s2. Calculate the tension of the
cable holding the elevator [10]
5. Two blocks, weighing 350 N and 250 N, respectively, are connected by a string that passes
over a massless pulley as shown. Calculate the tension in the string and explain why the
tension on the left is not greater than the tension on the right side. [10 marks]
Page 2 of 2
⃗⃗ has magnitude 12 N and 𝑩
6. In the diagram, 𝑨 ⃗⃗ has magnitude 8 N. Calculate the x component
⃗⃗ + 𝑩
of 𝑨 ⃗⃗ [15 marks]
7. A projectile is fired at an angle of 65 degrees to the horizontal with initial velocity of 100
m/s. Find:
i. Time of ascent [5 marks]
ii. Time of flight [5 marks]
iii. Maximum height reached [5 marks]
iv. Range [5 marks]
v. Maximum possible range [5 marks]
8. Find the center of mass of a system of particles in the Cartesian coordinates for Mass (x, y, z)
as follows: 10 kg (-2, 4, 2), 5 kg (6, 8, 2), and 15 kg (0, -7, 2). [10 marks]
`````` COVID19 IS REAL `````` STAY SAFE```` THE END ``````````````````
THE COPPERBELT UNIVERSITY
PHYSICS DEPARTMENT
TEST 1 – AUGUST 2020
PH 110 – INTRODUCTORY PHYSICS
TIME: 2 HOURS MAX MARKS: 100
ATTEMPT ALL QUESTIONS. ALL QUESTIONS CARRY EQUAL MARKS.
CLEARLY INDICATED YOUR STUDENT IDENTIFICATION NUMBER AND
LECTURE GROUP ON THE FRONT COVER OF THE ANSWER BOOKLET
You may use the following information:
Acceleration due to gravity, g = 9.8 m/s2
1
Q1. (a) A car travels 1 km between two stops. It starts from rest and accelerates at 2.5 m/s 2 until
it attains a velocity of 12.5 m/s. The car continues at this velocity for some time and
decelerates at 3 m/s2 until it stops. Calculate the total time for the journey. [10 marks]
(b) A crate slides from rest and accelerates uniformly at 4.9 m/s2 along a frictionless roof 3 m
long which is inclined at an angle of 30o to the horizontal as indicated in the Figure
below. Determine:
(i) the velocity of the crate just after losing contact with the roof,
(ii) the velocity (magnitude and direction) of the crate just before it hits the ground,
(iii) the time the crate takes to hit the ground after losing contact with the roof, and
(iv) the horizontal distance between the point directly below the roof and the landing
Point (i.e. the range). [15 marks]
Q2. (a) A block of weight W = 200 N is supported by a uniform beam of weight 140 N as shown
in the Figure below. If L1 = 1.1 m and L2 = 1.4 m, find the tension in the wire and the
vertical and horizontal components of the force exerted by the hinge on the beam.
[10 marks]
2
(b) (i) Give two conditions required for an object to be static equilibrium. [4
marks]
(ii) Two objects with masses m1 = 10 kg and m2 = 5 kg are connected by a light string
that passes over a frictionless pulley as shown in the Figure below. If, when the
system starts from rest, m2 falls 1 m in 1.2 seconds, determine the coefficient of
kinetic friction between m1 and the table. [11 marks]
Q3. (a) The magnitude and directions of three vectors ⃗, ⃗⃗ and ⃗ are as shown in the Figure
below. Find the magnitude and direction of a fourth vector ⃗⃗ which when added to these
three vectors will give a resultant of zero. [12
marks]
(b) Two people pull as hard as they can on ropes attached to a 200 kg object. If they pull in
the same direction the object accelerates at 1.52 m/s2 to the right. If they pull in opposite
directions the object accelerates at 0.518 m/s2 to the left. Ignoring any other forces, what
is the force exerted by each person on the object? [9 marks]
3
(c) If ⃗ and ⃗⃗ are nonzero vectors, is it possible for ⃗ ⃗⃗ and ⃗ ⃗⃗ both to be zero?
Explain.
[4 marks]
Q4. (a) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1
foot. How many gallons are in 1 acre-foot? [5 marks]
(b) You are using water to dilute small amounts of chemicals in the laboratory, drop by drop.
How many drops of water are in a 1.0-L bottle? [9 marks]
(c) (i) State the principle of homogeneity. [2 marks]
(ii) The wavelength associated with a moving particle depends on its mass m,
velocity v and Planck’s constant h which is measured in kgm2s-1. Show
dimensionally, that
[9 marks]
4
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THE COPPERBELT UNIVERSITY
SCHOOL OF MATHEMATICS AND NATURAL SCIENCES
DEPARTMENT OF PHYSICS
SESSIONAL EXAMINATION 2015/2016 ACADEMIC YEAR
PH 110
PHYSICS
INSTRUCTIONS:
There are SEVEN (7) questions in this examination paper, answer any five questions of your
choice, all questions carry equal marks.
Write the following on the front page of your answer booklet:
Student Identification Number (SIN)
Your Group (For Non Quota) or Programme of Study (For students from the School of
Natural Resources).
Marks are shown in the square brackets. Ma
DURATION: Three (3) Hours Maximum marks = 100
CONSTANTS:
1. Acceleration due to gravity g = 9.81 m.s-2
2. Electrostatic constant k = 9 x 109 N.m2/C2
SOME USEFUL FORMULA
L Mm qq xf
R , Fg G 1 2 2 , F k 1 2 2 , W F r F r cos , W Fx dx
A r r xi
Where necessary, use:
1.0 inch =2.54 cm, 1.609 km = 1.0 miles, 7.48 gallons =0.0283 m3, 1.0 cm3=1.0 ml,
746 W = 1.0 horsepower, 1000 kg = 1.0 tones.
QUESTION ONE
(a) The mass of the parasitic wasp can be as small as 5 x 10-6 kg. What is this mass in
(i) grams (g) (ii) milligrams (mg) (iii) micrograms ( g) [6]
a
(b) In the gas equation p 2 v b RT , where p is the pressure, v is the volume, R is the
v
universal gas constant and T is the temperature, what are the dimensions of a and b? [6]
(c) Suppose that two quantities G and F have different dimensions. Determine which of the
following operations could be physically meaningful:
(i) G F (ii) G / F (iii) F G (iv) GF [2]
(d) The square of the speed of an object undergoing a uniform acceleration a is some function of
a and the displacement s , according to the expression given by:
v 2 ka x s y
where k is a dimensionless constant. Show by dimensional analysis that this expression is
satisfied only if x y 1 . [6]
QUESTION TWO
(a) Find the vector sum of the following four displacements on a map or a graph paper, 60mm
north, 30 mm west, 40 mm at 600 west of north, and 50 mm at 300 west of south. [4]
(b) If and mm, find
(i) [2]
(ii) [2]
(iii) Find vector C , such that [3]
(c) Two vectors are given by A 4i j 3k and B 3 i 2 j 3 k .
(i) Define the dot (scalar) product of two vectors. [1]
(ii) Let the dot (scalar) product between A and B be vector D . Find the dot (scalar)
product D and the angle between vectors A and B [2,2]
(d) Let and , find:
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 2
(i) the vector product [2]
(ii) the magnitude of [2]
QUESTION THREE
(a) A projectile is launched from ground level to the top of a 155 m high cliff which is 195 m
away as shown in the Figure 1. If the projectile lands on top of the cliff 7.6 s later after it
was fired, find the magnitude and direction of the initial velocity of the projectile. Ignore air
resistance. [7]
Figure 1
(b) A car travelling at a constant speed of 70 kmh-1 passes a stationary police car. The police car
immediately gives chase, accelerating uniformly to reach a speed of 85 kmh-1 in 10 s and
continues at this speed until it overtakes the other car. Find:
(i) The time taken by the police to catch up with the car. [7]
(ii) The distance travelled by the police car when this happens. [2]
(c) Ball A falls freely from the top of a 80 m high tower and ball B is thrown from the ground
vertically upward at the same time as shown in figure 2. If the balls collide after 2s, find the
initial velocity of object B. [4]
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 3
Figure 2
QUESTION FOUR
(a) On planet X, an object weighs 10 N. On planet B, where the acceleration due to gravity is
1.6g, the object weighs 27 N. What is the mass of the object and what is the acceleration due
gravity (in m/s2) on planet X? Comment on the result. [2, 2, 2]
(b) A rifle bullet with a mass of 12 g and travelling with a speed of 400 m/s, strikes a large
wooden block, which it penetrates to a depth of 15 cm. Determine the magnitude of the
frictional force (assumed constant) that acts on the bullet. Explain your answers.
[2, 2, 2]
(c) A block moves up a 45⁰ incline with constant speed under the action of a force of 15 N
applied parallel to the incline.
(i) Show the forces acting on the block. [2]
(ii) If the coefficient of kinetic friction is 0.3, determine the weight of the block.
[6]
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 4
QUESTION FIVE
(a) The momentum of a 1250 kg car is equal to the momentum of 5000 kg truck travelling at a
speed of 10 km/s. What is the speed of the car? [2]
(b) An estimated force-time curve for a hockey puck struck by a bat is shown in figure 3. From
this curve, do the following:
Figure 3
(i) Determine the impulse delivered to the puck [3]
(ii) Find the average force exerted on the puck [3]
(iii) What is the peak force exerted on the puck and comment as to its duration? [2]
(c) A 75 kg ice skater moving at 10 m/s crashes into a stationary skater of equal mass. After the
collision, two skaters move as a unit at 5 m/s. The average force that the skater can experience
without breaking a bone is 4.5 kN. If the impulse time is 0.01 s, does a bone break?. Your
reasoning should be supported by calculations. [10]
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 5
QUESTION SIX
(a) An elevator cab of mass 500 kg is descending with a speed of vi 4.0m / s when its
supporting cable begins to slip, allowing it to fall with a constant acceleration a g / 5
(i) During the fall through a distance d of 10 m, what is the work W g done on the cab by
the gravitational force Fg . [2]
(ii) During the 10 m fall, what is the work WT done on the cab by the upward tension T
due to the elevator’s cable?. [2]
(iii) What is the net work Wnet done on the cab during the fall?. [2]
(iv) What is the cab’s kinetic energy at the end of the 10m fall?. [2]
(b) A force of F (6x 2 N )iˆ (4N ) ˆj acts on a particle that moves from coordinates (2 ,2) m to
(3,4) m changing only the kinetic energy of the particle.
(i) How much work is done on the particle as it moves from coordinates (2 ,2) m to (3,4)
m ?. [4]
(ii) Does the speed of the particle increase, decrease or remain the same? Give a reason for
your answer. [2]
(c) Consider a machine for which an applied force moves 3.5 m to raise a load by 9 cm. Find
(i) IMA [2]
(ii) AMA if the efficiency is 75%. [2]
(iii) What load can be lifted by an applied force of 60 N if the efficiency is 75% [2]
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 6
QUESTION SEVEN
(a) State Ohm’s law [1]
(b) Define the resistivity of a wire [2]
(c) A battery of EMF 1.5 volts and internal resistance of 0.2 ohms, is connected to a set of
two resistors 2 ohms and 3 ohms. Calculate the current in the circuit when
(i) the resistors of 2 are connected in series [2]
(ii) the resistors of 2 are connected in parallel [3]
(d) A test charge Q = + 2µC is placed halfway between a charge Q1 = + 6 µC and a charge
Q2 = + 4 µC, which are 10 cm apart. Find the force on the charge Q. [4]
(e) A metal rod is 3 m long and 6 mm in diameter. Compute its resistance if the resistivity of the
metal is 1.86x10-8 [4]
(f) In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.25x
10-11 m with a speed of 2.195 x 106 m.s-1. Determine its frequency ‘f ’ and the current ‘ I ’in
the orbit. [4]
GOOD LUCK
PH 110, SESSIONAL EXAMINATION, 2015 /2016 ACADEMIC YEAR
Page 7
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