Forces & Motion
1. Is it possible for an object to have a negative
velocity and positive acceleration? Explain.
2. State Newton’s First Law.
3. A driver of a car accelerates from rest at 5.5
m/s2 for 2.3 seconds. She then applies the brakes
and decelerates uniformly and stops 4.1 seconds
later. Find the total distance that she travels.
4. An airplane pilot wishes to fly north. There is a
wind from N 30E at 40 km/h. If the plane can
travel 280 km/h in still air, find the heading of the
plane and find how long it would take the plane to
travel 2400 km.
5. When a whale and a seal meet, the whale often
has a little fun with the seal by tossing it in the air
repeatedly. Suppose a whale and a seal meet at the
edge of a 40 metre waterfall. If the whale throws
the 175-kg seal over the edge of the waterfall with
an initial velocity of 3.8 m/s at an angle of 35
above the horizontal, find the maximum height
(above the bottom of the waterfall) that the seal
reaches and how far from the base of the waterfall
the seal lands. You can ignore any effects of air
resistance on the slippery seal.
6. Two neighbouring stars have mass 5m and 3m.
An asteroid of mass m collides with and embeds
into the lighter star. If the stars were originally a
distance r apart, find their new distance apart if the
gravitational force between them remains the same
after this collision.
7. A 350 kg piano begins sliding down a 5-m long
ramp that is inclined at an angle of 20 . If the
coefficient of kinetic friction is 0.45, find the
speed of the piano when it reaches the bottom of
the ramp.
8. Determine the acceleration of the system below
and the tension in the rope where m1  2.0 kg ,
m2  5.2 kg ,   35 and  k  0.3 .
9. A 4.5 kg bowling ball is being swung around in
a vertical circle. You can assume that the mass of
the rope attached to the bowling ball is negligible.
The ball is swinging with constant speed 4.5 m/s.
If the rope is 1.1 m long, determine the tension in
the rope at the top and bottom of the circle. Also,
find by how much the speed can be reduced while
still maintaining circular motion.
10. An object is pushed from rest across a sheet of ice,
accelerating at 5.0 m/s2 over a distance of 80.0 cm. The
object then slides with a constant speed for 4.0 s until it
reaches a rough section which causes it to stop in 2.5 s.
(a) What is the speed of the object when it reaches the
rough section?
(b) At what rate does the object slow down once it
reaches the rough section?
(c) What total distance does the object slide throughout
its entire trip?
11. A football quarterback attempts a pass to one of the
receivers. As the ball is snapped, the receiver leaves the
line of scrimmage and runs directly down field. The
quarterback releases the ball 2.0 s later and from a
position 3.0 m behind the line of scrimmage. He throws
the ball with a speed of 26 m/s at an elevation of
60above the horizontal. The receiver makes a diving
reception, catching the ball just as it reaches the
ground.
(a) What is the time of flight of the football?
(b) What is the average speed of the receiver?
12. A 12.0-kg box is pushed along a horizontal surface
by a 24 N force as illustrated in the diagram. The
frictional force (kinetic) acting on the object is 6.0 N.
(a) What is the acceleration of the object?
(b) Calculate the value of the normal force acting on
the object.
(c) If the 12.0-kg object then runs into a 4.0-kg object
that increases the overall friction by 3.0 N, what is
the new acceleration?
(d) What force does the 4.0-kg object exert on the
12.0-kg object when the two are moving together?
Energy and Momentum
1. What are the units of impulse? Is impulse a
vector or a scalar?
2. A 4.5-kg bowling ball traveling initially at 1.5
m/s [N] strikes a stationary 0.6-kg bowling pin.
After the collision, the ball is moving at 1.3 m/s
[N 8 W]. Find the final velocity of the pin.
3. Mike is standing on the edge of a 4.6-m cliff
over-looking a lake. He throws a 2.5-kg life
preserver upward with a speed of 9.5 m/s. The life
preserver eventually falls into the water. Find the
speed of the life preserver as it hits the surface of
the water.
4. A 1.2-kg ball bearing is placed in a slingshot.
The force constant of the slingshot is 50 N/m.
Find the speed as the ball bearing leaves the
slingshot if the slingshot is pulled back by 28 cm.
The unstretched length of the slingshot is 15 cm
and the maximum that the slingshot can be
stretched before it is damaged is 40 cm.
5. Two balls have a head-on elastic collision.
Initially the 4-kg ball has a velocity of 7.3 m/s [N]
and the 7-kg ball has a velocity of 12 m/s [S].
Find the velocity of each ball after the collision.
6. Two common and identical carts are used to
perform an experiment. Cart A is pushed toward
the stationary
cart B with a velocity of 2.6 m/s. After the
collision, cart A bounces back with a speed of 0.8
m/s and cart B
moves of with a speed of 3.4 m/s. Why is this not
possible? Justify your answer with appropriate
calculations.
7. A 0.40-kg cue ball makes a glancing blow to a
stationary 0.30-kg billiard ball so that the cue ball
deflects with a speed of 1.2 m/s at an angle of
30.0º from its original path. Calculate the original
speed of the cue ball if the billiard ball ends up
travelling at 1.5 m/s.
8. A child swings on a swing so that her centre of
mass is located 2.4 m from the point where the
rope is attached to the tree. If she swings so that
her maximum amplitude causes the rope to make
an angle of 47with the vertical, calculate the
child’s maximum speed during the swing.
9. A bullet with a mass of 45 g is fired into a 8.3kg block of wood resting on a floor against a
spring. This ideal spring (k = 76 N/m) has a
maximum compression of 28 cm. What was the
initial speed of the bullet?
10. In a new, yet much maligned, house league
event, advanced spring compression, you jump
from a height of 3.0 m onto a vertical ideal spring
that has a spring constant of k = 2000 N/m.
a) If your mass is a whopping 80.0 kg, what is the
maximum compression of the spring?
b) How fast would you be going if the spring is
compressed 1.0 m?
11. A 175 g air-track glider is moving with a
velocity of 8.0 m/s on a frictionless track and
collides with an identical stationary glider, which
is attached to a long ideal spring. The gliders
remain attached and compress the spring 15 cm
before coming to a stop.
a) What is the speed of the gliders immediately
after impact?
b) What is the spring constant of the ideal spring?
c) How fast are the masses going when the spring
is compressed 7.5 cm?
12. A 20 g bullet travelling at 450 m/s hits a 9.0 kg
mass that is free to swing on four long ropes (a
ballistics pendulum). The bullet remains
embedded in the mass and swings smoothly to its
maximum height. Ignore any frictional effects.
a) What is the speed of the mass immediately
after impact?
b) To what height above its initial position does it
rise?
13. A box of sand having a mass of 11.9 kg hangs
by a long tight rope. When a bullet of mass 200 g
and moving horizontally strikes the box and
remains buried in it, the box swings until its centre
of gravity is 3.5 m above its initial level. At what
speed is the bullet travelling when it strikes the
box?
Wave Nature of Light
1. An open-top aquarium is made of crown glass.
A ray of light enters the water through the top of
the aquarium and exits through the side of the
aquarium. If the light has an incident angle at the
air-water boundary of 35 , find the angle of
refraction in the glass.
2. Light of 550 nm illuminates two slits that are
5.8  10 6 m apart. Find the distance to the fourth
order maximum if the screen is 1.6 m away.
3. A film of gasoline formed on water is
illuminated by light of wavelength 378 nm. The
refractive indices of the gasoline and water are
1.65 and 1.33 respectively. Find the minimum
thickness of the gasoline that will produce a
maximum.
4. Monochromatic light illuminates a single slit of
width 1.2  10 2 mm. If the first order minimum
occurs at 4 , what is the wavelength of light used?
Furthermore, if the screen is 1.2 m from the slit,
find the distance of the second order maximum
from the middle of the diffraction pattern.
5. Young’s experiment was instrumental in
supporting Huygens’ wave theory of light. Explain
which two conditions Young satisfied in his
experiment that were not adequately done before.
Describe how he achieved these two conditions.
6. The diagram shown below illustrates the
possible paths followed by a light ray as it enters a
lens (n = 1.56) covered with a thin coating (n =
1.25). If the thin coating has a thickness of /4,
what type of interference occurs with rays 3 and 4?
Explain your answer.
7. A two-point source interference pattern is
generated in a swimming pool. A piece of
styrofoam, located on the second nodal line, is
12.0 m from one source and 20.0 m from the other
source. One wave crest takes 2.0 s to travel the
35.0 m width of the pool. Find the speed,
wavelength, and frequency of the waves.
8. Blue light with a wavelength of 475 nm is
passed through a double slit with a separation of
22.6 m. What is the maximum number of nodal
lines visible in the entire pattern?
9. A single-slit interference pattern using blue light
with a wavelength of 438 nm creates a central
maximum that is 6.50 cm wide. If the slit width
used is 17.5 m, how far away is the screen?
10. A picture frame manufacturer wishes to design
picture frames that provide minimal glare from the
glass cover. In order to achieve this, a thin plastic
film (nfilm = 1.35) is placed on the glass surface
(nglass = 1.52). If light reflected in the middle
of the visible spectrum with a wavelength of 550
nm is to be minimized, what film thickness is
required?
11. The thickness of a human hair is to be
measured using the interference pattern produced
by an air wedge. Red light with a wavelength of
638 nm is used on an air wedge that is 25.0 cm
long. If 10 bright fringes are counted across 1.06
cm in the air wedge, what is the thickness of the
hair?
Electric and Magnetic Fields
1. Two point charges, q1  7.5  10 6 C and
q2  5.8  10 6 C , are secured 25 cm apart from
one another. Let point A be the point halfway
between the charges.
a) Find the electric field strength at point A.
b) What force is exerted on a charge of
3.2  10 6 C placed at A?
2. Explain why the magnetic north pole is really a
south pole.
3. What is Oerstad’s principle?
4. An electric motor requires rotation. How is this
rotation achieved? Be sure to include a diagram
and clearly indicate the direction of rotation.
5. A straight wire 15 cm log, with a current of 12
A, lying at right angles to a uniform magnetic
field, experiences a magnetic force of magnitude
0.40 N. What is the magnitude of the magnetic
field?
6. A conductor 45 cm long, with a mass of 15 g,
lies in a horizontal position at 90 angle to a
uniform horizontal magnetic field of magnitude
0.20 T. What must the current in the conductor be
if the magnetic force is to support the weight of
the conductor?
7. Describe as many of the similarities and
differences between electrostatic fields,
gravitational fields and magnetic fields.