1. A skydiver of mass 80 kg falls vertically with a constant speed of

Exam Review: Topic 02 – Mechanics
Practice Test: 40 marks (54 minutes)
Additional Problem: 31 marks (45 minutes)
1.
Reagan IB Physics
A skydiver of mass 80 kg falls vertically with a constant speed of 50 m s–1. The upward force
acting on the skydiver is approximately
A. 0 N.
B. 80 N.
C. 800 N.
D. 4000 N.
(Total 1 mark)
2.
A brother and sister take the same time to run up a set of steps. The sister has a greater mass
than her brother. Which of the following is correct?
A.
B.
C.
D.
Has done the most work
brother
brother
sister
sister
Has developed the greatest power
brother
sister
brother
sister
(Total 1 mark)
3.
A nuclear power station produces 10 GW of electrical power. The power generated by the
nuclear reactions in the core of the reactor is 25 GW. The efficiency of the power station is
A. 15 %.
B. 35 %.
C. 40 %.
D. 60 %.
4.
A cyclist rides around a circular track at a uniform speed. Which of the following correctly
gives the net horizontal force on the cyclist at any given instant of time?
(Total 1 mark)
A.
B.
C.
D.
Net horizontal force along
direction of motion
zero
zero
non zero
non zero
Net horizontal force normal to
direction of motion
zero
non zero
zero
non zero
(Total 1 mark)
5.
The graph shows how the displacement d of an object varies with time t. The tangent to the
curve at time t1 is also shown.
Which of the following gives the speed of the object at point P?
A.
the gradient at P
C.
B.
the shaded area
D.
1
gradient at P
d1
t1
(Total 1 mark)
1/8
Exam Review: Topic 02 – Mechanics
6.
Reagan IB Physics
Which of the following is the condition for a body to be in translational equilibrium?
A.
The resultant force on the body in any direction is zero.
B.
The velocity of the body in any direction is zero.
C.
No external force is acting on the body.
D.
No work is done on the body.
(Total 1 mark)
7.
A particle P is moving anti-clockwise with constant speed in a horizontal circle.
Which diagram correctly shows the direction of the velocity v and acceleration a of the particle
P in the position shown?
(Total 1 mark)
8.
A ball moves along the inside of a horizontal semi-circular ring as shown. The diagram is a
view from above.
Which arrow represents the direction of the average force on the ball?
2/8
Exam Review: Topic 02 – Mechanics
9.
Reagan IB Physics
(Total 1 mark)
A raindrop falling from rest at time t = 0 reaches terminal velocity. Which graph best represents
how the speed v varies with time t?
(Total 1 mark)
10.
A lamp of weight W is suspended by a wire fixed to the ceiling. With reference to Newton’s
third law of motion, the force that is equal and opposite to W is the
A.
tension in the wire.
B.
force applied by the ceiling.
C.
force exerted by the lamp on the Earth.
D.
force exerted by the Earth on the lamp.
11.
Mandy stands on a weighing scale inside a lift (elevator) that accelerates vertically upwards as
shown in the diagram below. The forces on Mandy are her weight W and the reaction force
from the scale R.
(Total 1 mark)
The reading of the scale is
A.
R + W.
B.
W.
C.
R.
D.
R – W.
(Total 1 mark)
12.
A general expression for Newton’s second law of motion is
Δp
F=
.
Δt
What condition is applied so that the law may be expressed in the form F = ma?
A.
The mass m is constant.
B.
The acceleration a is constant.
C.
The force F is constant.
D.
The direction of the force F is constant.
(Total 1 mark)
3/8
Exam Review: Topic 02 – Mechanics
13.
Reagan IB Physics
In 1997 a high-speed car of mass 1.1 × 104 kg achieved the world land speed record. The car
accelerated uniformly in two stages as shown in the table. The car started from rest.
Stage 1
Stage 2
Time / s
0.0 – 4.0
4.0 – 12
Speed attained at end of stage / m s–1
44
280
Use the data to calculate the
(a)
average acceleration of the car in stage 1.
......................................................................................................................................
(1)
(b)
average net force required to accelerate the car in stage 2.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(c)
total distance travelled by the car in 12 s.
......................................................................................................................................
......................................................................................................................................
(2)
(Total 6 marks)
14.
A ball of mass 0.25 kg is attached to a string and is made to rotate with constant speed v along a
horizontal circle of radius r = 0.33 m. The string is attached to the ceiling and makes an angle
of 30° with the vertical.
(a)
(i)
On the diagram above, draw and label arrows to represent the forces on the ball in
the position shown.
(ii)
State and explain whether the ball is in equilibrium.
(2)
...........................................................................................................................
(2)
(b)
Determine the speed of rotation of the ball.
......................................................................................................................................
......................................................................................................................................
(3)
(Total 7 marks)
4/8
Exam Review: Topic 02 – Mechanics
15.
Reagan IB Physics
This question is about momentum, energy and power.
(a)
In his Principia Mathematica Newton expressed his third law of motion as “to every
action there is always opposed an equal reaction”. State what Newton meant by this law.
......................................................................................................................................
(1)
(b)
A book is released from rest and falls towards the surface of Earth. Discuss how the
conservation of momentum applies to the Earth-book system.
......................................................................................................................................
......................................................................................................................................
(3)
(c)
A large swinging ball is used to drive a horizontal iron spike into a vertical wall. The
centre of the ball falls through a vertical height of 1.6 m before striking the spike in the
position shown.
The mass of the ball is 3.5 kg and the mass of the spike is 0.80 kg. Immediately after
striking the spike, the ball and spike move together. Show that the
(i)
speed of the ball on striking the spike is 5.6 m s–1.
...........................................................................................................................
(1)
(ii)
energy dissipated as a result of the collision is about 10 J.
...........................................................................................................................
...........................................................................................................................
(4)
(d)
As a result of the ball striking the spike, the spike is driven a distance 7.3 × 10–2 m into
the wall. Calculate, assuming it to be constant, the friction force F between the spike and
wall.
......................................................................................................................................
......................................................................................................................................
(3)
(e)
The machine that is used to raise the ball has a useful power output of 18 W. Calculate
how long it takes for the machine to raise the ball through a height of 1.6 m.
......................................................................................................................................
(3)
(Total 15 marks)
5/8
Exam Review: Topic 02 – Mechanics
Reagan IB Physics
Additional Problems
16.
The graph shows the variation with force F of the extension s
of a spring.
The work done in changing the extension of the spring from
3.0 cm to 6.0 cm is
A.
15 N cm.
B.
30 N cm.
C.
45 N cm.
D.
60 N cm.
(Total 1 mark)
17.
Stephen pushes two boxes P and Q, that stay in contact, along a rough table, with a force F of
30 N. Box P has a mass of 2.0 kg and box Q has a mass of 4.0 kg. Both boxes move with
constant speed.
The resultant force on box Q is
A. 0 N.
B. 5.0 N.
C.
15 N.
D.
30 N.
(Total 1 mark)
18.
A ball is suspended from a ceiling by a string of length 7.5 m. The ball is kicked horizontally
and rises to a maximum height of 6.0 m.
(a)
Assuming that the air resistance is negligible, show that the initial speed of the ball is
11 m s–1.
......................................................................................................................................
(2)
(b)
The mass of the ball is 0.55 kg and the impact time of the kicker’s foot with the ball is
150 ms. Estimate the average force exerted on the ball by the kick.
......................................................................................................................................
(2)
(c)
(i)
Explain why the tension in the string increases immediately after the ball is kicked.
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
Calculate the tension in the string immediately after the ball is kicked. Assume that
the string is vertical.
...........................................................................................................................
...........................................................................................................................
(3)
(Total 10 marks)
6/8
Exam Review: Topic 02 – Mechanics
19.
Reagan IB Physics
This question is about circular motion and global warming.
(a)
A car is travelling at constant speed of 18 m s–1 around a horizontal bend in the road.
The mass of the car is 1.5 × 103 kg and the bend forms part of a circle of radius
2.0 × 103 m.
(i)
State why the car is accelerating.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
Determine the frictional force between the tyres of the car and the surface of the
road that produces the acceleration.
...........................................................................................................................
...........................................................................................................................
(2)
(b)
It is suggested that the use of fossil fuels to power cars has led to an enhancement of the
greenhouse effect.
(i)
State the reason for this suggestion.
...........................................................................................................................
(1)
(ii)
Outline one mechanism by which the enhanced greenhouse effect may lead to an
increase in global warming.
...........................................................................................................................
...........................................................................................................................
(3)
(Total 7 marks)
20.
This question is about force and energies.
(a)
A system consists of a bicycle and cyclist travelling at a constant velocity along a
horizontal road.
(i)
State the value of the net force acting on the cyclist.
...........................................................................................................................
(1)
7/8
Exam Review: Topic 02 – Mechanics
(ii)
Reagan IB Physics
On the diagram draw labelled arrows to represent the vertical forces acting on the
bicycle.
(2)
(iii)
With reference to the horizontal forces acting on the system, explain why the
system is travelling at constant velocity.
...........................................................................................................................
...........................................................................................................................
(2)
(b)
The total resistive force acting on the system is 40 N and its speed is 8.0 m s–1. Calculate
the useful power output of the cyclist.
......................................................................................................................................
(1)
(c)
The cyclist stops pedalling and the system comes to rest. The total mass of the system is
70 kg.
(i)
Calculate the magnitude of the initial acceleration of the system.
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Estimate the distance taken by the system to come to rest from the time the cyclist
stops pedalling.
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
State and explain one reason why your answer to (c)(ii) is only an estimate.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 12 marks)
8/8
Exam Review: Topic 02 – Mechanics
Reagan IB Physics
Mark Scheme
1.
C
3.
C
5.
A
7.
C
9.
B
11.
C
2.
D
4.
B
6.
A
8.
B
10.
C
12.
A
13.
(a)
11 m s–2;
(b)
∆v = 236;
⎛ 236 ⎞
= ⎟ 29.5(m s–2);
a = ⎜
8
⎝
⎠
(F = 1.1 × 104 × 29.5) = 3.2 × 105N;
Award [2 max] for omission of initial speed (answer is 390 kN).
(c)
phase 1 distance 88 m / phase 2 distance 1296 m;
total 1400 m;
Watch for significant figure penalty in this question (1384 m).
1
Award [1 max] for at2 substituted correctly for first phase, if
2
no distances evaluated and answer incorrect.
Award [1 max] for correct addition of incorrect phase 1 and/or 2 distance(s).
1
3
2
[6]
14.
(a)
(i)
[1] each for correct arrow and (any reasonable) labelling;
2
Award [1 max] for arrows in correct direction but not
starting at the ball.
(ii)
(b)
no;
because the two forces on the ball can never cancel out /
there is a net force on the ball / the ball moves in a circle /
the ball has acceleration/it is changing direction;
Award [0] for correct answer with no or wrong argument.
2
mg ⎞
⎛
T ⎜ =
⎟ = 2.832 N;
⎝ cos 30° ⎠
mv 2
= T sin 30°;
r
⎛ Tr sin 30°
2.832 × 0.33 × sin 30° ⎞⎟
v = ⎜
= 1.4 m s–1;
=
⎜
⎟
m
0
.
25
⎝
⎠
or
T cos 30° =mg;
T sin 30° = mg;
9/8
Exam Review: Topic 02 – Mechanics
Reagan IB Physics
2
mv
;
r
v = ( gr tan 30° = 9.81× 0.33 × tan 30° ) = 1.4 m s–1;
T sin 30° =
3
[7]
15.
(a)
(b)
(c)
when a force acts on a body an equal and opposite force acts
on another body / in the interaction between two bodies A
and B, the force that A exerts on B is equal and opposite to
the force that B exerts on A;
1
forces on Earth and book are equal and opposite / no external
force acts on the system;
changes in momentum of Earth and book are equal and opposite /
net force on Earth-book system is zero;
hence momentum of Earth-book system stays the same/is always
zero and so is conserved;
3
(i)
(ii)
(d)
2 × 9.8 × 1.6 ;
= 5.6 m s–1
v=
calculation of speed of ball and spike 3.5 × 5.6 = 4.3V;
⎛ 3.5 × 5.6 ⎞
V = ⎜
= ⎟ 4.6 m s–1;
⎝ 4.3
⎠
1
1
KE before = [3.5 × 5.62] KE after = [4.3 × 4.562];
2
2
energy dissipated = 54.88 – 44.70 ;
= 10 J
Accept 9.4 J if 4.6 used for V.
ΔKE
;
s
∆KE = 0.50 × 4.3 × 4.62 = 45 (J);
45
⎛
⎞
= ⎟ 6.2 × 102 N;
F = ⎜
−2
⎝ 7.3 × 10
⎠
1
4
F=
3
or
v2
;
2s
a = 1.45 × 102 m s–2;
F = ma = 4.3 × 1.45 × 102 = 6.2 × 102 N;
a=
(e)
work
;
power
work = (3.5 × 1.6 × 9.8 =) 55(J);
⎛ 55 ⎞
= ⎟ 3.1s;
time = ⎜
⎝ 18 ⎠
time =
3
[15]
10/8
Exam Review: Topic 02 – Mechanics
Reagan IB Physics
Additional Problems
16.
C
17.
A
18.
(a)
attempt to equate gpe and ke;
v = 9.8 × 6.0 × 2 ;
2
–1
11 m s
Award [0] for use of v2 = 2as. Allow use of g = 10 N kg1
(b)
(c)
mΔv
;
Δt
40 N ;
F=
(i)
(ii)
2
ball accelerates towards centre of circular path / OWTTE;
therefore force towards centre / upwards;
that adds to tension;
3
⎛ mv 2 0.55 × 112 ⎞
F = ⎜⎜
=
= ⎟⎟ 8.9 N;
7.5
⎝ r
⎠
weight = (mg = 0.55 × 0.98) = 5.4N;
total = 14N;
Allow use of g = 10 N kg–1.
3
[10]
19.
(a)
(i)
(ii)
(b)
the velocity direction is changing/the friction force between
tyres and road produces a centripetal force on the car;
recognize to use F =
1
mv 2
;
r
⎛ 1.5 × 10 3 × 18 2 ⎞
= ⎜⎜
= ⎟⎟ 240 N;
3
2
.
0
×
10
⎝
⎠
2
(i)
releases extra carbon dioxide/greenhouse gases into the atmosphere;
1
(ii)
reduces the ice/snow cover;
this decreases the albedo;
leading to an increase in rate of thermal energy absorption
by the atmosphere;
3
or
increases temperature of the sea;
reduces the solubility of carbon dioxide in the sea;
so increases amount of carbon dioxide in the atmosphere;
To award [3] a description of a mechanism must be present.
Award [2 max] for a description of the enhanced greenhouse effect.
[7]
11/8
Exam Review: Topic 02 – Mechanics
20.
(a)
(i)
Reagan IB Physics
zero;
1
correct position and labelling of
weight/gravity force/mg;
two reactions drawn as shown;
force downwards on pedals;
Ignore any other vertical forces and all horizontal forces.
The total upward vector lengths should approximately
equal the downward vector lengths.
2 max
(ii)
(iii)
drag force = thrust/forward force/driving force;
net force=zero therefore acceleration is zero;
(b)
320W ;
(c)
(i)
(ii)
1
⎡ 40 ⎤
acceleration = ⎢ ⎥
⎣ 70 ⎦
–2
= 0.57 m s ;
use of F∆s =
2
2
1 2
mv ;
2
56m;
2
or
v2 = u2 + 2as equivalent seen and substituted correctly;
56m;
(iii)
sensible physical reason e.g. air resistance / bearing friction/
brakes’ effectiveness varies with speed;
attempt at explanation:
e.g. air resistance drops as speed drops, underestimate /
distance travelled will be further;
2
[12]
12/8