Forces 1 – vectors, resultant forces and work
Task – multiple choice
Answer the following questions.
1. Which of the following situations of forces acting on a ball would cause the ball to move
the greatest distance?
A.
C.
5N
10 N
25 N
35 N
B.
D.
50 N
60 N
10 N
30 N
2. A sprinter pushes back as hard as possible on the starting block at the beginning of a
race. The force that pushes back on the sprinter is …
a. the same.
b. much less because energy is lost.
c. zero as a stationary block cannot produce forces.
d. greater so the sprinter moves forward.
3. The diagram shows four spring balances (K, L, M and N) connected to a knot X. The
strings attached to the spring balances are at 90◦ to each other.
L
spring balance
string
K
M
knot X
N
© www.teachitscience.co.uk 2016
26016
Page 1 of 9
Forces 1 – vectors, resultant forces and work
If knot X is stationary, which set of readings (in newtons) for the four spring balances
K, L, M and N are correct?
K
L
M
N
A
80
80
50
50
B
80
50
80
50
C
80
65
65
80
D
50
65
65
80
4. It is found that when a force of 8 N is applied to a spring, it extends by 14 cm. Two of
these springs are arranged in parallel to each other, as shown in the diagram. A weight of
4 N is added.
4N
What is the overall extension of this parallel arrangement? (Assume that the springs obey
Hooke’s Law.)
A
3.5cm
B
7cm
C
14cm
D
28cm
5. Two forces of 30 N act simultaneously on a body of mass M. Which of the following
arrangements would produce the greatest acceleration of this mass?
30 N
30 N
30 N
30 N
M
M
B
A
30 N
M
30 N
30 N
30 N
D
C
© www.teachitscience.co.uk 2016
M
26016
Page 2 of 9
Forces 1 – vectors, resultant forces and work
6. Two forces F1 and F2 act simultaneously on a body of mass M, as shown in the diagram.
A
B
C
F1
M
D
F2
In which direction A, B, C or D would the body move?
7. Two strings are attached to an object at the same point. They are each capable of
sustaining a tension of 60 N before snapping, and they subtend at an angle of 120◦.
60 N
60 N
120
o
Object
What is the maximum weight of the object these two strings can support?
A
30 N
© www.teachitscience.co.uk 2016
B
60 N
C
26016
90 N
D
120 N
Page 3 of 9
Forces 1 – vectors, resultant forces and work
8. The work done by a force …

is calculated by multiplying the force in newtons by the distance moved in metres.

indicates the amount of energy change.

is measured in joules.
Which of these statements is correct?
A
9.
1 only
B
1 and 2
C
2 and 3
D
1, 2 and 3
A block of wood is pulled along a horizontal bench at a constant speed of 10 m/s by a
force of 7 N. How much work is done in 5 seconds against the frictional force?
10 m/s
wooden
block
7N
bench
A
35 J
B
70 J
C
175 J
D
350 J
10. A climber whose weight is 800 N climbs a vertical distance of 20 metres in 4 minutes.
How much work does he do?
A
3 200 J
© www.teachitscience.co.uk 2016
B
4 000 J
C
26016
16 KJ
D
64 KJ
Page 4 of 9
Forces 1 – vectors, resultant forces and work
11. A trolley of 5 kg is pushed 13 m up a slope to a platform which is 5 m above the ground.
platform
13 m
5m
trolley
How much work has been done? (Assume 1 kg = 10 N)
A
60 J
B
65 J
C
250 J
D
600 J
12. At the recent Olympic Games four weightlifters, of different nationalities, lifted the
following weights above their heads. (Assume 1 kg = 10 N)
Nationality
Weight lifted (kg)
Height lifted (m)
Chinese
1800
2.4
German
1600
2.7
Russian
1400
2.8
French
1650
2.5
Which two weightlifters did the same amount of work?
a. Chinese and German weightlifters
b. Chinese and French weightlifters
c. German and Russian weightlifters
d. Russian and French weightlifters.
13. A barrel is rolled up an incline to a height of 1 metre. Which of these statements is true?
Rolling the barrel …
a. involves less work than lifting the barrel vertically up 1 metre.
b. requires less force than lifting the barrel.
c. involves less energy than lifting the barrel 1 metre.
d. involves less frictional force.
© www.teachitscience.co.uk 2016
26016
Page 5 of 9
Forces 1 – vectors, resultant forces and work
14. A weight is to be lifted from a level X to a higher level Y along different paths labelled L,
M and N.
Y
L
M
N
X
Which of these paths requires the least amount of work?
a. Path L
b. Path M
c. Path N
d. An equal amount of work is done along each path.
15. A bullet had a mass of 10 g and is fired from a high powered rifle at a fixed target which
offers a resistive force of 20 000 N. It was found that the bullet penetrated the target by
1 cm. How far away was the target? (Assume 1 kg = 10 N)
A
500 m
© www.teachitscience.co.uk 2016
B
1 000 m
C
26016
1.5 km
D
2 km
Page 6 of 9
Forces 1 – vectors, resultant forces and work
Answers
1.
Forces
A
B
C
D
Resultant
15 N
5N
10 N
50 N
60 N
10 N
25 N
35 N
10 N
10 N
30 N
20 N
D has the greatest resultant force moving the ball to the left with a force of 20 N.
2. A - Newton’s Third law states that for every action there is an equal but opposite
reaction. Therefore the force from the starting block is the same as the force from the
sprinter.
3. B - For the knot to be stationary forces L and N must be equal and forces K and M must
be equal. This is only true in B.
4. A - When two identical springs are arranged in parallel they share the load equally and
the overall extension is half the extension of a single spring with the same load. For
a 4 N weight a single spring extends by 4 N ÷ 8 N x 14 cm = 7 cm.
Therefore a parallel arrangement extends by 7 cm ÷ 2 = 3.5 cm.
5. A - The greatest acceleration is produced by the arrangement which has the greatest
resultant force on mass M. This is arrangement A where the resultant of the two
forces is 60 N as they are both parallel and in the same direction.
When the angle between the forces is 90◦ (B and C), the resultant is always less
than the sum of the two forces. When the forces are equal and in the opposite
direction (D), they cancel each other out.
6. C - The body will move in the direction which is the resultant of the two forces F1 and
F2. This cannot be B or D as these are in line with forces F1 and F2. However C has a
direction between these two forces so it must be the resultant force.
© www.teachitscience.co.uk 2016
26016
Page 7 of 9
Forces 1 – vectors, resultant forces and work
7. B - The resultant of the two forces shown in the diagram is
= 60 N x cos 60◦ + 60 N x cos 60◦
= 60 N
resultant = 2 x 60 N cos 60 o = 60 N
60 N
60 N
120 o
Object
8. D - the work done by the force is calculated by multiplying the force in newtons by the
distance moved in metres. This is equal to the energy change and is measured in
joules. All three statements are correct.
9. D - in 5 seconds, at a constant speed of 10 m/s, the block of wood is pulled 50 m.
Using the relationship
work done (J) = force (N) x distance (m)
= 7 N x 50 m
= 350 J
10. C - the work done by the climber can be calculated from the weight of the climber and
the vertical distance he has climbed. The time is not relevant in this calculation and
need only be used to find the rate of working (power) of the climber which is not
asked for.
Using the relationship ..
work done (J) = weight (N) x distance (m)
= 800 N x 20 m
= 16 000 J = 16 kJ
11. C - the trolley of mass 5 kg has a weight of 50 N. When it has reached the top of the
platform it has risen 5 m above the ground.
Using the relationship ..
work done (J) = weight (N) x distance (m)
= 50 N x 5 m
= 250 J
© www.teachitscience.co.uk 2016
26016
Page 8 of 9
Forces 1 – vectors, resultant forces and work
12.
Nationality
Amount of work done
Chinese
1 800 N x 2.4 m = 4 320 J
German
1 600 N x 2.7 m = 4 320 J
Russian
1 400 N x 2.8 m = 3 920 J
French
1 650 N x 2.5 m = 4 125 J
A – the Chinese and German weightlifters did the same amount of work.
13. B - rolling a barrel 1 metre up an incline requires the same amount of work as lifting a
barrel 1 metre vertically (eliminates A and C). The force needed to push the
barrel up the incline is less (B) as the force acts over a longer distance, but still
does the same amount of work as lifting a barrel 1 metre vertically.
14. D - work done is calculated from force x distance. No work is done when the weight is
moved horizontally. Equal amounts of work are done along each of the paths as the
weight is lifted to the same height and therefore have the same potential energy.
15. D - work done in joules when the bullet penetrates the target
= resistive force (N) x distance penetrated in metres
= 20 000 N x 0.01 m = 200 J
This must be equal to the work done by the bullet in travelling to the target.
Therefore
200 J = weight of bullet (N) x distance travelled in metres
200 J = 0.1 N x Distance travelled
Distance travelled = 200 ÷ 0.1 = 2 000 m = 2 km
© www.teachitscience.co.uk 2016
26016
Page 9 of 9