This document contains answers to questions from a student workbook on forces and equilibrium. It provides the answers to multiple choice and free response questions on topics like vectors, forces between objects, resultant forces, moments, levers, gears, center of mass, and the resolution and parallelogram of forces. The answers include diagrams, explanations, and numerical values as needed.

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This resource sheet may have been changed from the original. 1
P8 Forces in balance
Student Book answers
P8.1 Vectors and scalars
Question
number
Answer Marks Guidance
1 a size of quantity 1
1 b scalar has magnitude only, vector has direction too 1
2 between 20 and 21 km 1
3
scale diagram with ratio B : A = 1.25 : 1 (=
15 N
12 N )
therefore arrow for B is 1.25 times the length of the arrow for A
1
1
4 a depends on 48 N arrow length: e.g., 60 mm arrow → scale 10 mm ≡ 8.0
N
1
4 b
ratio B : A = 0.75 : 1 (=
36 N
48 N ), arrow for B points downwards from
object along dashed line, arrow ∴ 0.75 times length of arrow for A
1

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P8 Forces in balance
Student Book answers
P8.2 Forces between objects
Question
number
Answer Marks Guidance
1 a decelerates 1
1 b force equal and opposite to force road exerts on each tyre 1
2 a 50 N upwards 1
2 b 200 N 1
3 a forces equal in magnitude to each other and opposite in direction
because book presses on table and table exerts equal and opposite
force on book
1
1
3 b forces vertically downwards but force of table on floor > force of book on
floor
because floor supports weight of table and book, table only supports
book
1
1
4 a 500 N downwards 1
4 b 500 N upwards 1
4 c 500 N upwards 1

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P8 Forces in balance
Student Book answers
P8.3 Resultant forces
Question
number
Answer Marks Guidance
1 glider makes contact with track and stops moving along it, friction
between glider and track no longer absent when glider makes contact
with track so glider stops because friction opposes its motion
2
2 a opposite in direction to velocity 1
2 b zero 1
3 a force of mud on car > force on car from tractor 1
3 b 300 N 1
4 a weight vector downward vertical arrow with non-arrow end on car mid-
way between wheels
1
4 b support force vectors upward and vertical from point of contact of each
wheel on road
1

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P8 Forces in balance
Student Book answers
P8.4 Moments at work
Question
number
Answer Marks Guidance
1 a i increased 1
1 a ii unchanged 1
1 a iii reduced to a quarter 1
1 b 18
N m
1
1
2 a anticlockwise 1
2 b i increased 1
2 b ii decreased 1
3 a moment of applied force about pivot is greater the longer the handle, so
greater force exerted on nail
1
3 b rust on hinge increases frictional forces in hinge,
so greater moment so more force must be applied to door to overcome
moment of frictional forces at hinge
1
1
4 72 N 1

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P8 Forces in balance
Student Book answers
P8.5 More about levers and gears
Question
number
Answer Marks Guidance
1 force applied to each handle of T bar acts at much greater distance
from axis of T bar than force of nut on T bar so force applied to nut
much > force applied to T bar,
as moment of forces applied to T bar must least = moment of nut on T
bar to turn nut
1
1
2 120 N 1
3 uphill, climb force of wheel on road > on flat road,
turning effect of chain on gear wheel opposed by turning effect of
frictional force of road on wheel,
if use larger gear wheel, turning effect of force of chain on gear wheel
increases so force of wheel on road increases
1
1
1
4 forces and fulcrum shown correctly,
correct direction of each force,
line of action of applied force 8 times further from line of action of cable
force
1
1
1

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P8 Forces in balance
Student Book answers
P8.6 Centre of mass
Question
number
Answer Marks Guidance
1 a centre of mass is where two diagonal lines from corners cross 1
1 b centre of mass found by drawing two diametric lines at right angles,
centre of mass is where the two lines cross
1
1 c centre of mass is where two diagonal lines from corners cross 1
2 centre of mass of child then directly below midpoint M of points of
suspension of swing,
at this position, moment of child about M = 0
1
1
3 make hole in one corner of card and suspend from rod
use plumb line to draw vertical line on card from rod
repeat, hanging card from different corner
point where two lines meet is centre of mass
1
1
1
1
4 in a resultant force = 0 because basket at rest,
b magnitude of resultant force is non-zero and acts towards wall in
direction perpendicular to line between centre of mass and point of
suspension
1
1

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P8 Forces in balance
Student Book answers
P8.7 Moments and equilibrium
Question
number
Answer Marks Guidance
1 a i 3.0 N 1
1 a ii 1.2 N 1
1 b in both examples line of action of effort at greater perpendicular
distance from pivot than corresponding distance for load,
smaller effort ∴ gives equal and opposite moment about pivot to load’s
moment
1
1
2 a Dawn 1
2 b 340 N, 1.84 m 1
2 c
Dawn needs to move 0.5 ×
450
340 = 0.66 m towards pivot,
Dawn’s distance from pivot = 1.84 m
1
1
3 1.5 N 1
4 20 N 1

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P8 Forces in balance
Student Book answers
P8.8 The parallelogram of forces
Question
number
Answer Marks Guidance
1 Figure 6: 50 N vertically upwards
Figure 7: 500 N up the slope
1
1
2 a 5.0 N at 37° to 4.0 N force 2
2 b 6.1 N at 26° to 4.0 N force 2
2 c 6.5 N at 28° to 4.0 N force 2
3 5400 N (to 2 s.f.) correct diagram
correct answer
1
1
4 a diagram shows vertical line intersected at same point P by 2 upward
straight lines at 70° to vertical line
1
4 b i weight vector as downward vertical arrow from P, scale shown and
arrow labelled ‘weight’
1
4 b ii resultant of two tension arrows is equal and opposite to weight vector,
resultant arrow ∴ vertically upwards from P and same length as weight
arrow,
completing parallelogram of forces gives length of the two tension
arrows,
using scale should then give 2.9 N for each tension
1
1
1

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P8 Forces in balance
Student Book answers
P8.9 Resolution of forces
Question
number
Answer Marks Guidance
1 690 N correct diagram
correct answer
1
1
2 a 130 N (to 2 s.f.) correct diagram
correct answer
1
1
2 b friction on bearings of trolley wheels makes trolley harder to push or
force exerted by student may not be parallel to slope
1
3 not enough friction on ladder at floor
so weight pulls ladder down
1
1
4 a correct diagram
with parallel component = 25 N,
perpendicular component = 43 N
1
1
1
4 b friction on box equal and opposite to parallel component of weight
(25 N)
1