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Resultants and
Components of Forces
Question Paper 4
Level
A Level
Subject
Maths
Exam Board
OCR
Module
Mechanics 1
Topic
Force as a Vector
Sub Topic
Resultants and Components of Forces
Booklet
Question Paper - 4
Time Allowed:
58 minutes
Score:
/48
Percentage:
/100
Grade Boundaries:
A*
>85%
A
77.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
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1
3x N
xN
Two perpendicular forces have magnitudes x N and 3x N (see diagram). Their resultant has magnitude
6 N.
(i) Calculate x.
[3]
(ii) Find the angle the resultant makes with the smaller force.
[3]
2
12 N
9N
150°
5N
Three horizontal forces of magnitudes 12 N, 5 N, and 9 N act along bearings 000◦ , 150◦ and 270◦
respectively (see diagram).
(i) Show that the component of the resultant of the three forces along bearing 270◦ has
magnitude 6.5 N.
[2]
(ii) Find the component of the resultant of the three forces along bearing 000◦ .
[2]
(iii) Hence f nd the magnitude and bearing of the resultant of the three forces.
[5]
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3
4
Two perpendicular forces have magnitudes 8 N and 15 N. Calculate the magnitude of the resultant
force, and the angle which the resultant makes with the larger force.
[4]
A
B
q
5N
R
7N
A small smooth ring R of weight 7 N is threaded on a light inextensible string. The ends of the string
are attached to fixed points A and B at the same horizontal level. A horizontal force of magnitude 5 N
is applied to R. The string is taut. In the equilibrium position the angle ARB is a right angle, and the
portion of the string attached to B makes an angle θ with the horizontal (see diagram).
(i) Explain why the tension T N is the same in each part of the string.
[1]
(ii) By resolving horizontally and vertically for the forces acting on R, form two simultaneous
equations in T cos θ and T sin θ .
[4]
(iii) Hence find T and θ .
[6]
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5
Two forces of magnitudes 8 N and 12 N act at a point O.
(i) Given that the two forces are perpendicular to each other, find
(a) the angle between the resultant and the 12 N force,
[2]
(b) the magnitude of the resultant.
[2]
(ii) It is given instead that the resultant of the two forces has magnitude R N and acts in a direction
perpendicular to the 8 N force (see diagram).
1
51
2
1
(a) Calculate the angle between the resultant and the 12 N force.
[3]
(b) Find R.
[2]
6
10 N
6N
110°
P
Twoforcesofmagnitudes6Nand10Nseparatedbyanangleof110°actonaparticleP,whichrestsona
horizontalsurface(seediagram).
(i) F
indthemagnitudeoftheresultantofthe6Nand10Nforces,andtheanglebetweentheresultantand
the10Nforce.
[6]
Thetwoforcesactinthesameverticalplane.TheparticlePhasweight20Nandrestsinequilibriumonthe
surface.Giventhatthesurfaceissmooth,find
(ii) themagnitudeoftheforceexertedonPbythesurface,
[1]
(iii) theanglebetweenthesurfaceandthe10Nforce.
[2]