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HORIZONTAL PROJECTION
HORIZONTAL PROJECTION
PROJECTION AT AN ANGLE
PROJECTION AT AN ANGLE
RESOLUTION OF FORCES
Situation 4: Two forces acting on an object in directions that are not perpendicular to each other
Method and sample of scaled drawing
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Video of triangle of
forces method

http://bit.ly/2T2joj0

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Table 1.2

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Triangle of forces method Parallelogram of forces method

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(i) Choose a suitable scale to draw lines that (i) Choose a suitable scale to draw lines that
represent the magnitude of the forces. represent the magnitude of the forces.

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(ii) By using a ruler and a protractor, draw the (ii) By using a ruler and a protractor, draw the

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force F1 followed by force F2 to form two force F1 and force F2 from a point to form
sides of a triangle. two adjacent sides of a parallelogram.
F2
IK F2
ID
D

α α
N

F1 F1
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(iii) Complete the triangle. The third side (iii) With the aid of a pair of compasses,
represents the resultant force, F. complete the parallelogram. Draw the
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diagonal from the point of action of the

forces. The diagonal represents the resultant
force, F.
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F
F2 F2
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F
α
F1
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F1

(iv) Measure the length of side F and calculate (iv) Measure the length of the diagonal and
the magnitude of the resultant force using calculate the magnitude of the resultant
the scale you have chosen. force using the scale you have chosen.

(v) Measure the angle, q. (v) Measure the angle, q.

6 LS 1.1.2
 Example 1 I 2

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1 An object of weight W is suspended by two ropes from a beam, as shown in Fig. 1.1.

86.6 N
30°
50.0 N 60°

Fig. 1.1

The tensions in the ropes are 50.0 N and 86.6 N, as shown.

(a) In the space below, draw a scale diagram to find the resultant of the two tensions.

Use a scale of 1.0 cm = 10 N.

Clearly label the resultant. [3]

© UCLES 2010 0625/31/O/N/10

 f
3

(b) From your diagram, find the value of the resultant.

resultant = ......................................................... [1]

(c) State the direction in which the resultant is acting.

............................................................................................................................................. [1]

(d) State the value of W. W = ......................................................... [1]

[Total: 6]

2 A car travels around a circular track at constant speed.

(a) Why is it incorrect to describe the circular motion as having constant velocity?

............................................................................................................................................. [1]

(b) A force is required to maintain the circular motion.

(i) Explain why a force is required.

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [2]

(ii) In which direction does this force act?

..................................................................................................................................... [1]

(iii) Suggest what provides this force.

..................................................................................................................................... [1]

[Total: 5]

© UCLES 2010 0625/31/O/N/10 [Turn over

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1. A billboard of 100 kg has to be placed 50 m up from the ground. It was lifted up by a crane with a
power of 5 kW. Two strong cables were used to keep the billboard in equilibrium.

a. What does ‘equilibrium’ mean?

b. How long dies the crane take to lift the billboard up 50 m?

c. Calculate the tension, T1

d. Calculate the tension, T2

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2. A lamp of weight 25 N is supported by two ropes.

Given that the tension in rope A is 20 N, find

(a) the angle θ.

(b) the tension in rope B

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3. A traffic light of mass 15 kg is suspended from two cables as shown in the figure.

Find the tension in each rope

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4. Diagram below shows a wooden block of mass, m placed on an inclined plane. F is the frictional
force between the block and the plane R is the normal force. W is the weight of the block and X and
Y are its components. [g = 10 m s-2]

a. Define gravitational field

b. Write the expression for X and Y in terms of W.

X:

Y:

c. If the block is in equilibrium, write an equation to show the relationship between F, W and θ and
another between R, W and θ

F:

R:

d. If the block is not in equilibrium, it will slide down with an acceleration of a.

i. Write an equation to show the relationship between F, W and θ.

ii. If m = 1.0 kg, F = 5.0 N and θ = 40⁰, calculate the acceleration, a

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5. A boy exerts a force of F to pull a box of mass 2 kg up an inclined plane which makes an angle of
30⁰ with the floor.

Given that the friction acting on the box is 3 N, find

a. the normal reaction force, R acting on the box.

b. the component of the weight down the plane

c. the value of F if the box is moving up the plane with an acceleration of 1 m s-2.
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6. A wooden box of mass 50 kg is lowered from a lorry using a ramp placed at 30⁰ from the horizontal
ground. The wooden box accelerated at 1.0 m s-2 along the ramp. Given that the length of the ramp is
2.0 m.

a. When the box reaches the end of the ramp, calculate

i. Its velocity

ii. Its kinetic energy

b. What is the amount of gravitational potential energy lost after the wooden block reaches ground level?

c. Based on your answer above:

i. Determine the work done to overcome the frictional force between the wooden box and the
ramp

ii. What is the magnitude of the frictional force

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7. In the diagram below, a car of weight 6000 N travels at a constant speed of 10 m s-1 up a road inclined
at 15⁰ to the horizontal. The frictional force that opposes the motion of the car is 450 N.

Calculate

(a) the force, F, produced by the car engine.

(b) the gain in the potential energy of the car per second.

(c) the work done per second against friction.

(d) the power of the car engine.

(e) the efficiency of the car engine.

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10. At a children’s playground, Calvin of 30 kg mass climb uo a concrete slide of 2.3 m height. He slides
down the slope that has a length of 5 m.

(a) What is his change in potential energy?

(b) What is his kinetic energy at the end of the slope?

(c) Find the average frictional force against his motion along the slope.

(d) Find the work done against the motion along the slope.
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11. David rides his bicycle down a slope of 5 m vertical height without pedaling his bicycle. The velocities
of the bicycle before and at the end of the slope are 2 m s-1 and 8 m s-1 respectively.

Given that the total distance travelled by David along the slope is 10 m and mass of David and his bicycle
is 70 kg.

(a) Find the kinetic energy of David before he moves down the slope.

(b) Find the potential energy of David before he moves down the slope.

(c) What is the kinetic energy of David after he moves down the slope?

(d) Find the work done by David against friction along the slope.

(e) What is the average frictional force acting on David and his bicycle?
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12. A boy throws a basketball vertically upwards with a velocity of 30 m s-1

(a) What is the time taken for the ball to reach the maximum height?

(b) Find the potential energy of the basketball when it reaches the maximum height.

(c) What is the speed of the basketball when it returns to his hand?

(d) Find the kinetic energy of the basketball when it reaches the maximum height.

(e) How long is the ball in the air before it comes back to his hands?