The resultant of several forces
Figure 9.1 shows a motor car stalled on the road due to a mechanical fault being
pushed by one person in the forward direction. Since the force exerted was not
sufficient to move the vehicle, it did not move. Figure 9.2 shows two people trying
to push the car. The motor car did not move in this attempt either. In Figure 9.3,
three people are shown to push the motor car. In this attempt, the car has moved.
Figure 9.2 – Two persons pushing the car
Figure 9.3 – Three persons pushing the car
Figure 9.1 – One person pushing a car
In order to move the car all the forces have to be applied in the direction that the
car needs to be moved.
If many people take part in pushing the car instead of just one person, all the
individual forces combine to form a larger force in the same direction and the task
becomes easier.
The result of many people exerting forces in the same direction is that all the forces
add up to give a larger single force.
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When more than one force is applied, the single force that gives the
same result as that of all the contributing forces is known as the
resultant force of the individual contributing forces.
Forces applied on objects can have various directions. In this lesson will discuss
about,
B
Figure 9.5 - Two forces acting on the trolley in the same direction
C
B
A
● Apply two forces from the two Newton balances B and C. Record the readings
of the balances.
● Record also, the reading of the balance A.
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● Find a relationship between the reading on the balance A and the readings
recorded from B and C balances.
● Applying different forces from the B and C, repeat the activity several times
and find the relationship between the measurements.
You will observe that the sum of the readings of B and C is equal to the reading of A.
That is, when two collinear forces act along the same direction, the
resultant of the two forces is equal to the sum of the two individual forces
with a direction in the direction of forces.
Example 1
Two children are pulling a thread connected to a box placed on a table in the same
direction. The force applied by one child is 8 N while that of the other child is 6 N.
What is the resultant force with which the children are pulling the box?
8 N 6 N
The resultant force applied by both children = 8 N + 6 N
= 14 N
Exercise 9.1
(3) Find the resultant force in each of following situations.
(2) A child is pushing an object placed on a table with a force of 5 N in a certain
dierection while another child is pulling it in the same direction with a force of
7 N. What is the resultant of these two forces?
100 N 200N 40 N
20 N (i) (ii)
(2)
(1)
(To the same direction)
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Resultant of two collinear forces acting along opposite
directions
Have you seen the national sport of pulling ropes during the Sinhala new year
season? The participants of such competitions form two groups and pull a rope
in two directions. The rope will be dragged in the direction of the resultant force
which lies in the direction of the larger force.
Figure 9.6 – Pulling a rope
When we want to pull an object along a certain direction, the resultant force or the
net force of forces applied along that direction is given by the summation of the
forces.
The result of applying forces in various directions is a non-utilization of the forces
productively.
It is possible to obtain a large net force only if all the contributing forces are applied
in the same direction.
It is an experience that in order to drag a heavy object along the floor easily, the
object should be pushed from behind and pulled from the front.
Go carts used to carry children can be pulled from the front or pushed from the back
in order to move it. If both a pull from the front and a push from the back are given
to the go cart, moving the cart would be easier as a large resultant will operate on
the cart.
Now let us find the resultant of two collinear forces acting in opposite directions.
In order to do it, let us engage in the following activity.
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Activity 2
Items required : a trolley, two Newton balances, two smooth pulleys, measuring
weights
A B
Newton balance
trolley
smooth pulley
Figure 9.7 - Forces acting in opposite directions on a trolley
● Place the trolley on a table as shown in Figure 9.7 and fix two pieces of string
to the two ends of the trolley. Allow the other ends of the pieces of string to
pass over the two pulleys and attach two Newton balances A and B.
● Record your observations on the motion of the trolley after applying a 4 N
force on each balance.
● Record your observations on the motion of the trolley after applying a 4 N
force on the balance A and a 6 N force on balance B.
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