Q3.1 Forces are vectors (S)
A body of mass 2 kg experiences three forces, as shown. Forces
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Solution
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Solution
Saying that the system is in static equilibrium means the body is is (and remains) stationary: thus it has zero acceleration and by Newton’s 2nd law (Key Point 2.2) must experience zero net force. Let x and y denote horizontal and vertical directions. Then (since forces are vectors!) both the x and y components of the net force must vanish.
By inspection the y components of the forces
and
are equal and opposite; and
has no vertical component. So there is
indeed no net y-component.To ensure that there is no x-component we require that
(entirely in the x-direction) is balanced by the sum of the x-components of
and
. Thus
![\[ F_3= F_1 \cos{30} + F_2 \cos{30} = 2 \times 10 \times \frac{\sqrt {3}}{2} = 10\sqrt{3} \, N \]](mastermathpng-8.png)
- In this case the horizontal components of the forces no longer balance.
There will be a net force in the x direction and thus an
acceleration (also in the x
direction) given by
implying
The minus sign means that the acceleration is to the left.![\[ a = -3.66 \,ms^{-2}\hspace{0.5cm}\mbox{\rm (3sf)}\hspace{0.5cm} \]](mastermathpng-10.png)
