The net work done on the trunk by the three forces is 1.50J and the kinetic energy of the trunk will increase
The data given in the question is:
F 1 =5.00N,
F2 =9.00N,
F3 =3.00N,
θ=60°
d=3m
Work done by each force can be found as
We know that, work done by a force is given by:
W =F d cosϕ,
where ϕ is the angle between Force and displacement vectors.
F₁ is in the direction of the displacement.
So,
W₁=F₁dcosϕ
=(5.00N)(3.00m)cos0°
=15.0J.
Force F₂ makes an angle of
ϕ ₂=180°−θ
=180° −60°
=120°
with the displacement i.e. in negative x direction.
So,
W₂=F₂dcosϕ₂
=(9.00N)(3.00m)cos120°
=−13.5J.
Force F₃ is perpendicular to the displacement.
So, W₃=F₃dcosϕ
=(3.00N)(3.00m) cos90°
=0J
Net Work done by three forces is
As work is a scalar quantity, so total work done will be the algebraic sum of all the individual works.
So, W=W₁+W₂+W₃
=15−13.5+0
=+1.50J.
According to Work energy theorem, total work done on a system equal the change in kinetic energy of the system.
Here, a positive work of 1.5 Joules is done on the trunk, so its Kinetic Energy will increase by 1.5 Joules.
Figure was missing it is attached with the answer
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