Three students are fighting over a T-shirt. Student 1 exerts a constant force F⃗ 1=F0i^ on the shirt, student 2 exerts a constant force F⃗ 2=−3F0j^ and student 3 exerts a constant force F⃗ 3=−4F0i^+Gj^. (In these expressions F0 and G are positive constants with units of force.) As the three students exert these forces, the T-shirt undergoes a straight-line displacemen 2di^+dj^ where d is a positive constant with units of distance. Find the work done on the T-shirt by student 1.

W₁ = 2F₀d

Explanation:

When a force is applied on a body, due to which the body displaced by some distance, then the work is said to be done. Hence, the work is the dot product of the force nd displacement.

W = F.d

where,

W = Work Done

F = Force Applied

d = Displacement

For student 1:

W = W₁ = ?

F = F₁ = F₀ i

d = 2d i + d j

Therefore,

W₁ = (F₀i).(2di + dj)

W₁ = 2F₀d(i.i) + F₀d(i.j)

W₁ = 2F₀d(1) + F₀d(0)

W₁ = 2F₀d + 0

W₁ = 2F₀d

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