Question

A 2 kg particle starts at the origin and moves along positive x axis . The net force acting on it measured at intervals of 1m are 28,30,45,48,50,64.5,13.5,12.2,40.8,27 and 23 newtons. Find the total work done during the whole process.​

Answer 1

Given info : A 2 kg particle starts at origin and moves positive direction of x - axis . The net force acting on it is measured at intervals 1 m are 28N, 30N, 45N, 48N, 50N, 64.5N, 13.5N, 12.2N, 40.8N, 27N and 23N .

We have to find the total workdone during the whole process.

Solution : we know, work is the product of force and displacement along it.

I.e., W = Fx

If F₁, F₂, F₃, F₄ F₅ ... Are force applied on the body and its displacements to due to applied forces are x₁ , x₂ , x₃, x₄ .... Respectively.

then work done during the whole process , W = F₁x₁ + F₂x₂ + F₃x₃ + F₄x₄ + F₅x₅ + ... ...

Now applying above equation here,

Here, x₁ = x₂ = .... = x₁₁ = 1

so, W = 28 × 1 + 30 × 1 + 45 × 1 + 48 × 1 + 50 × 1 + 64.5 × 1 + 13.5 × 1 + 12.2 × 1 + 48.5 + 27 × 1 + 23 × 1

= 389.7 J

therefore workdone during the whole process is 389.7 J