Question

A 4.00-kg particle moves from the origin to position C, having coordinates x = 5.00 m and y = 5.00 m. One force on the particle is the gravitational force acting in the negative y direction . calculate the work done by the gravitational force in going from O to C
along (a) OAC. (b) OBC. (c) OC. Your results should all be identical. Why?

Answer 1

a)

$$W_{OAC}=W_{OA}+W_{AC}\\=-(4)(9.8)(0)-(4)(9.8)(5)=-196\ J$$

b)

$$W_{OBC}=W_{OB}+W_{BC}\\=-(4)(9.8)(5)-(4)(9.8)(0)=-196\ J$$

c)

$$W_{OC}=-(4)(9.8)\sqrt{5^2+5^2}\cos{45}=-196\ J$$

It is because the gravitational force is the conservative force.