A sleeve of mass 2 kg at origin can move on wire of parabolic shape x 2 = 4 y . Two forces F 1 = 6 N and F 2 = 8 N are applied on the sleeve. F 1 is constant and is in x -direction. F 2 is con

Question

A sleeve of mass 2 kg at origin can move on wire of parabolic shape $x^{2} = 4 y$ . Two forces $F_{1} = 6 N$ and $F_{2} = 8 N$ are applied on the sleeve. $F_{1}$ is constant and is in $x$ -direction. $F_{2}$ is constant in direction and magnitude. Body is displaced from origin to $x = 4$ , then net work done (in J ) by $F_{1}$ and $F_{2}$ is (approx)

TestHub · Accepted Answer

⇒ x 2 = 4 y ⇒ 2 x d x = 4 d y F N e t ​ d s W W ​ = ( 6 + 4 3 ​ ) i ^ + 4 j ^ ​ = d x i ^ + d y j ^ ​ = ∫ ( 6 + 4 3 ​ ) d x + ∫ 0 4 ​ 4 d y = ( 6 + 4 3 ​ ) ∫ 0 4 ​ d x + 2 ∫ 0 4 ​ x d x = ( 6 + 4 3 ​ ) [ 4 − 0 ] + 2 [ 2 x 2 ​ ] 0 4 ​ = [ 6 + 4 2 ​ ] × 4 + 16 = ( 40 + 16 3 ​ ) J ​

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