A box with weight of magnitude F_G = 2.00 N is lowered by a rope down a smooth plane that is inclined at an angle φ = 30.0 degrees about ve the horizontal. The normal force acting on the box has a magnitude n = 1.73 N, the tension force is 1.00 N, and the displacement Δr of the box is 1.80 m down the cloned plane.

What is the work W_G done on the box by the gravity?

I had this exact question today and found someone who had solved it before, this was their response to the work done by gravity. They used the name "physicsmom"

Vertical distance = 1.8 sin 30 = .9 m

W = 2 N * .9 m = 1.8J

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onyebuchinnaji onyebuchinnaji · Answer 2 · 2021-10-21T15:11:58+02:00

The work done on the box by the gravity is 0.072 J.

The given parameters;

weight of the box, [tex]F_g[/tex] = 2 N
inclination of the rope, φ = 30⁰
normal force acting on the box, n = 1.73 N
tension on the rope, T = 1 N
displacement of the box, Δr = 1.8 m

The work done on the box by gravity is calculated as follows;

W = FΔr

where;

F is the net horizontal force on the block

The net horizontal force on the box is calculated as follows;

[tex]\Sigma F_x = F_g sin(\theta ) - F_k\\\\ \Sigma F_x = F_g sin(\theta ) - \mu_k F_n \\\\ \Sigma F_x = 2 \times sin(30 ) - (tan \theta) \times F_n\\\\ \Sigma F_x = 1 - (tan\ 30) \times 1.73\\\\ \Sigma F_x = 0.04 \ N[/tex]

The work done on the box by gravity is calculated as;

W = 0.04 x 1.8

W = 0.072 J.

Thus, the work done on the box by the gravity is 0.072 J.

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