Logan is standing on a dock holding onto a rope swing that is L = 4.30 m long and suspended from a tree branch above. The rope is taut and makes a 30.0 ° angle with the vertical. Logan swings in a circular arc, passing through the bottom of the arc then releasing the rope when it makes an angle of θ = 13.9 ° with the perpendicular. If Logan's mass is 79.0 kg , how much work W g r a v does gravity do on him up to the point where he releases the rope?

The work done on Logan by gravity is 348.75 Joules

Explanation:

The work done on Logan by gravity would be equal to the loss of gravitational potential energy (G.P.E) of Logan.

We can calculate this as follows:

Lets find the initial height of Logan above the lowest point of the swing.

Initial Height = 4.3 -  (4.3 * Cos(30.0))

Initial Height = 0.576 m

Let's also find the final height of Logan above the lowest point of the swing in a similar manner:

Final Height = 4.3 - (4.3 * Cos(13.9))

Final Height = 0.126 m

Change in gravitational potential energy  = Initial G.P.E - Final G.P.E

Change in G.P.E = Mass * Gravity * Initial Height - Mass * Gravity * Final Height

Change in G.P.E = 79 * 9.81 * 0.576 - 79 * 9.81 * 0.126

Change in G.P.E = 446.4 - 97.65

Change in G.P.E = 348.75 Joules

Thus, the work done on Logan by gravity is 348.75 Joules

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