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

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.