In order to cross a pit filled with fresh elephant dung the fearless George of t

Question

In order to cross a pit filled with fresh elephant dung the fearless George of the Jungle has a
plan: He wants to grab a vine to bring it up to a horizontal position and then swing down,
cross the poop and let go of the vine when the ground is safe again.
The typical vine in the area breaks when its tension exceeds twice of George’s weight.
1. Use conservation of energy to relate George’s speed
at the bottom of the swing to his initial height (r).
2. Draw a free-body diagram for George (still hanging
on the vine) at the bottom of his swing. Also include
the direction of the acceleration at this point in your
drawing.
3. Since the path that George takes follows a circular arc, the net force on him at the bottom of
his swing will be centripetal. Apply Newton’s second law in radial direction for this situation.
Use your result from part 1 for the speed.
4. What would you recommend George to do?
? proceed as planned and use the vine to cross the pit.
? come up with an alternate plan, since the vine will likely break.
? tell him that the tension at the bottom of the swing will be exactly twice his weight and let
him continue at his own risk.

Explanation / Answer

1. conservation of energy 1/2 m (v1)^2 + mg(h1) = 1/2 m (v2)^2 + mg(h2) consider at the top of the swing, h1 will be the radius (r) there is no velocity 1 (v1 = 0) at the bottom of the swing there is a (v2) which = (vt) that is tangential velocity co-responding to the uniform circular motion. there is no hight. (h2=0) this gives: 0 + mgr = 1/2 m (vt)^2 + 0 gr = 1/2 (vt)^2 2) the free body diagram will look like a quarter circle. starting at the starting position with the vine horizontal. with (vt) being tangent to the circle at the bottom of the circle. 3) F(c) = T F(c) = m * (a(c)) ac = (vt^2)/r t = m (vt^2) / r recall gr = 1/2 (vt)^2 (vt)^2 = 2gr t = m (2gr) / r t = 2mg mg = weight of George. t = 2 times the weight. 4) recommend him to continue at his own risk.

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