Potential and Kinetic Energy on a swing as well as Tension in the rope

[lesleymarie785]

Homework Statement

A 23.0 kg child plays on a swing having support ropes that are 2.10 m long. A friend pulls her back until the ropes are 41.0-degrees from the vertical and releases her from rest.

a.)What is the potential energy for the child just as she is released compared with the potential energy at the bottom of the swing?

b.) How fast will she be moving at the bottom of the swing?

c.) How much work does the tension in the ropes do as the child swings from the initial position to the bottom?

Homework Equations

Potential Energy (U) = mgr
Kinetic Energy (K) = 05*m*v^2
W(noncons force) = ΔE = E(initial) + W(nc) = E(final)

The Attempt at a Solution

a.) U(top)= mgr
Potential energy at the top = (mass of child)(gravity)(radius or length of ropes)
= 23kg * 9.8m/s^2 * 2.10m
U(top) = 473 J

b.) U(top) = KE(bottom) so, mgr = .5mv^2
Mass cancels as it is on both sides of the equation, so you're left with: gr = .5v^2
2gr = v^2 then square-root the whole thing to yield 2gr^.5 = v
v = (2*9.8*2.10)^.5
v = 6.42 m/s

c.) I think nonconservative forces Work equation should come into play here:
W(nc) = ΔE
E(i) + W(nc) = E(f) or E(i) = E(f) + W(nc) <--not sure which way this should go. Also not sure how to go about solving for the Tension.

Thank you so much for any help.

 

[paisiello2]

c.) I think nonconservative forces Work equation should come into play here:
W(nc) = ΔE
E(i) + W(nc) = E(f) or E(i) = E(f) + W(nc) <--not sure which way this should go. Also not sure how to go about solving for the the Tension.

Not sure why you think non-conservative forces apply here. Usually these are things like friction and air resistance. The big hint here is that this is a bit of a trick question. Look back at the definition of what work is.

 

[guitarphysics]

Ok, you need to think more conceptually before beginning to apply the equations (by which I mean think about what's going in before just plugging stuff in). For example, in part a- the gravitational potential energy is not mgr, it is mgh (the height of the kid compared with the bottom of the swing isn't equal to the rope length! How do you find this height? Use a bit of trigonometry :). Remember that the mom pulls the swing back 41 degrees). For the kinetic energy at the bottom you're on the right track- you just used an incorrect value for the potential energy, so make sure to correct that. For part c, consider the definition of work- work is the *dot product* of the force and displacement. Why is this relevant? Consider what the dot product between the force (tension) and displacement will always be in this case (think about the angle between the force and the direction in which the kid moves). That's probably enough hints, you can take it from here. Good luck and have fun