A 28.0 kg child plays on a swing having support ropes that are 2.30 m long. A friend pulls her back until the ropes are 45.0 ∘ from the vert

Question

A 28.0 kg child plays on a swing having support ropes that are 2.30 m long. A friend pulls her back until the ropes are 45.0 ∘ 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?

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Gia Bảo 5 months 2021-08-11T00:13:25+00:00 1 Answers 95 views 0

Answers ( )

    0
    2021-08-11T00:15:21+00:00

    Answer

    A)184.9J

    B)=3.63m/s

    C) Zero

    Explanation:

    A)potential energy of the child at the initial position, measured relative the her potential energy at the bottom of the motion, is

    U=Mgh

    Where m=28kg

    g= 9.8m/s

    h= difference in height between the initial position and the bottom position

    We are told that the rope is L = 2.30 m long and inclined at 45.0° from the vertical

    h=L-Lcos(x)= L(1-cosx)=2.30(1-cos45)

    =0.674m

    Her Potential Energy will now

    = 28× 9.8×0.674

    =184.9J

    B)we can see that at the bottom of the motion, all the initial potential energy of the child has been converted into kinetic energy:

    E= 0.5mv^2

    where

    m = 28.0 kg is the mass of the child

    v is the speed of the child at the bottom position

    Solving the equation for v, we find

    V=√2k/m

    V=√(2×184.9/28

    =3.63m/s

    C)we can find work done by the tension in the rope is given using expresion below

    W= Tdcosx

    where W= work done

    T is the tension

    d = displacement of the child

    x= angle between the directions of T and d

    In this situation, we have that the tension in the rope, T, is always perpendicular to the displacement of the child, d. x= 90∘ and cos90∘=0 hence, the work done is zero.

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