An elementary student of mass m = 38 kg is swinging on a swing. The length from

Question

An elementary student of mass m = 38 kg is swinging on a swing. The length from the top of the swing set to the seat is L = 4.6 m. The child is attempting to swing all the way around in a full circle.

a) What is the minimum speed, in meters per second, the child must be moving with at the top of the path in order to make a full circle?

b) Assuming the child is traveling at the speed found in part (a), what is their apparent weight, Wa in newtons, at the top of their path? (At the top, the child is upside-down.)

c) If the velocity at the bottom is the same as the velocity at the top from part (a), what is the child's apparent weight, in newtons, at the very bottom of the path?

Explanation / Answer

given m = 38 kg
length of swing, L = 4.6 m
a) To make full circle, ,let the speed at top of the loop be v
then from force balance
mv^2/L = mg
v = sqroot(Lg) = 6.717 m/s
b) At the top of trhe swing, apparent weight = Normal reaction of the swing
byt for minimum speed at top, N = 0 N
hence apparent weigfht at the top = 0 N
c) at the bottom, let aspparent weight be N
then from force balance
mv^2/L + mg = N = 38[v^2/4.6 + g] = 745.56 N

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