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 = 4.1 m. The child is attempting to swing all the way around in a full circle. 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? Assuming the child is traveling at the speed found in part (a), what is their apparent weight,  W_a in newtons, at the top of their path? (At the top, the child is upside-down.) If the velocity at the very top is the same velocity from part (a), what is the child's apparent weight, in newtons, at the very bottom of the path? W_a2 = 745.56

Explanation / Answer

given that

m = 38 kg

L = 4.1 m

(a)

To, make a full circle, the centrifugal acceleration at the top should be equal to the acceleration due to gravity.

g = v2 / R

9.8 = v2 / 4.1

v2 = 40.18

v = 6.33 m/s

(b)

At the top, the centrifugal force will be acting radially outwards, i. e vertically upwards and the weight due to gravity is acting downwards.

So, they both cancel each other (since the centrifugal acceleration in this case, is equal in magnitude to the acceleration due to gravity) resulting in an apparent weight

W = m*g - m*v2 / R = 0

W = 0

(c)

The centrifugal acceleration and hence the centrifugal force always acts radially outwards. So, at the bottom it acts vertically downwards along with the gravity.

So, they both add up to give a net apparent weight

W = m*g + mv2/ R

W = 2*m*g (since v2 /R = g )

Apparent weight at the bottom = 2 *38* 9.8 = 744.8 N

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