Swing Set Support Forces


A 40 kg child is swinging on a swing supported by a pair of A frames with a beam connecting them at the top from which the swing is hung. The A frame angle is 60 degrees, each post being tipped in 30 degrees from the vertical. If she is swinging to a maximum angle of 60 degrees from the vertical, determine the force developed along each of the supporting posts as a result of her swinging, at the instant the swing passes through the vertical. The length of the swing is two meters.


The gravitational potential energy of the child at the top of a swing is m*g*h where h is 2 m minus 2*cos(60) m, h = 1 m. So PE=40*9.8*1= 392 Joules. When the swing passes through the vertical, the potential energy is zero so the kinetic energy is 392 Joules = 1/2*m*v2 = 1/2*40*v2. So v2=392/20 = 19.6 m2/s2, v=4.43 m/s. The tension in the swing is then the sum of the force providing the centripetal acceleration and the child's weight. Her weight is 40*9.8 N = 392 N. The centripetal acceleration is v2/r = 19.6/2 = 9.8 m/s2. The force is her mass times this acceleration or 392 N. This total force of 784 N is acting straight downward on the beam holding the swing. The four A frame legs each acting at an angle of 30 degrees from the vertical must provide the counter force. If they were vertical each would support 784/4 N. Because they are at an angle, each must support 784/4/cos(30) = 227 N.

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