A 38.0-kg child swings in a swing supported by two chains, each 2.90 m long. The tension in each chain at the lowest point is 436 N.
(a) Find the child's speed at the lowest point.
__ m/s
(b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
__ N (upward)
We can analyze the system as it follows in Figure 1., where x and y are the displacements on both axis, is the angle of displacement from the equilibrium point.
Then, since at the lowest point x = 0, y = 0, the forces acting on the child will be the sum of the tension forces acting on the swing and the weight mg of the child:
Then, the force exerted by the seat on the child at the lowest point can be found with the net force, defined as , where F' = 2T is the force that we're looking for or the force that the seat is exerting on the child and is equal to twice the value for the tension T.
Reference:
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