Why are you able to make someone on a swing have very large swings by only exerting very small forces on them?

Because almost all of the force is done by the weight of the person and the mechanism of the swing itself, when you push someone you only give them an increase in velocity, the acceleration comes from the weight at first and then from gravity when the person is coming down, which is why we bend our legs when coming down

    5.5 n======    assuming that      we have      m = 0.145 kg    a = 38 m/s²therefore    5.51 n, but two significant figures.final answer: 5.5 n