A boy with a mass of 50kg is sitting on a seesaw. He is sitting 2m from the pivot. He has a friend who weighs 40kg, how far away from the pivot must she sit to balance the seesaw? (gravitational accelleration (g) = 10m/s2)
This is a question relating to turning forces, known as moments. For the seesaw to be balanced the moment caused by the 50kg boy must be equal and opposite to the moment caused by the 40kg girl. A moment is given by the equation M (moment, Nm) = F (force, N) x d (distance from pivot, m). To calculate the force (F) resulting from the mass of each person, we must use newton's 2nd law (F = m x a) . The acceleration (a) here is equal to the gravitational acceleration (g) which is approximately 10N/s2 as given in the question. The force, or weight of the boy is therefore 500N (50 x 10), and the girl 400N (400 x 10). The moment of the boy can then be calculated using M = F x d, 1000 (moment) = 500 (force or weight) x 2(distance from pivot). The moment of the girl must be equal and opposite to this, so we have 1000 (moment) = 400(force or weight) x d (distance). If we divide this equation by 400 we get 1000/400 = d which gives the d = 2.5 m. The girl must sit 2.5 m from the pivot to balance the seesaw with the boy.
