|
1. Three children are trying to balance on a seesaw, which has a pivot at the center, and a very light board `5.0\ m` long. Two playmates are already on either end. Boy `A` has a mass of `50\ kg`. and girl `B` a mass of `35\ kg`. Where should girl `C`, whose mass is `25\ kg`, place herself so as to balance the seesaw?
1. Three children are trying to balance on a seesaw, which has a pivot at the center, and a very light board 5.0\ m long. Two playmates are already on either end. Boy A has a mass of 50\ kg. and girl B a mass of 35\ kg. Where should girl C, whose mass is 25\ kg, place herself so as to balance the seesaw?  `τ =rF`
`1.5\ m`
Given:
`L = 5.0\ m`
`m_A = 50\ kg`
`m_B = 35\ kg`
`m_C = 25\ kg`
Solution:
Torque equation:
let counterclockwise be positive:
`sum τ = τ_A - τ_C-τ_B`
`sum τ = m_Ag(2.5\ m)-m_Cg x - m_B g(2.5\ m)=0`
`m_Ag(2.5\ m)- m_B g(2.5\ m)=m_Cg x`
`m_A(2.5\ m)- m_B(2.5\ m)=m_C x`
`x = (m_A- m_B)/m_C (2.5\ m)`
`x = ((50\ kg)- (35\ kg))/(25\ kg) (2.5\ m)`
`x = 1.5\ m` |