Question

A father and his young son get on a teeter-totter. The son sits 2 m fromthe center, but the father has to sit closer to balance. Where does the father have to sit to balance the teeter-totter if he weighs 4 times as much as his son?

Answer 1

The distance of the father from the center is
`d_f = (1)/(2) \ m`

Step-by-step explanation:

From the question we are told that

The distance of the son from the center is
`d_s = 2 \ m`

Let the mass of the son be
`m_s`

then the mass of the father is
`m_f = 4m_s`

Now for the teeter-totter to be balanced the torque due to the weight of the father must be equal to the torque due to the weight the son, this is mathematically represented as

`\tau_s = \tau_f`

Where
`\tau_s` is the torque of the son which is mathematically represented as

`\tau_ s = m_s * d_s * g`

while
`\tau_f` is the torque of the father which is mathematically represented as

`\tau_f = m_f * d_f * g`

=>
`\tau_f = 4 m_s * d_f * g`

So

`4 m_s * d_f * g = m_s * d_s * g`

substituting values

`4 * d_f * = 2`

=>
`d_f = (1)/(2) \ m`