Question

Two kids create a makeshift seesaw by setting a 4-m long uniform plank on a saw horse. The saw horse is 0.5 m to the left of the center of mass of the plank. The child of mass m1 = 42 kg sits at the left end of the plank. The child of mass m2 = 31 kg sits 1 m to the right of the center of mass of the plank. What is the mass of the plank?

Answer 1

The mass of the plank is 33 kg.

Step-by-step explanation:

Given that,

Length of plank = 4 m

Distance in left from the center= 0.5 m

Mass of child = 42 kg

Mass of other child = 31 kg

Distance in right from the center= 1 m

We can sum torques around the saw horse; each force generates a torque equal to force x distance from saw horse

We need to calculate the torque for first child

Using formula of torque

`\tau =mg* d`

Put the value into the formula

`\tau=42*9.8*1.5`

`\tau=617.4\ N-m`

We need to calculate the torque for second child

The child is 1.5 m from the saw horse

Using formula of torque

`\tau' =mg* d`

Put the value into the formula

`\tau'=31*9.8*1.5`

`\tau'=455.7\ N-m`

The weight of the plank produces a clockwise torque

`\tau''=mg* d`

`\tau''=mg* 0.5`

We need to calculate the mass of the plank

Using balance equation of torque

`\tau=\tau''+\tau'`

Put the value into the formula

`617.4=mg*0.5+455.7`

`m=(617.4-455.7)/(0.5*9.8)`

`m=33\ kg`

Hence, The mass of the plank is 33 kg.