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

Answer:

The mass of the plank is 33 kg.

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

$\tau =mg\times d$

Put the value into the formula

$\tau=42\times9.8\times1.5$

$\tau=617.4\ N-m$

We need to calculate the torque for second child

The child is 1.5 m from the saw horse

Using formula of torque

$\tau' =mg\times d$

Put the value into the formula

$\tau'=31\times9.8\times1.5$

$\tau'=455.7\ N-m$

The weight of the plank produces a clockwise torque

$\tau''=mg\times d$

$\tau''=mg\times 0.5$

We need to calculate the mass of the plank

Using balance equation of torque

$\tau=\tau''+\tau'$

Put the value into the formula

$617.4=mg\times0.5+455.7$

$m=\dfrac{617.4-455.7}{0.5\times9.8}$

$m=33\ kg$

Hence, The mass of the plank is 33 kg.