Question

A plank of wood of length 4.00m with a fulcrum (pivot) at it's center forms a seesaw. Suppose a child of mass 30.0kg sits 1.50m to the left of center, and a second child sits at the end on the far right side. The system is in equilibrium. Find the mass of the second child. (options: 30.0 kg, 22.5 kg, 7.5 kg, 40.0 kg)

For the same setup with the two children sitting on the seesaw used in question 4 except now the first child's mass is 33.333kg and the second child's mass is known to be 25kg, find the normal force acting at the pivot point (fulcrum). The mass of the seesaw is 12.5kg.
(Hint: Remember if you can show the system is in equilibrium then you can set the sums of forces/torques to zero and solve for whichever quantity you want.)
Options:
O 804 N
O 515 N
O 695 N
O 486 N

Answer 1

The mass of the second child on the seesaw required for equilibrium is 22.5 kg, and the normal force acting at the pivot point with the given masses of the children and seesaw is 695 N. Option c is the correct answer.

Step-by-step explanation:

Finding the Mass of the Second Child on a Seesaw

To solve the first problem about the seesaw in equilibrium, we need to utilize the principle of moments. The torque produced by the first child sitting 1.50m from the center must be equal to the torque produced by the second child sitting at the other end.

This is based on the equation τ= r × F, where τ is the torque, r is the distance from the pivot, and F is the force due to the child's weight.

So, for the first child, we have τ1 = 1.50m × 30.0kg × 9.8m/s2, and for the second child, τ2 = 4.00m/2 × m2× 9.8m/s2, where m2 is the unknown mass. Setting τ1 equal to τ2 and solving for m2 gives us m2 = (1.50m × 30.0kg) / (2.00m) = 22.5 kg. Hence, the correct option is 22.5 kg.

Calculating the Normal Force at the Pivot Point

For the second problem, we again apply the equilibrium conditions. The total torque around the pivot is zero, and the normal force Fp at the pivot must balance the gravitational forces of both children and the seesaw.

Hence, Fp = (m1+ m2 + mseesaw) × g. Substituting the values, we get Fp = (33.333kg + 25kg + 12.5kg) × 9.8m/s2 = 695 N, which is the correct answer.