Question

The fulcrum of a uniform 20-kg seesaw that is 4.0 m long is located 2.5 m from one end. A 29-kg child sits on the long end.

Determine the mass a person at the other end would have to be in order to balance the seesaw.

Answer 1

To balance the seesaw, the person on the other end must have a mass of 17.4 kg, as calculated by setting the product of their mass, gravitational acceleration, and distance from the fulcrum equal to the moment created by the 29-kg child on the opposite side.

Step-by-step explanation:

To balance the seesaw, the moments (torques) on both sides of the fulcrum must be equal. The moment on one side is the product of the force (weight of the child) and the distance from the fulcrum. The seesaw is in static equilibrium, which means the net torque around the fulcrum must be zero.

The 29-kg child creates a moment of 29 kg × 9.8 m/s² × 1.5 m, as the distance from the fulcrum to where the child is sitting is 4.0 m - 2.5 m = 1.5 m. To balance this, the person on the other end must create an equal moment. Therefore, the mass of the person m times the acceleration due to gravity 9.8 m/s² and the distance from the fulcrum 2.5 m must be equal to the moment created by the child.

Setting up the equation: m × 9.8 m/s² × 2.5 m = 29 kg × 9.8 m/s² × 1.5 m. Solving for m, we find that m = (29 kg × 1.5 m) / 2.5 m = 17.4 kg.

The person on the other end must have a mass of 17.4 kg to balance the seesaw.

Answer 2

To balance the seesaw, a person at the other end would have to have a mass of 89 kg and be located 1.5 m from the fulcrum.

Step-by-step explanation:

To balance the seesaw, the torques on both sides of the fulcrum must be equal. Torque is given by the formula: Torque = Force x Distance from the fulcrum. We can calculate the torque on each side using the masses and distances given. Let's denote the unknown mass as M and the distance from the fulcrum as D. On one side, the torque is given by: 80 kg x (4.0 m - 2.5 m). On the other side, the torque is given by: M kg x (2.5 m - D).

Since the seesaw is balanced, the torques on both sides must be equal: 80 kg x (4.0 m - 2.5 m) = M kg x (2.5 m - D). We can solve this equation to find the value of M: 55 kg = M kg x (2.5 m - D). Now we need one more equation to solve for both M and D. The total mass on each side of the fulcrum must be equal: 80 kg + 29 kg = M kg + 20 kg. This equation allows us to solve for M: 109 kg = M kg + 20 kg. Solving this equation gives us M = 89 kg. Substituting this value into the first equation allows us to solve for D: 55 kg = 89 kg x (2.5 m - D). Solving for D gives us D = 1.5 m. Therefore, a person at the other end would have to have a mass of 89 kg and be located 1.5 m from the fulcrum in order to balance the seesaw.