A boy with a mass of 40kg is seated a distance of 3.0m from the fulcrum of a seesaw.
a. Calculate the load force exerted by the boy (Hint: What force is pulling him down?)
b. Calculate the torque exerted by the boy.
c. If his sister with a mass of 24 kg wants to balance the seesaw, how far away from the fulcrum should she sit?
To answer these questions, we need to understand the concepts of torque and balance in terms of a seesaw.
Torque (τ) is a measure of how effectively a force can rotate an object around a certain point. It is calculated using the formula: torque = force × lever arm. The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.
Now let's proceed to answer each question:
a. To calculate the load force exerted by the boy, we need to consider the force pulling him down. In this case, the force is his weight, which can be calculated using the formula: weight = mass × gravitational acceleration. The standard gravitational acceleration is approximately 9.8 m/s² on Earth. Therefore, the load force exerted by the boy is given by: load force = weight.
load force = mass × acceleration due to gravity
= 40 kg × 9.8 m/s²
= 392 N
So, the load force exerted by the boy is 392 Newtons.
b. To calculate the torque exerted by the boy, we need to consider both the load force and the distance between the boy and the fulcrum. The torque (τ) can be calculated using the formula: torque = load force × lever arm.
torque = load force × distance from the fulcrum
= 392 N × 3.0 m
= 1176 N·m
Therefore, the torque exerted by the boy is 1176 Newton-meters (N·m).
c. To balance the seesaw, the torque exerted by the sister must be equal and opposite to the torque exerted by the boy. Since torque is dependent on the distance from the fulcrum, we can use the equation: torque = load force × distance.
Let x be the distance the sister should sit from the fulcrum. The torque exerted by the sister can be calculated using the same formula as before.
torque by sister = load force by sister × x
Because we want the seesaw to be balanced, the torque exerted by the sister and the torque exerted by the boy should be equal. Therefore, we can set the two torques equal to each other and solve for x.
torque by sister = torque by boy
load force by sister × x = load force by boy × distance by the boy
load force by sister × x = 392 N × 3.0 m
load force by sister × x = 1176 N·m
Given that the sister has a mass of 24 kg, the load force by the sister can be calculated.
load force by sister = mass by sister × acceleration due to gravity
load force by sister = 24 kg × 9.8 m/s²
= 235.2 N
Now we can solve for x:
235.2 N × x = 1176 N·m
Dividing both sides of the equation by 235.2 N:
x = 1176 N·m / 235.2 N
x = 5.0 m
Therefore, the sister should sit a distance of 5.0 meters from the fulcrum to balance the seesaw.