a person stands a distance of 0.300 meters from the right end of a 2.00 meter long uniform platform that is supported by two posts, one at each end. The board has a mass of 20.0 kg and the person's mass is 75.0 kg.
a. determine the force exterted on the board by the post on the left end.
b. determine the force exerted on the board by the post on the right end.
To solve this problem, we can use the principle of equilibrium, which states that the sum of all the forces acting on an object in equilibrium is equal to zero. We can consider the platform as a seesaw or a beam in equilibrium.
a. To determine the force exerted on the board by the post on the left end, we need to calculate the torque or the moment.
The torque (or moment) about a point is defined as the force applied perpendicular to the lever arm (distance from the point) multiplied by the lever arm.
In this case, the left end of the board is the fulcrum or the point about which the torques are being calculated.
The person's weight (mass times acceleration due to gravity) creates a downward force of (75.0 kg) * (9.8 m/s^2) = 735 N. This force acts at a distance of 0.300 m from the left end of the platform.
The platform's weight creates a downward force of (20.0 kg) * (9.8 m/s^2) = 196 N. This force acts at a distance of 2.00 m - 0.300 m = 1.700 m from the left end of the platform.
Now, we can calculate the torques generated by these forces:
Torque by person = force by person * distance from fulcrum = 735 N * 0.300 m
Torque by platform = force by platform * distance from fulcrum = 196 N * 1.700 m
The torque generated by the person should be equal to the torque generated by the platform since the platform is in equilibrium. Therefore,
Torque by person = Torque by platform
(735 N * 0.300 m) = (196 N * 1.700 m)
Now, we can solve this equation to find the force exerted on the board by the post on the left end.
b. To determine the force exerted on the board by the post on the right end, we can use the same principle.
The torque generated by the person should be balanced out by the torque generated by the platform and the force exerted by the right post.
(735 N * 0.300 m) = (196 N * 1.700 m) + (force by right post * 2.00 m)
Now, we can solve this equation to find the force exerted on the board by the post on the right end.