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.
I got 21.25 for F left and -73.75 for F right.
Is that right?
I can tell you right off it is wrong. The sum of the forces on the two supports have to equal the weights on the board, which is 20g+75g.
i am sorry but i don't get how to do it
To determine the forces exerted on the board by the posts, we need to consider the torque and equilibrium of the system. Here's how you can find the correct values:
a. To determine the force exerted on the board by the post on the left end, we need to calculate the torque. Torque is the product of the force and the lever arm distance. Since the left end is the pivot point, the torque due to the person's weight is zero. The only torque acting on the system is due to the gravitational force on the board.
The torque due to the gravitational force on the board is given by:
Torque_left = weight_board * lever_arm_distance_board
Since the board is uniform, we can assume the weight is evenly distributed along its length. The weight of the board can be calculated using the formula:
Weight_board = mass_board * acceleration_due_to_gravity
Weight_board = 20.0 kg * 9.8 m/s^2 = 196 N
The lever arm distance is the distance from the pivot point (left end) to the center of mass of the board. Since the person is standing 0.300 meters from the right end, the center of mass is at the midpoint of the board, which is at 1.00 meter from the left end.
lever_arm_distance_board = 1.00 m
Torque_left = 196 N * 1.00 m = 196 N·m
Since the system is in equilibrium, the torque exerted on the board by the left post is equal in magnitude and opposite in direction to the torque exerted by the right post. Therefore, the force exerted on the board by the left post is equal in magnitude and opposite in direction to the force exerted by the right post.
b. To determine the force exerted on the board by the post on the right end, we can use the torque equilibrium equation:
Torque_right = Torque_left
To find the torque exerted by the right post, we need to consider both the weight of the person and the weight of the board. The person's weight will have a torque since they are standing off-center.
The torque due to the person's weight is given by:
Torque_person = weight_person * lever_arm_distance_person
The weight of the person can be calculated using the formula:
Weight_person = mass_person * acceleration_due_to_gravity
Weight_person = 75.0 kg * 9.8 m/s^2 = 735 N
The lever arm distance for the person is the distance from the pivot point (left end) to the person's position.
lever_arm_distance_person = 0.300 m
Torque_person = 735 N * 0.300 m = 220.5 N·m
To find the torque exerted by the right post, we subtract the torque exerted by the person from the total torque on the system:
Torque_right = Torque_total - Torque_person
Torque_right = Torque_left - Torque_person
Torque_right = 196 N·m - 220.5 N·m = -24.5 N·m
Since the right post is exerting the same force as the left post but in the opposite direction, the force exerted on the board by the right post is equal in magnitude and opposite in direction to the force exerted by the left post:
Force_right = -196 N
Therefore, the correct values are:
a. The force exerted on the board by the post on the left end is 196 N in the positive direction.
b. The force exerted on the board by the post on the right end is 196 N in the negative direction (opposite to the positive direction).