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.
Sum moments about any point. I will choose the Right end.
-.3*75g -1*20g+Fleft*2=0
That gives you Fleft end.
Now, sum forces vertically
Fleft+Fright-20g-75g=0
solve for fright.
This is a sum of torque problem.
T(left) = F(board)*Distance from left + F(person)*Distance left + F(right)*Distance from left = 0
T(right) = F(board)*dist from right + F(person)*dist from right + F(left)*distance from right.
In reality, we are summing clockwise torques with counter clockwise torques and since there is no motion ( we are in equilibrium) setting this equal to 0.
This also works with the diving board problems, or the stacked books problem (after establishing the center of gravity for the books).
To determine the forces exerted on the board by the posts, we need to consider the equilibrium of forces acting on the system.
a. To find the force exerted on the board by the post on the left end, we need to calculate the torque exerted on the board about the right post. Torque is given by the formula:
Torque = Force * Distance from the pivot
In this case, the pivot is the right post. The torque exerted by the weight of the person can be calculated as:
Torque_person = person's mass * acceleration due to gravity * distance from the pivot
Torque_person = 75.0 kg * 9.8 m/s^2 * 0.300 m
Now, since the board is in rotational equilibrium, the sum of all torques acting on it must be zero. So, the force exerted by the left post can be calculated as:
Force_left_post = Torque_person / Distance from the pivot
Now, we can calculate the force exerted on the board by the post on the left end.
b. To find the force exerted on the board by the post on the right end, we need to consider the forces acting on the system. There are two main forces: the weight of the board and the weight of the person. The weight of the person can be calculated as:
Weight_person = person's mass * acceleration due to gravity
Weight_person = 75.0 kg * 9.8 m/s^2
Similarly, the weight of the board can be calculated as:
Weight_board = board's mass * acceleration due to gravity
Weight_board = 20.0 kg * 9.8 m/s^2
Since the board is in vertical equilibrium, the sum of all vertical forces acting on it must be zero. So, the force exerted by the right post can be calculated as:
Force_right_post = Weight_person + Weight_board
By calculating these values, we can determine the forces exerted on the board by the posts.