a 500 N person stands on a uniform board of weight 100 N and length 8 m. the board is supported at each end. if the support force at the right end is three times that at the left end, how far from the right end is the person?
please explain
The sum of the forces at the two ends mut be 500 + 100 = 600 N. If the support force is three times higher at the right end, then the left end must be supporting 150 N and the right end 450 N.
The person must be standing closer to the right end to distribute the weight in this manner.
To determine the distance x from the right end that the person is standing, set the total moment about the right end equal to zero.
500x + 100*4 = 150*8 = 1200
500 x = 800
x = 8/5 ft = 1.6 ft
The 100*4 term is the moment due to the weight of the board, which acts as if it were applied at the center of the board, 4 ft from the right end.
PLEASE!!!!!!I really need help. I don't understand it at all!
drwls is correct, except change everything labeled in FEET to METERS since the original problem is in meters.
To solve this problem, we need to understand the concept of torque. Torque is the rotational force generated around a point or an axis. In this case, we are considering the torque around the left end of the board.
Torque (T) is calculated by multiplying the force (F) applied at a certain distance (r) from the axis of rotation. Mathematically, torque is defined as T = F x r.
Let's break down the problem step-by-step:
1. We are given that a person with a weight of 500 N stands on the board, and the weight of the board itself is 100 N. Hence, the total load applied to the board is 500 N + 100 N = 600 N.
2. Since the support force at the right end is three times that at the left end, let's assume the force at the left end is F and the force at the right end is 3F.
3. We can calculate the torque generated by the person and the board around the left end:
Torque generated by the person = Person's weight x Distance from the left end
T1 = 500 N x r1
Torque generated by the board = Board's weight x Distance from the left end
T2 = 100 N x r1
4. Since the board is uniform, the total torque around the left end is the sum of T1 and T2:
Total torque around the left end = Torque generated by the person + Torque generated by the board
600 N x r1 = 500 N x r1 + 100 N x r1
5. Simplifying the equation:
600r1 = 500r1 + 100r1
600r1 = 600r1
r1 = 1
From the equation, we find that r1 = 1, which means that the distance from the left end of the board to the person is 1 meter.
6. Now, we can find the distance from the right end of the board to the person:
Total length of the board = Distance from the right end to the left end
8 m = Distance from the right end to the person + Distance from the left end to the person
8 m = r2 + 1 m
Rearranging the equation:
r2 = 8 m - 1 m
r2 = 7 m
Therefore, the person is located 7 meters from the right end of the board.