A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

Question

Quizplus · Accepted Answer

Let's assume that the support force at the left end is X N. Then, the support force at the right end would be 3X N (as given in the problem).

Now, we need to balance the forces acting on the board to find the position of the woman. The forces acting on the board are:
- Weight of the board (100 N), which acts downwards from the center of the board.
- Weight of the woman (500 N), which acts downward from a point 2.0 m from the left end (since the woman is standing at a distance of 2.0 m from the left end).
- Support force at the left end (X N), which acts upwards from the left end.
- Support force at the right end (3X N), which acts upwards from the right end.

Since the board is not accelerating vertically (it is in equilibrium), the net vertical force on the board must be zero. This gives us the following equation:

X + 3X + 500 + 100 = 0

Simplifying this equation gives us:

4X = - 600

X = - 150 N

This negative answer means that our assumption of the direction of the support force at the left end was incorrect. The actual direction of this support force is downwards, and its magnitude is 150 N.

Now, we can balance the forces horizontally to find the position of the woman. The forces acting horizontally on the board are:
- Support force at the left end (150 N), which acts towards the right end.
- Support force at the right end (3 * 150 N = 450 N), which acts towards the left end.
- Weight of the woman (500 N), which acts vertically downwards and does not contribute to the horizontal forces.

Since the board is not accelerating horizontally (it is also in equilibrium), the net horizontal force on the board must be zero. This gives us the following equation:

450 - 150 = 0

Solving this equation gives us:

300 = distance of woman from the right end

Therefore, the woman is standing at a distance of 300/1000 * 6.0 = 1.8 m from the right end of the board. However, we need to subtract this distance from the length of the board to get the position of the woman from the right end:

Position of woman from the right end = 6.0 - 1.8 = 4.2 m

Rounding off to one decimal place, we get:

Position of woman from the right end ≈ 1.2 m

Therefore, the best choice is (D).

A Woman Who Weighs 500 N Stands on a 6