A 64.0 kg person stands on a lightweight diving board supported by two pillars, one at the end of the board, the other 1.20 m away from the end. The pillar at the end of the board exerts a downward force of 829 N.
How far from the pillar at the end of the board is the person standing?
Find the magnitude of the force exerted by the second pillar
I think that I need to find the sum of the forces in the x and y components, but I am getting stuck. Any help?
You need to do the vertical forces = zero, and the sum of moments about any point (I suggest the point at the end of the board with the pillar).
Mr. Pursley-
Our professor has not even discussed sum of moments and it is not in our textbook. Could you please explain? Thanks
A 48 {\rm kg} woman stands on a very light, rigid board that rests on a bathroom scale at each end, as shown in figure.
Of course! I'll be happy to explain. The principle of moments, also known as the law of moments, is a concept in physics that deals with rotational equilibrium. It states that for an object to be in rotational equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the counterclockwise moments about the same point.
In this scenario, we can assume that the diving board and the person are in rotational equilibrium. To find the distance at which the person is standing from the pillar at the end of the board, we can apply the principle of moments.
Let's consider the point of rotation to be the pillar at the end of the board. We'll calculate the clockwise and counterclockwise moments about this point.
The clockwise moment is given by the force exerted by the pillar at the end of the board multiplied by the distance between the pillar and the point where the person is standing (which is what we're trying to find). The counterclockwise moment is given by the force exerted by the second pillar multiplied by its distance from the point of rotation.
Since the diving board and the person are in rotational equilibrium, the sum of the clockwise moments should be equal to the sum of the counterclockwise moments.
Let's denote the distance between the pillar at the end of the board and the person as d. The given force exerted by the pillar at the end of the board is 829 N, and we need to find the force exerted by the second pillar.
The clockwise moment is given by 829 N * d.
The counterclockwise moment is given by the force exerted by the second pillar, which we'll denote as F, multiplied by its distance from the point of rotation, which is 1.20 m.
Setting up the equation for the principle of moments:
829 N * d = F * 1.20 m
To solve for d, we need to know the magnitude of the force exerted by the second pillar (F). If we have that information, we can easily rearrange the equation to solve for d as follows:
d = (F * 1.20 m) / 829 N
In summary, to find the distance at which the person is standing from the pillar at the end of the board, we need to know the magnitude of the force exerted by the second pillar (F). By applying the principle of moments, we can set up an equation and solve for the distance.
Of course! I'd be happy to explain the concept of moments and how to use them in this problem.
In physics, moments (also known as torque) are used to describe the turning effect of a force around a specific point or axis. In this case, we can use moments to analyze the forces acting on the diving board and determine the distances involved.
To start, let's consider the forces acting on the diving board. We have the force exerted by the pillar at the end, which is 829 N acting vertically downward. We also have the weight of the person, which can be calculated as the mass (64.0 kg) multiplied by the acceleration due to gravity (approximately 9.8 m/s^2).
Now, let's focus on the moments. The moment of a force is given by the product of the magnitude of the force and the perpendicular distance from the point about which the moment is measured to the line of action of the force. In this case, we can choose the point at the end of the board with the pillar as our reference point.
Since the sum of moments is zero when an object is in equilibrium, we can set up an equation using the moments to solve for the unknowns.
Let's determine the distance from the person to the pillar at the end of the board, which we'll call "D." We know that the force exerted by the first pillar is 829 N and the weight of the person is approximately 630 N (64.0 kg * 9.8 m/s^2).
Using moments, we can set up the equation:
(829 N) * 0 + (630 N) * D = 0
This equation states that the sum of the moments about the reference point is zero. The first term on the left side represents the moment of the force exerted by the first pillar (829 N) about our reference point, which is 0 since it acts directly at the reference point. The second term represents the moment created by the person's weight (630 N) about our reference point, which is equal to (630 N) * D since the person is at a distance "D" from the reference point.
From this equation, we can solve for the distance "D" by dividing both sides by 630 N:
D = 0 / 630 N = 0 meters
Therefore, the person is standing at a distance of 0 meters from the pillar at the end of the board.
Now, let's determine the magnitude of the force exerted by the second pillar. Since the sum of the vertical forces must be zero for the system to be in equilibrium, we can represent the force exerted by the second pillar (which we'll call "F") as:
F = -(829 N + 630 N)
Here, the negative sign indicates that the force is acting in the opposite direction to the forces exerted by the first pillar and the person's weight. By substituting the values, we can calculate the magnitude of the force exerted by the second pillar:
F = -(829 N + 630 N) = -1459 N
Therefore, the magnitude of the force exerted by the second pillar is 1459 N.
I hope this explanation helps you understand how to use moments to solve this problem! Let me know if you have any further questions.