A panel is supported on supports a and b. A 60-kg person walks on the board from point a. Despise the deformation of the table
A) find its expression for the magnitude of the force exerted by each support in function x of the person
B) in what position will the person be found at the instant when the tab begins to separate from the support a?
i try to find the net force but i just can't do it
can someone help pls? me am really lost
Certainly! I can help you with this problem. Let's break it down step by step.
A) To find the expression for the magnitude of the force exerted by each support in terms of the person's position, we need to consider the equilibrium of forces acting on the person and the panel.
1. Begin by drawing a free-body diagram of the person and panel system. The person's weight acts downwards with a magnitude of 60 kg times the acceleration due to gravity, which is approximately 9.8 m/s^2. This force can be represented as 60 kg * 9.8 m/s^2 = 588 N.
2. Since the person is standing on the panel, they exert an equal and opposite force on it. This force is normal to the panel's surface. Let's call the magnitude of this force "F".
3. Now, let's consider the forces acting on the panel. At each support, there will be a vertical force acting upwards to counterbalance the weight of the person and the panel itself. Let's call the magnitude of the force at support "a" as "Fa" and the force at support "b" as "Fb".
4. Since the panel is in equilibrium, the sum of all vertical forces acting on it must be zero. This can be expressed as Fa + Fb - 588 N = 0.
5. Recall that the vertical support forces at each end are equal and opposite in magnitude since the panel is symmetric. Therefore, we can write Fa = Fb.
6. Solving the equation Fa + Fa - 588 N = 0, we find Fa = Fb = 294 N.
So, the expression for the magnitude of the force exerted by each support is 294 N, regardless of the person's position (x).
B) To determine the position where the table begins to separate from support "a", we need to analyze the forces acting on the panel when it is just about to lose contact with the support. At that moment, the vertical force at support "a" must be zero.
1. Consider the equilibrium of forces in the vertical direction. Since the person exerts a downward force of 588 N, and support "a" exerts an upward force "Fa", we can write:
Fa - 588 N = 0
2. Solving the equation, we find Fa = 588 N.
This means that when the force exerted by support "a" becomes less than 588 N, the table will begin to separate from support "a". The position at that instant can be determined by considering the person's weight distribution on the panel, the panel's deflection, and the support conditions, which require more information about the specific situation.
I hope this helps! Let me know if you have any further questions.