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
Sure, I can help you with that!
To find the expression for the magnitude of the force exerted by each support in function of x (the position of the person), we need to analyze the forces acting on the panel.
Let's say the distance between supports a and b is L, and the position of the person is x (measured from support a).
A) To find the expression for the force exerted by each support, we need to consider the equilibrium of forces in the vertical direction. At any position x, the sum of the vertical forces acting on the panel should be zero.
Let's denote the force exerted by support a as Fa and the force exerted by support b as Fb.
Vertical forces acting on the panel:
1. The weight of the person (60 kg): Fp = mg (where g is the acceleration due to gravity, approximately 9.8 m/s^2).
2. The vertical component of the reaction force at support a: Ra. Since support a is perpendicular to the panel, Ra acts vertically upward.
3. The vertical component of the reaction force at support b: Rb. Since support b is perpendicular to the panel, Rb acts vertically upward.
Equilibrium condition:
Fa + Fb + Ra + Rb - Fp = 0
Now, let's consider the deformation of the table. When the person walks on the board from point a, the board will deform, and the distance between supports a and b will change.
At the instant when the table begins to separate from support a (when the person reaches the end of the board), the force exerted by support a becomes zero. This means that Ra = 0.
B) To find the position of the person at that instant, we need to find the value of x when Ra = 0.
By substituting Ra = 0 into the equilibrium condition mentioned earlier, we get:
Fa + Fb + Rb - Fp = 0
Since Ra = 0, the term containing Ra is eliminated.
Now, you mentioned that you have tried finding the net force but couldn't do it. However, by using the equilibrium condition and substituting the appropriate values (m, g, Fa, Fb, Rb, Fp), you should be able to solve for the expressions for Fa and Fb as functions of x.
If you provide the specific values for the constants and any attempt you made to solve for Fa and Fb, I can help you further with the calculations.