Two people are holding up the ends of a 4.40-kg wooden board that is l = 1.95 m long. A m = 2.00-kg box sits on the board, 0.50 m from one end, as shown below. What forces do the two people exert?
To find the forces that the two people exert on the wooden board, you need to use the principle of equilibrium. According to this principle, the sum of all the forces acting on an object must be zero.
In this case, there are three forces acting on the wooden board: the weight of the board itself, the weight of the box, and the forces exerted by the two people. Since the board is not moving vertically, the sum of the vertical forces must be zero.
First, let's find the weight of the board. The weight is equal to the mass of the object multiplied by the acceleration due to gravity (g ≈ 9.8 m/s^2). The weight of the board is calculated as:
Weight of the board = mass of the board × acceleration due to gravity
Weight of the board = 4.40 kg × 9.8 m/s^2 = 43.12 N
Next, let's find the weight of the box. Similarly, the weight of the box can be found using the mass of the box and the acceleration due to gravity:
Weight of the box = mass of the box × acceleration due to gravity
Weight of the box = 2.00 kg × 9.8 m/s^2 = 19.6 N
Since the box is 0.50 m from one end of the board, we could treat the forces exerted by the two people as a linear system, and we will assume that they pull or push the board upwards. So we will refer to the forces as upward forces.
Let's assume the force exerted by one person is F1 and the force exerted by the other person is F2.
To set up the equation based on the equilibrium principle, we need to consider both the vertical and horizontal forces. Taking the clockwise direction as positive:
∑Fx = F2 - F1 = 0 (The board is not moving horizontally)
∑Fy = F1 + F2 - weight of the board - weight of the box = 0 (The board is not moving vertically)
From the first equation, we can determine that F1 = F2.
Substituting F1 for F2 in the second equation, we get:
2F1 - (43.12 N + 19.6 N) = 0
Simplifying the equation:
2F1 - 62.72 N = 0
2F1 = 62.72 N
F1 = 31.36 N
Since F1 = F2, the force exerted by each person will be 31.36 N.
Therefore, the two people will exert a force of 31.36 N each on the wooden board.