A uniform beam of length L = 8.00 m and weight 3.80 102 N is carried by two workers, Sam and Joe, as shown in the figure below. Determine the force that each person exerts on the beam.
To determine the force that each person exerts on the beam, we can use the principle of equilibrium. Since the beam is in equilibrium, the sum of the forces acting on it must be zero.
First, let's consider the forces acting horizontally. There are two forces in the horizontal direction: the force exerted by Sam (Fs) and the force exerted by Joe (Fj). Since the beam is not moving horizontally, the sum of these forces must be zero:
Fs + Fj = 0
Next, let's consider the forces acting vertically. There are three forces in the vertical direction: the weight of the beam (W), the force exerted by Sam (Fs), and the force exerted by Joe (Fj). Since the beam is not moving vertically, the sum of these forces must also be zero:
W + Fs + Fj = 0
Given that the weight of the beam is 3.80 * 10^2 N and the length of the beam is 8.00 m, we can calculate the weight using the formula:
Weight = Mass * gravity
where
Mass = Weight / gravity
Gravity = 9.8 m/s^2 (approximate acceleration due to gravity)
Let's calculate the weight:
Mass = 3.80 * 10^2 N / 9.8 m/s^2 = 38.78 kg (approximate)
Now, let's substitute the values into the equations:
Fs + Fj = 0
W + Fs + Fj = 0
Substituting the weight value:
38.78 kg + Fs + Fj = 0
Simplifying the equation:
Fs + Fj = 0
Fs + Fj = -38.78 kg
Now, we have two equations and two unknowns. We can solve them simultaneously to find the values of Fs and Fj.