A uniform beam of length 7.60 m and weight 4.30 102 N is carried by two workers, Sam and Joe, as shown in the figure below.
(a) Determine the forces that each person exerts on the beam.
F_Sam = ___ N
F_Joe = ___ N
Points:
left end - A, Sam - B, center of mass - C , Joe - D , right end - E
Torques about the point B:
mg•BC –F(J) •BD =0
F(J) =mg•BC/BD= 430•2.8/4.6 = 261.7(N)
Torques about the point D
F(S) •BD - mg•CD = 0
F(S)= mg•CD/BD = 430•1.8/4.6=168.2N
To determine the forces that Sam and Joe exert on the beam, we first need to consider the equilibrium of forces acting on the beam.
In this case, we have two forces acting on the beam: the weight of the beam and the forces exerted by Sam and Joe. The weight of the beam acts downward and can be calculated as the product of its weight and the acceleration due to gravity:
Weight of the beam = 4.30 * 10^2 N
Since the beam is in equilibrium, the sum of the forces on the beam must be zero. In other words, the upward forces exerted by Sam and Joe must balance the downward force of the weight of the beam.
Let's assume that Sam is holding the beam at a distance of x meters from one end, and Joe is holding it at a distance of L - x (where L is the length of the beam) from the same end.
The forces exerted by Sam and Joe can then be determined using the principle of moments (also known as torque). The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the counterclockwise moments about the same point.
Applying the principle of moments:
Clockwise moments = Counter-clockwise moments
The clockwise moment is the weight of the beam acting at its center of gravity (which is L/2) and the counter-clockwise moment is the sum of the forces exerted by Sam and Joe at their respective distances from the same end of the beam.
Clockwise moment = Weight of the beam * (L/2)
Counter-clockwise moment = Force exerted by Sam * x + Force exerted by Joe * (L - x)
Setting up the equation:
Weight of the beam * (L/2) = Force exerted by Sam * x + Force exerted by Joe * (L - x)
Now we can solve this equation to find the forces exerted by Sam and Joe.
Let's substitute the known values:
Weight of the beam = 4.30 * 10^2 N
L = 7.60 m
Weight of the beam * (L/2) = Force exerted by Sam * x + Force exerted by Joe * (L - x)
(4.30 * 10^2 N) * (7.60 m / 2) = Force exerted by Sam * x + Force exerted by Joe * (7.60 m - x)
Simplifying the equation:
(215 * 10^2) N*m = Force exerted by Sam * x + Force exerted by Joe * (7.60 m - x)
Since we do not know the exact values of x, we cannot determine the individual forces exerted by Sam and Joe. We would need additional information or constraints to solve for the forces specifically.