A staging that weighs 410 N supports two
painters, one 450 N and the other 510 N. The
reading in the left scale is Fℓ = 470 N .
What is the reading Fr in the right hand
scale?
Answer in units of N.
the sum of the two scales shows the total load
To find the reading in the right-hand scale, we can use the principle of equilibrium. According to the principle of equilibrium, the sum of the forces acting on the staging must be zero.
Let's denote the reading in the right-hand scale as Fr.
In this case, we have two forces acting on the left side of the staging: the weight of the staging itself (410 N) and the weight of the first painter (450 N). These two forces create a clockwise moment.
On the right side of the staging, we have the weight of the second painter (510 N) and the unknown force measured by the right-hand scale (Fr). These two forces create a counterclockwise moment.
Since the staging is in equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
(clockwise moment) = (counterclockwise moment)
(410 N + 450 N) x (distance from the left side to the center of mass) = (510 N + Fr) x (distance from the right side to the center of mass)
Assuming that the center of mass is at the center of the staging, the distances from the left and right sides to the center of mass are equal. Therefore:
(410 N + 450 N) = (510 N + Fr)
860 N = 510 N + Fr
Fr = 860 N - 510 N
Fr = 350 N
Therefore, the reading in the right-hand scale (Fr) is 350 N.
To find the reading in the right hand scale (Fr), we can use the principle of equilibrium. According to this principle, the sum of all the forces acting on an object at rest must be zero.
In this case, the staging is at rest, which means the sum of the forces acting on it is zero. We have three forces acting on the staging: the weight of the staging (410 N), the weight of the first painter (450 N), and the weight of the second painter (510 N). The reading on the left scale (Fℓ) is given as 470 N.
Using these values, we can set up the following equation:
Fℓ + Fr - (Weight of the staging) - (Weight of the first painter) - (Weight of the second painter) = 0
Substituting the given values:
470 N + Fr - 410 N - 450 N - 510 N = 0
Simplifying the equation:
470 N + Fr - 1370 N = 0
Rearranging the equation to solve for Fr:
Fr = 1370 N - 470 N
Fr = 900 N
Therefore, the reading in the right hand scale (Fr) is 900 N.