A <69.0> kg construction worker is standing on an 18.0 kg plank. The plank is <12.50> m long and it is suspended by vertical cables at each end. If the worker stands 2.80 from the right end of the plank, what is the tension in right cable? Give your answer in newtons (N) and with 3 significant figures.
let tension right and left=Tr,Tl
Tr+Tl=69*g
now sum of moments about the right end..
69g*2.8+Tl*12.5=0
solve for Tl in that equation, then go back to the first equaion, and solve for Tr
To find the tension in the right cable, we need to analyze the forces acting on the plank and the construction worker.
First, let's calculate the weight of the construction worker and the plank separately. The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity
For the construction worker:
Weight of worker = mass of worker × acceleration due to gravity
= (69.0 kg) × (9.81 m/s²)
≈ 676.89 N (rounded to 3 significant figures)
For the plank:
Weight of plank = mass of plank × acceleration due to gravity
= (18.0 kg) × (9.81 m/s²)
≈ 176.58 N (rounded to 3 significant figures)
Now let's determine the center of gravity (CG) of the combined system of the worker and the plank. We can use the formula:
CG = (distance to CG of worker × weight of worker + distance to CG of plank × weight of plank) / (weight of worker + weight of plank)
Since the CG of the worker is located at a distance of 2.80 m from the right end of the plank, and the CG of the plank is at its center (6.25 m from either end), we can substitute these values into the formula:
CG = (2.80 m × 676.89 N + 6.25 m × 176.58 N) / (676.89 N + 176.58 N)
≈ 3.528 m (rounded to 3 significant figures)
Now, let's analyze the forces acting on the plank and the worker. There are three forces to consider:
1. The weight of the plank acting downward, which is equal to 176.58 N.
2. The weight of the worker acting downward, which is equal to 676.89 N.
3. The tension in the right cable acting upward.
Since the plank is in equilibrium, the sum of the forces in the vertical direction must be zero. Therefore, the tension in the right cable must be equal to the sum of the weights of the plank and the worker. The tension in the right cable is given by the formula:
Tension in right cable = weight of plank + weight of worker
= 176.58 N + 676.89 N
= 853.47 N (rounded to 3 significant figures)
Therefore, the tension in the right cable is approximately 853.47 N.