A construction worker on a high-rise building is on a platform suspended between two cables as illustrated below. The construction worker weighs 850 N, the plank weighs 450 N, and the tension in the left cable is 550 N.
a. What is the tension (in N) in the right cable?
b. Explain your answer.
What is the answer
a. To find the tension in the right cable, we need to consider the forces acting on the platform.
Let's label the tension in the right cable as T2.
The forces acting on the platform are:
1. The weight of the construction worker (850 N) acting downwards.
2. The weight of the plank (450 N) acting downwards.
3. The tension in the left cable (550 N) acting upwards.
4. The tension in the right cable (T2) acting upwards.
Since the platform is in equilibrium (not accelerating), the sum of the vertical forces must be zero.
So, the equation for the vertical forces can be written as:
T2 - (850 N + 450 N) + 550 N = 0
Simplifying the equation:
T2 - 1300 N + 550 N = 0
T2 - 750 N = 0
T2 = 750 N
Therefore, the tension in the right cable is 750 N.
b. The tension in the right cable is 750 N because the sum of the vertical forces acting on the platform must be zero for it to be in equilibrium. Since the construction worker's weight, the plank's weight, and the tension in the left cable act downwards, the tension in the right cable must be equal and opposite to balance these forces. Hence, the tension in the right cable is 750 N.
a. To find the tension in the right cable, we can use the principle of equilibrium. According to this principle, the sum of the forces acting on the construction worker and the plank must be zero if they are not accelerating.
Let's consider the forces acting on the construction worker and the plank. In this case, there are three forces involved: the weight of the construction worker (Ww), the weight of the plank (Wp), and the tension in the left cable (Tl).
The weight of the construction worker and the plank act vertically downwards. Therefore, the total downward force is the sum of their weights, which is given by:
Total downward force = Ww + Wp
The tension in the left cable acts diagonally upwards and to the left. Since the forces acting vertically upwards cancel out the vertical downward forces, the net vertical force is zero. This implies that the tension in the right cable must balance out the net horizontal force created by the tension in the left cable.
Hence, the tension in the right cable can be found by subtracting the horizontal component of the tension in the left cable from the total horizontal force, which is:
Total horizontal force = Tl x cos(θ)
where θ is the angle between the cables.
b. To determine the tension in the right cable, we need to know the angle between the cables. Once we have this information, we can use trigonometric functions to calculate the horizontal component of the tension in the left cable. Finally, subtracting this value from the total horizontal force, we can find the tension in the right cable.
5. A construction worker on a high-rise building is on a platform suspended between two cables as illustrated below. The construction worker weighs 850 N, the plank weighs 450 N, and the tension in the left cable is 550 N.
a. What is the tension (in N) in the right cable?