Consider two masses that hang from an overhead beam. The first mass of 86.4 kg is attached to the beam using an ideal rope. The second mass of 20.8 kg is attached to the first mass with an ideal rope and hangs directly under the first mass.
(a) Find the tension in the lower rope.
b) Find the tension of the upper rope
On earth I assume
weight on first line = (86.4+20.8)(9.81)
weight on second (lower) line = 20.8 (9.81)
To find the tension in the lower rope and the tension in the upper rope, we can make use of the concept of equilibrium for each mass.
(a) Finding the tension in the lower rope:
The tension in the lower rope is equal to the weight of the second mass. This is because the second mass is hanging directly under the first mass and is not providing any additional force in the horizontal direction.
The weight of an object can be calculated using the formula:
Weight = mass * gravitational acceleration
Given that the mass of the second object is 20.8 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight of the second mass as:
Weight = 20.8 kg * 9.8 m/s^2 = 203.84 N
Therefore, the tension in the lower rope is 203.84 N.
(b) Finding the tension in the upper rope:
To find the tension in the upper rope, we need to consider the equilibrium of the first mass. Since the first mass is attached to the beam using an ideal rope and the second mass is hanging directly under it, the tension in the upper rope must balance the combined weights of both masses.
The combined weight of the masses can be calculated by adding their individual weights.
Weight of the first mass = mass * gravitational acceleration
Weight of the first mass = 86.4 kg * 9.8 m/s^2 = 846.72 N
Weight of the second mass = 20.8 kg * 9.8 m/s^2 = 203.84 N
The total weight (combined weight) is the sum of the weights of the two masses:
Combined weight = 846.72 N + 203.84 N = 1050.56 N
Since the tension in the upper rope balances the combined weight, the tension in the upper rope is also 1050.56 N.
Therefore, the tension in the upper rope is 1050.56 N.