Question

A rope of length L and mass m is suspended from the ceiling. Find an expression for the tension in the rope at position y, measured upward from the free end of the rope.

Answer 1

To find the tension in the rope at a position y measured upward from the free end of the rope, use the equation T = m * g * (L - y) / L.

Step-by-step explanation:

To find the tension in the rope at a position y measured upward from the free end of the rope, we need to take into account the weight of the rope and the mass m. The tension T at position y can be calculated using the equation:

T = m * g * (L - y) / L

where g is the acceleration due to gravity, L is the length of the rope, and y is the position measured upward from the free end of the rope.

Answer 2

The tension in a rope suspended from the ceiling can be found by considering the forces acting on the rope. At any position y along the rope, the tension can be calculated using the formula: T = mg + (m/L)ay. The tension at position y can be calculated as 5.4 N.

Step-by-step explanation:

The tension in a rope suspended from the ceiling can be found by considering the forces acting on the rope. At any position y along the rope, the tension can be calculated using the formula: T = mg + (m/L)ay, where T is the tension, m is the mass of the rope, g is the acceleration due to gravity, L is the length of the rope, and ay is the acceleration of the rope at position y.

For example, if the mass of the rope is 0.5 kg, the length of the rope is 2 meters, the acceleration due to gravity is 9.8 m/s², and the acceleration of the rope at position y is 2 m/s², the tension at position y can be calculated as follows:

T = (0.5 kg)(9.8 m/s²) + (0.5 kg/2 m)(2 m/s²) = 4.9 N + 0.5 N = 5.4 N

Therefore, the tension in the rope at position y is 5.4 Newtons.