Question

A horizontal rope is tied to a 80 kg box on frictionless ice. Part A What is the tension in the rope if the box is at rest? Express your answer in newtons. Part B What is the tension in the rope if the box moves at a steady 4.0 m/s ? Express your answer in newtons. Part C What is the tension in the rope if the box has vx = 4.0 m/s and ax = 5.0 m/s² Express your answer in newtons.

Answer 1

The tension in the rope when the box is at rest is 784 N. When the box moves at a steady 4.0 m/s, the tension in the rope is still 784 N. If the box has a velocity of 4.0 m/s and an acceleration of 5.0 m/s², the tension in the rope is 1184 N.

Step-by-step explanation:

Part A: The tension in the rope when the box is at rest is equal to the weight of the box. The weight can be calculated using the formula W = mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s²). Therefore, the tension in the rope is T = 80 kg * 9.8 m/s² = 784 N.

Part B: When the box moves at a steady 4.0 m/s, there is no acceleration. This means that the net force acting on the box is zero. The tension in the rope is still equal to the weight of the box, which is 784 N.

Part C: In this case, the box has a velocity of 4.0 m/s and an acceleration of 5.0 m/s². The net force acting on the box can be calculated using the formula Fnet = ma, where m is the mass of the box and a is the acceleration. Rearranging the formula to solve for tension, we get T = Fnet + W. Plugging in the values, T = (80 kg * 5.0 m/s²) + (80 kg * 9.8 m/s²) = 400 N + 784 N = 1184 N.