Question

A horizontal rope is tied to a 10 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

In the described scenarios on frictionless ice, the tension in the rope is 0 newtons when the box is at rest or moving at a constant velocity, and 50 newtons when it is accelerating at 5.0 m/s^2.

Step-by-step explanation:

When analyzing the tension in the rope in different scenarios, Newton's second law of motion provides the basis for our calculations. The law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.

Part A: If the 10 kg box is at rest on frictionless ice, the tension in the rope will be 0 newtons because no net force is required to maintain its state of rest.

Part B: If the box moves at a steady velocity of 4.0 m/s, the tension in the rope still remains 0 newtons. A constant velocity implies zero acceleration; thus, no net force is needed, which means no tension is developed in the rope.

Part C: When the box has a velocity of 4.0 m/s and an acceleration of 5.0 m/s2, the tension in the rope can be calculated using the equation Fnet = ma. With a mass m of 10 kg and acceleration a of 5.0 m/s2, the tension will be 10 kg * 5.0 m/s2 = 50 newtons.