Question

A 55.0 kg box hangs from a rope. What is the tension in the rope if: Part A The box is at rest? Express your answer with the appropriate units. Part B The box moves up a steady 4.90 m/s ? Express your answer with the appropriate units. Part C The box has vy = 4.60 m/s and is speeding up at 4.90 m/s2 ? The y axis points upward. Express your answer with the appropriate units. Part D The box has vy = 4.60 m/s and is slowing down at 4.90 m/s2 ? Express your answer with the appropriate units.

Answer 1

Part (A)

The tension in the rope when the mass is at rest is 539 N.

If the mass isn't accelerating, the tension force has to equal the weight of the mass or mg, which is (55)(9.8) = 539 N.

Part (B)

The tension in the rope when the mass is at the constant velocity is 539 N.

The tension in the rope when the mass is at constant velocity is the same as the tension when the mass is at rest because there is no acceleration.

Part (C)

The tension in the rope when the mass is accelerating upward at 4.9 m/s2 is 808.5 N.

The product of mass and acceleration is added to the weight of the mass.

T=(55)(4.9)+(55)(9.8)

T=808.5N

Part (D)

The tension in the rope when the mass is accelerating in the opposite direction of its velocity is 269.5 N.

The product of the mass and acceleration is subtracted from the mass's weight since the acceleration is in the opposite direction of the mass's velocity.

T=(55)(−4.9)+(55)(9.8)T = 269.5 N

In case of any doubt, please comment sir.