Calculating Tension in Rope as Student B Accelerates

Student A to be lifted off the ground.In summary, the conversation discusses the forces and tensions involved in a scenario where two students, A and B, are holding onto opposite ends of a rope attached to a pulley. Student B then starts climbing up the rope with a constant acceleration, and the conversation explores the minimum acceleration needed for Student A to be lifted off the ground.
  • #1
cflemer
2
0

Homework Statement


A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling. One end of the rope is held by Student A of mass 70 kg, who is at rest above the floor. the opposite end of the rope is held by Student B of mass 60 kg, who is suspended at rest above the floor.

a. Calculate the magnitude of force exerted by the floor on Student a.

Student B now climbs up the rope at a constant acceleration of .25 m/s^2 with respect to the floor.
b. Calculate the tension in the rope while Student B is accelerating.

c. As Student B is acceleration, is Student A pulled upward off the floor? Justify your answer.

d. With what minimum acceleration must Student B climb up the rope to life Student A upward off the floor?

Homework Equations


Ma=70 kg
Mb= 60 kg

Attempt:
(a)F=ma
F=(130 kg) (9.81 m/s^2)
F= 1,275.3 N

d. No, Student B has a smaller mass than student A, thus they will not be able to lift A off the ground.
 
Last edited:
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  • #2
b. T=maT=(130 kg) (0.25 m/s^2)T= 32.5 Nd. The minimum acceleration must be the acceleration of Student A, 9.81 m/s^2
 

1. What is tension in a rope?

Tension is a force that is applied to an object by a rope or cable when it is pulled tight. It is a pulling force that acts in both directions along the rope.

2. How do you calculate tension in a rope?

To calculate tension in a rope, you need to know the mass of the object being pulled, the acceleration of the object, and the angle of the rope. You can then use the formula T = (m x a) / cosθ, where T is tension, m is mass, a is acceleration, and θ is the angle of the rope.

3. What is the difference between static and dynamic tension?

Static tension is the force applied to an object by a stationary rope, while dynamic tension is the force applied by a moving rope. In the case of calculating tension in a rope as a student accelerates, we are dealing with dynamic tension.

4. How does student B's acceleration affect the tension in the rope?

As student B accelerates, the tension in the rope will increase. This is because an increase in acceleration means an increase in the force being applied to the object, which in turn increases the tension in the rope.

5. What other factors can affect tension in a rope?

Aside from the mass, acceleration, and angle of the rope, other factors that can affect tension include the length and thickness of the rope, as well as any external forces acting on the object being pulled.

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