Calculate tension in a rope (pulley-rope-mass system)

In summary: The most-significant forces are the weight of each mass and the tension in each section of rope. The 3.0kg mass has the most acceleration, so it might be best to use that mass's force diagram to find the tension in the rope above it. Then use that tension to find the tension in the rope between the 2.0kg mass and the pulley. Finally, use the rope's tension to find the acceleration of the 2.0kg mass.In summary, the system of a 2.00-kg textbook and a hanging 3.00-kg book connected by a rope over a pulley is released from rest and observed to move 1.20m in
  • #1
MarliesM
3
0
Mhmm okay thanks, so if the rope had a mass, the two people would exert a force to make sure the rope didn't fall..

But now what about this (still can't solve a tension problem); a 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150m to a hanging book with mass 3.00 kg. The system is released from rest, and the books are observed to move 1.20m in 0.800s. (a) What is the tension in each part of the cord?

My attempt; before the system is released from rest, the tension equals 3.00 x 9.81 = 29.4 N. This is because the rope is in equilibrium and no forces act except at its ends, so the tension is the same at both ends and throughout the rope. (Right?)

But I don't understand what to do after the system starts moving. There is only one force acting, so the tension should be 3.00 x 2.00 x 9.81 = 58.9 N, but the answer is 7.5 N, 18.2 N.
 
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  • #2
Hi,

Since this is a specific physics problem, I have moved your post to the Homework & Coursework Questions area from the other thread where we were discussing rope tension.

... a 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150m to a hanging book with mass 3.00 kg. The system is released from rest, and the books are observed to move 1.20m in 0.800s. (a) What is the tension in each part of the cord?

My attempt; before the system is released from rest, the tension equals 3.00 x 9.81 = 29.4 N. This is because the rope is in equilibrium and no forces act except at its ends, so the tension is the same at both ends and throughout the rope. (Right?)
Well, the pulley could cause the two sections of rope to have different tensions.
But I don't understand what to do after the system starts moving. There is only one force acting, so the tension should be 3.00 x 2.00 x 9.81 = 58.9 N, but the answer is 7.5 N, 18.2 N.
A pulley can cause the two sections of rope to have different tensions, and that appears to be the case here. The same-tension-through-the-rope rule only applies to a section of rope that connects objects at each end; i.e. the 2.0kg-to-pulley section, and separately to the pulley-to-3.0kg section of rope.

To solve the problem, draw a force diagram for each mass, then relate the net force to the acceleration of that mass.
 

1. How do you calculate the tension in a rope?

To calculate the tension in a rope, you need to know the mass of the object being lifted, the acceleration due to gravity, and the angle of the rope. Then, you can use the formula T = mgcosθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle of the rope.

2. What is the difference between tension and weight?

Tension is the force exerted by a rope or string on an object, while weight is the force of gravity acting on an object. Tension can be greater or less than an object's weight depending on the angle and direction of the rope. Weight is always directed straight down towards the center of the Earth.

3. Can the tension in a rope ever be greater than the weight of an object?

Yes, the tension in a rope can be greater than the weight of an object if the rope is pulling at an angle. This is because the tension force is divided into two components: one that is perpendicular to the object's weight, and one that is parallel to the object's weight. The perpendicular component is equal to the weight, but the parallel component can be greater than the weight.

4. How does the number of pulleys affect the tension in a rope?

The number of pulleys in a system can affect the tension in a rope by changing the direction of the force being applied. Each additional pulley will change the direction of the force, resulting in a decrease in tension. However, if the pulleys are used to create a mechanical advantage, the tension in the rope can be increased.

5. Can the tension in a rope ever be zero?

No, the tension in a rope can never be zero as long as it is supporting an object. If the tension were to become zero, the object would fall due to the force of gravity. However, the tension can be reduced to a very small value if the angle of the rope approaches 90 degrees and the mass of the object is relatively light.

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