Newton's Law question -> Tension

In summary, there is a question regarding Newton's Law and tension in an inextensible rope. The answer, according to the teacher, is A because the rope cannot stretch and the two individuals are treated as separate systems. However, the student initially believed the answer was D by treating the two as one system and calculating the acceleration. The conversation also mentions the importance of Newton's third law and the external force affecting the center of mass. Ultimately, it is determined that the answer is A and the two individuals must reel in the rope as they accelerate to maintain a constant force of 100N.
  • #1
nguyentech
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0
Newton's Law question --> Tension

Attached in this message is a question from my school pastpaper... I believe the answer is D... This is because I took John and Joan as one system... Therefore their mass is 130kg (together)...
F = ma
100 = 130*a
a = 0.77 each

However, my teacher says its A, she took the question as two separate systems... I don't think that's right... because it says "inextensible rope" therefore it cannot be stretched.. therefore they can't accelerate at different speeds otherwise it will be stretched... is my logic correct?
 

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  • #2
No, I'm afraid your teacher is correct. It's a good idea to remember Newtons third law in this case.
 
  • #3
No, I'm afraid your teacher is correct.

Don't you hate when that happens?

If you REALLY treated the two as a single system you would have come to the conculusion that there is NO acceleration because there is no external force.

Because there is no external force, the center of mass of the system must remain fixed.

The rope is inextensible so the two cannot move farther apart but they CAN move closer together!

John pulls with (and is pulled by- Newton's third law) a force of 100 N. His mass is 80 kg so his acceleration is 100/80= 1.25 m/sec^2

Joan is pulled by a force of 100 N. Her mass is 50 kg so his acceleration is 100/50= 2 m/ sec^2.
 
  • #4
Its a little bit of a trick question. For starters if Joan is pulling with a force of 100N then John also must be pulling with a force of 100N.

Also, whether or not the rope can stretch is irrelevant - John and Joan are doing whatever is necessary to keep the force a constant 100n (which means reeling it in as they accelerate).
 

1. What is Newton's Law of Tension?

Newton's Law of Tension states that the tension in a string or rope is always equal to the force applied on either end of the string or rope. This means that if an object is being pulled in opposite directions by two equal forces, the tension in the string will be equal to the force applied by either force.

2. How is tension related to Newton's Second Law?

In Newton's Second Law, force is equal to mass multiplied by acceleration (F=ma). Tension is a type of force, and according to Newton's Law of Tension, it is equal to the force applied on either end of a string or rope. Therefore, tension is directly related to Newton's Second Law.

3. How does tension affect an object's motion?

Tension can affect an object's motion in different ways depending on the situation. In some cases, tension can act as an equal and opposite force to another force, keeping an object stationary or in equilibrium. In other cases, tension can cause an object to accelerate in the direction of the tension force.

4. What factors can affect the tension in a string or rope?

The tension in a string or rope can be affected by factors such as the force applied on either end, the mass of the object being pulled, and the angle at which the string or rope is being pulled. Friction and the material properties of the string or rope can also affect tension.

5. How is tension used in real-world applications?

Tension is used in many real-world applications, such as in engineering and construction to support and stabilize structures. Tension is also used in sports equipment, such as in the strings of a tennis racket, to provide the necessary force for the ball to bounce off the racket. In physics experiments, tension is often used to demonstrate the principles of Newton's Laws of Motion.

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