Problem applying Newtons third law

In summary, two people with a mass of 70kg each are wearing in-line skates and holding opposite ends of a 15m rope. One person pulls on the rope with a force of 35N, causing both of them to accelerate towards each other. Assuming negligible friction, it will take 5.5 seconds for them to meet. The correct tension in the rope is 35N and each person experiences a 35N force from the rope.
  • #1
Neil Melnick
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Homework Statement


Two people each with a mass of 70kg are wearing in line skates and holding opposite ends of a 15m rope. One person pulls forward on the rope by moving hand over hand and gradually reeling in more of the rope. In doing so, he exerts a force of 35N (backwards) on the rope. This causes him to accelerate toward the other person. Assuming that the friction on the skaters is negligible, how long will it take for them to meet? Explain.

Homework Equations


F=MA and D= T x init. Veloc.+ 0.5 AT²

The Attempt at a Solution


Book says 7.7, I say 5.5. Book splits the 35N between the two masses, I say equal and opposite means 35N acts on each. Consulted with several engineers, no consensus. Help!
 
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  • #2
Welcome to PF!

Your answer of 5.5 seconds is correct. The tension in the rope will be 35 N. Each person is acted on by a 35 N tension force from the rope.
 
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  • #3
There will be 35 N forces acting on both persons. There is no "splitting".
 
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1. What is Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert a force back on the first object that is equal in strength and opposite in direction.

2. How does Newton's Third Law apply to real-life situations?

Newton's Third Law can be seen in many everyday situations. For example, when you walk, your feet push against the ground, and the ground pushes back with an equal force, propelling you forward. Another example is when you push a door open, the door exerts an equal and opposite force on you, causing you to move backwards.

3. What is an example of a problem applying Newton's Third Law?

An example of a problem applying Newton's Third Law is when two objects with different masses collide. According to the third law, both objects will experience an equal force in opposite directions, but due to their different masses, their accelerations will be different. This can lead to difficulties in predicting the motion of the objects after the collision.

4. How can Newton's Third Law be used to solve problems?

To solve problems involving Newton's Third Law, it is important to identify the action and reaction forces and their directions. Then, using the law of conservation of momentum, the resulting accelerations of the objects can be calculated. This can help in predicting the motion of the objects and solving the problem.

5. How does Newton's Third Law relate to the other laws of motion?

Newton's Third Law is closely related to the first and second laws of motion. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The third law explains the forces that act on objects and how they interact with each other. The second law relates the force, mass, and acceleration of an object, which can be calculated using the principles of Newton's Third Law.

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