Newton's Third Law Problem - Tightrope

In summary, Newton's Third Law states that for every action, there is an equal and opposite reaction. This applies to all objects, including those in motion and at rest. Examples of this law can be seen in everyday situations, such as walking or sitting in a chair. Newton's Third Law is a proven fundamental law of physics and is essential for understanding the interactions between objects and their motion.
  • #1
danshawvassar
1
0

Homework Statement



A 66.0 kg tightrope walker stands at the center of a rope. The rope supports are 10 m apart and the rope sags 9.00* at each end. The tightrope walker crouches down, then leaps straight up with an acceleration of 8.40 m/s2 to catch a passing trapeze.

What is the tension in the rope as he jumps?

Homework Equations



F=ma

The Attempt at a Solution



I literally have no idea how to solve this problem whatsoever. I was thinking that the y-component of the tension (T*sin(9) N) minus the weight of the man (646.8 N) is equal to the man's mass times his acceleration.

So: Tsin9 - 646.8 = 66 * 8.4
Or: T=7678.6 N

I don't think this is right though.
 
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  • #2
welcome to pf!

hi danshawvassar! welcome to pf! :smile:

(award yourself a degree: ° :wink:)

when he straightens his legs, his centre of mass accelerates upward, so there must be a downward force by his feet on the rope, and an equal upward force by the rope on his feet

that is the force you need to find, and then find the (extra) tension that will produce that upward force :smile:
 

Related to Newton's Third Law Problem - Tightrope

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 an object exerts a force on another object, the second object will exert an equal force in the opposite direction.

2. How does Newton's Third Law apply to the tightrope problem?

In the tightrope problem, the tightrope walker exerts a downward force on the rope, while the rope exerts an equal and opposite upward force on the walker. This allows the walker to maintain their balance and stay on the rope.

3. Is Newton's Third Law limited to just objects in motion?

No, Newton's Third Law applies to all objects, regardless of whether they are in motion or not. The forces may not always be noticeable, but they are always present.

4. Can you give an example of Newton's Third Law in everyday life?

One example is when you walk. As your foot pushes against the ground, the ground exerts an equal and opposite force back on your foot, propelling you forward. Another example is when you sit in a chair. Your weight pushes down on the chair, while the chair pushes up on you with an equal force.

5. Is Newton's Third Law always true?

Yes, Newton's Third Law is a fundamental law of physics and has been proven to be true in countless experiments and observations. It is a crucial concept in understanding the interactions between objects and their motion.

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