Does Tarzan's Vine Hold During His Daring Swing?

[matt57017]

Homework Statement

Tarzan, who weighs 678 N, swings from a cliff at the end of a convenient vine that is 16.0 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 3.2 m. A) If the vine doesn't break, what is the maximum of the tension in the vine? B) The vine will break if the force on it exceeds 928.6 N. Does the vine break? If yes, at what angle does it break

Homework Equations

F=ma, Emec=Δk+ΔU, F=mv²/r

The Attempt at a Solution

A) here is my thought process to this problem, if i am wrong in my approach please correct me...tarzan starts at let's say point 1 with no potential energy, but has kinetic energy as he begins his swing. At the bottom of his swing (lowest point) will be where the max tension will occur. So, F=ma becomes F=mv²/r and you also have mgh=1/2mv² because he drops 3.2m so by figuring out the GPE and equating that to the final KE (bottoms of swing) you will derive the velocity at the bottom of the swing. i end up with F=mg(1+2h/r) and get 949.2 N which is correct.
B) i have no idea how to find the angle where it breaks at or even how to derive the formula...this is where i am hoping someone can guide me in the right direction (how to analyze the problem).

Thank you for your time!

 

[Yosty22]

tarzan starts at let's say point 1 with no potential energy

I believe that is an incorrect statement. I don't have the picture to go off of, but in the problem, it says he descends 3.2m, which means he would have had to have started at least 3.2m off the ground, if not more. In this case, he would have potential energy.

 

[matt57017]

Yosty,

that is true my fault. i have attached a picture for further clarification.

 

[Fluxthroughme]

I believe that is an incorrect statement. I don't have the picture to go off of, but in the problem, it says he descends 3.2m, which means he would have had to have started at least 3.2m off the ground, if not more. In this case, he would have potential energy.

You can define potential energy to be zero wherever you'd like, provided you're alright with using negatives.

 

[Nickie]

As a scientist, it is important to approach problems like this in a systematic and logical manner. Let's start by breaking down the problem into its components and identifying the key variables and equations that we can use to solve it.

First, we have the weight of Tarzan, which is given as 678 N. This is the force that is acting downwards on the vine.

Next, we have the length of the vine, which is 16.0 m. This will be important in calculating the tension in the vine.

We also have the height that Tarzan drops during his swing, which is 3.2 m. This will be used to calculate the velocity at the bottom of the swing.

Based on the given information, we can use the equation F=ma to calculate the force acting on the vine at the bottom of the swing. This will give us the maximum tension in the vine.

F=ma=678 N

Next, we can use the equation Emec=Δk+ΔU to calculate the velocity at the bottom of the swing. This equation takes into account the change in kinetic and potential energy as Tarzan swings. We know that at the top of the swing, Tarzan has no kinetic energy and all of his energy is in the form of potential energy. At the bottom of the swing, all of his potential energy is converted into kinetic energy.

Emec=Δk+ΔU

1/2mv2=mgh

Solving for v, we get v=√(2gh)

Plugging in the values for g (9.8 m/s^2) and h (3.2 m), we get v=6.32 m/s.

Now, we can use the equation F=mv2/r to calculate the maximum tension in the vine.

F=mv2/r

=678 N

Therefore, the maximum tension in the vine is 678 N.

Moving on to part B of the problem, we are given the maximum force that the vine can withstand before breaking, which is 928.6 N. This means that if the tension in the vine exceeds this value, the vine will break.

To determine if the vine breaks, we need to compare the maximum tension we calculated in part A (678 N) to the maximum force that the vine can withstand (928.6 N).

Since the maximum tension is less than the maximum force, the vine will not break.

To find the