Tarzan's Vine Dilemma: Will the Rope Break? | Simple Physics Homework Solution

[zim70094]

Homework Statement

Tarzan has a mass of 80 kg. Starting from rest. He swings over a river, on a vine of length 4m long. However, the vine will break if its tension exceeds 100 N. Will the vine break?

Homework Equations

(total) F=ma ... (in both directions?)
Newton's second law.
W=FD=mgh(final)-mgh(intial)

The Attempt at a Solution

At first I thought to find the acceleration using Newton's second law( Tmax=100N, m=80kg, g=9.81 m/s^2. I used the formula T-mg=ma and got an acceleration of 2.69.

...I then thought to use the formula for work and got 3139.2 J (80kg*9.81m/s^2*4m)

I'm just completely stuck at this point. It seems like I need to find velocity but I can't come up with a good answer. I also thought to maybe find the tension used, but I can't seem to find an answer that way ether. I've also tried finding the weight that the max force can handle but that doesn't work for me. I just seem to be going in circles. I think this is simple I'm just forgetting something.
SOLUTION UPDATE?

I just had an idea. since I used W=mgh (3139.2 J) ... can I use W=fd (all in the y direction) so W=(T-mg)(4m) ... (3139.2J / 4m) + (80kg*9.81m/s^2) ... (W/m) + mg = T ... T=1569.6 N COuld that be the answer? resulting in the rope breaking?

 

[gneill]

Homework Statement

Tarzan has a mass of 80 kg. Starting from rest. He swings over a river, on a vine of length 4m long. However, the vine will break if its tension exceeds 100 N. Will the vine break?

Homework Equations

(total) F=ma ... (in both directions?)
Newton's second law.
W=FD=mgh(final)-mgh(intial)

The Attempt at a Solution

At first I thought to find the acceleration using Newton's second law( Tmax=100N, m=80kg, g=9.81 m/s^2. I used the formula T-mg=ma and got an acceleration of 2.69.

...I then thought to use the formula for work and got 3139.2 J (80kg*9.81m/s^2*4m)

I'm just completely stuck at this point. It seems like I need to find velocity but I can't come up with a good answer. I also thought to maybe find the tension used, but I can't seem to find an answer that way ether. I've also tried finding the weight that the max force can handle but that doesn't work for me. I just seem to be going in circles. I think this is simple I'm just forgetting something.



SOLUTION UPDATE?

I just had an idea. since I used W=mgh (3139.2 J) ... can I use W=fd (all in the y direction) so W=(T-mg)(4m) ... (3139.2J / 4m) + (80kg*9.81m/s^2) ... (W/m) + mg = T ... T=1569.6 N COuld that be the answer? resulting in the rope breaking?

Is that really the complete problem statement as given? It seems to leave a lot of things unspecified. For example, details which would pin down the change in height over the arc of the swing so that maximum velocity might be found...

 

[zim70094]

Yes that is the whole problem. I believe the professor is saying it is a pendulum maybe? this is from a test the professor gave out last year.

 

[gneill]

Was there a diagram included with additional information?

 

[zim70094]

no there is no diagram. Although after reading a bit i believe I need to use the centripetal force at least for the lowest point on the rope swing. (which I guess should be the max tension area?) so T-mg=m*(v^2/r) ... but how do I find the velocity?

 

[gneill]

no there is no diagram. Although after reading a bit i believe I need to use the centripetal force at least for the lowest point on the rope swing. (which I guess should be the max tension area?) so T-mg=m*(v^2/r) ... but how do I find the velocity?

That's why I asked. You need to know the change in height through the swing in order to find the maximum velocity (read: kinetic energy) and thus centripetal force at the bottom of the arc. The radius of the arc is given as the length of the vine, but you need to know the starting elevation of Tarzan above the lowest point of the arc or the total angle of the swing, or some data that will let you know the change in elevation through the arc so that you can calculate the speed, and hence the centripetal force, of Tarzan at the lowest point (Be sure to include the effect of gravity on the total force!).

If the Problem Statement is just as you've specified and no more, then that information is not available and you would have to make assumptions instead (a dangerous proposition for questions which are to be marked and counted towards your final grade!).

 

[NascentOxygen]

Homework Statement

Tarzan has a mass of 80 kg. Starting from rest. He swings over a river, on a vine of length 4m long. However, the vine will break if its tension exceeds 100 N. Will the vine break?

I wonder whether that vine can support Tarzan's weight?

 

[Nlc11]

I think that this is a trick question. Tarzan's weight is approximately 800 N (784 N to be more precise). The vine would not support his weight in the first place.

 

[zim70094]

I think it is assumed he started at 0 then went to 0 during the swing so he traveled to the other side of the circle (8 total)? that's really all the information provided. how would you find velocity if you had distance?

 

[Nlc11]

I think it is assumed he started at 0 then went to 0 during the swing so he traveled to the other side of the circle (8 total)? that's really all the information provided. how would you find velocity if you had distance?

I don't think this problem is that complex. Tarzan has a mass of 80kg, therefore his weight is around 800N, a little less in reality. The rope will only hold 100N. Without even swinging, the rope will break.

 

[gneill]

I wonder whether that vine can support Tarzan's weight?

Ah! Excellent catch. I should've seen that

 

[NascentOxygen]

I don't think this problem is that complex. Tarzan has a mass of 80kg, therefore his weight is around 800N, a little less in reality.

But what value is $g$ on the Planet of the Apes?

 

[Orodruin]

But what value is $g$ on the Planet of the Apes?

Tarzan lives in Africa ... :P