Finding max force at bottom of a 2.8m decline swinging on a vine?

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In summary, Tarzan weighing 662 N swings from a cliff with a convenient vine of 21 m long, descending 2.8 m. The vine can only withstand a force of 1340 N. To find the greatest force on the vine during the swing, we need to find the tension in the vine at the greatest acceleration and velocity. Using the equations F=ma and a=\frac{V^2}{r}, we can find the greatest acceleration and velocity. By using both PE=mgh and KE=\frac{1}{2}mV^2, we can find the energy gained and velocity at that energy. Adding the force due to swinging and gravity, we can determine the greatest force on the vine during the
  • #1
rockchalk1312
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Tarzan, who weighs 662 N, swings from a cliff at the end of a convenient vine that is 21 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 2.8 m. The vine will break if the force on it exceeds 1340 N. What would the greatest force on the vine be during the swing?


PE=mgh
KE=1/2mv2


Not sure which equation to use here...

Thank you!
 
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  • #2
You're looking for the tension in the vine. Draw a diagram showing all the forces and proceed from there.
 
  • #3
Greatest force is at the largest acceleration.

[itex]F=ma[/itex]
[itex]a=\frac{V^2}{r}[/itex]
[itex]F=\frac{mV^2}{r}[/itex]

∴ Greatest acceleration is at the greatest velocity.

You will need both ##P.E=mgh## and ##K.E=\frac{1}{2}mV^2##
##P.E## to find the energy gained and you will need to rearrange ##K.E## to find the velocity at that energy.

If he decends 2.8m ##h=2.8##

That is the force due to swinging, you must also add on gravity [itex]F=mg[/itex]
 

Related to Finding max force at bottom of a 2.8m decline swinging on a vine?

1. What is the purpose of finding the maximum force at the bottom of a 2.8m decline while swinging on a vine?

The purpose of finding the maximum force is to ensure the safety and stability of the swing and its rider. It also helps in determining the strength and durability of the vine and other materials used in the construction of the swing.

2. How is the maximum force calculated?

The maximum force can be calculated by using the formula F = m * a, where F is the force, m is the mass of the rider, and a is the acceleration due to gravity. In this case, a = 9.8 m/s² as the swing descends down the decline.

3. What factors can affect the maximum force at the bottom of the decline?

The maximum force can be affected by the weight of the rider, the length and type of the vine, the angle of the decline, and external forces such as wind and friction.

4. What safety precautions should be taken when conducting this experiment?

It is important to ensure that the vine and other materials used in the swing are strong and in good condition. The rider should also wear appropriate safety gear, and the experiment should be conducted in a controlled and supervised environment.

5. How can the results of this experiment be used in real-life applications?

The results of this experiment can be used to design and construct safe and stable swings, zip lines, and other recreational activities that involve swinging and descending on a decline. It can also be applied in engineering and construction to determine the maximum force and stress on materials in similar situations.

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