Find max mass regarding circular motion and tension

In summary, the question asks for the maximum mass Tarzan can have while safely crossing a river using a 10.0 m vine with a breaking strength of 1.0 x 10^3 N. The solution involves finding the centripetal acceleration of Tarzan, ensuring it does not exceed the vine's breaking strength, and ultimately solving for Tarzan's maximum mass.
  • #1
freepancakes
5
0

Homework Statement


This is the question straight from my worksheet...

Tarzan tries to cross a river by swinging a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 X 10^3 N. What is the largest mass Tarzan can have and make it safly across the river?


Homework Equations



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The Attempt at a Solution


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  • #2
The tension T balances the weight mg and provides the required centripetal force mv^2/R both.
 
  • #3
Find the centripetal force acting on Tarzan and his weight, and equate it to the breaking strength of the vine.
 
  • #4
is the answer 15.625 Kg?
 
  • #5
freepancakes said:
is the answer 15.625 Kg?
How did you get that answer. Please show.
 
  • #6
First and foremost, you need to solve for centripetal acceleration of Tarzan. Also, we are assuming that Tarzan is traveling at a constant velocity, or else the centripetal acceleration is changing, in which the problem requires a lot more work, so I'll assume that Tarzan is traveling at a constant velocity throughout the swing.

In that case, centripetal acceleration is v^2 / R. v being the velocity, and R being the radius. I won't show you the work, but from there you solve for acceleration.

Now that you have your acceleration, we need to make sure that Tarzan's force on the rope does not exceed the vine's rated strength of 1.0 x 10^3. so ma < 1.0 x 10^3. m being Tarzan's mass and a being the centripetal acceleration of the Vine.

I think that's enough information for you to solve it.
 

Related to Find max mass regarding circular motion and tension

1. How do you find the maximum mass for circular motion?

To find the maximum mass for circular motion, you need to use the equation M = T*v^2/R, where M is the maximum mass, T is the tension in the string, v is the velocity of the object, and R is the radius of the circular path. This equation takes into account the centripetal force required for circular motion.

2. What is the relationship between tension and maximum mass in circular motion?

The relationship between tension and maximum mass in circular motion is inverse. This means that as the tension in the string increases, the maximum mass that can be moved in a circular motion decreases. This is because a higher tension in the string requires a greater centripetal force, which is limited by the strength of the string.

3. Can the maximum mass for circular motion be greater than the tension in the string?

No, the maximum mass for circular motion cannot be greater than the tension in the string. This is because the centripetal force required for circular motion cannot exceed the tension in the string. If the maximum mass is greater than the tension, the object would not be able to move in a circular path.

4. How does the radius of the circular path affect the maximum mass for circular motion?

The radius of the circular path has a direct relationship with the maximum mass for circular motion. As the radius increases, the maximum mass that can be moved in a circular motion also increases. This is because a larger radius requires less centripetal force, allowing for a greater maximum mass.

5. Is the maximum mass for circular motion affected by the speed of the object?

Yes, the maximum mass for circular motion is affected by the speed of the object. As the speed increases, the maximum mass that can be moved in a circular motion decreases. This is because a higher speed requires a greater centripetal force, limiting the maximum mass that can be sustained by the tension in the string.

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