Calculating Tension in Rotational Motion: Stuntman on a Vertical Circle

In summary, a stuntman swings from a 4 m long rope along the arc of a vertical circle with a mass of 70 kg. To make him follow his circular path, the tension in the rope is calculated to be 2.07 x 10^3 N at the beginning of his motion and at the bottom of his arc, with a speed of 8.9 m/s at the bottom. Total mechanical energy is conserved as the man swings.
  • #1
mizzy
217
0
Please help...rotational motion

Homework Statement


A stuntman swings from the end of 4 m long rope along the arc of a vertical circle. If his mass is 70kg, find the tension in the rope required to make him follow his circular path, assuming he starts from rest when the rope is horizontal:
a) at the beginning of his motion

b) at the bottom of his arc


Homework Equations



centripetal acceleration = v^2/r

F = mv^2/r

The Attempt at a Solution


For part a) at the beginning of his motion, is the tension equal to zero? The tension of the rope is pointing to the center and therefore the equation is F = mv^2/r. However, v is equal to 0 because he starts from rest. is that right?

For part b) at the bottom of the arc, tension in the rope and mg causes acceleration and therefore the equation is F - mg = mv^2/r. But what's v?

Can someone help me please?
 
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  • #2


mizzy said:
For part a) at the beginning of his motion, is the tension equal to zero? The tension of the rope is pointing to the center and therefore the equation is F = mv^2/r. However, v is equal to 0 because he starts from rest. is that right?
Right.

For part b) at the bottom of the arc, tension in the rope and mg causes acceleration and therefore the equation is F - mg = mv^2/r. But what's v?
You'll need to figure out the speed at the bottom. (What's conserved?)
 
  • #3


Doc Al said:
Right.


You'll need to figure out the speed at the bottom. (What's conserved?)

Kinetic energy
 
  • #4


mizzy said:
Kinetic energy
Total mechanical energy is conserved as man swings, not just kinetic.
 
  • #5


Doc Al said:
Total mechanical energy is conserved as man swings, not just kinetic.

Ok. In that case:

KEmiddle + PEmiddle = KEbottom +PEbottom
1/2mv^2 +mgh = 1/2mv^2 +mgh
0 + mgr = 1/2mv^2 + 0
mgr = 1/2mv^2
(70)(9.8)(4) = 1/2(70)v^2

therefore, v = square root off 2gr = 8.9m/s

F1 - mg = mv^2/r
F1 = mv^2/r +mg
= (70)(8.9)^2/4 + (70)(9.8)
= 2.07 x 10^3 N

Can you confirm if this is right? THANKS
 
  • #6


Looks good! (Don't round off until the end.)
 
  • #7


Thanks for your help! =)
 

What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion is commonly seen in objects such as wheels, planets, and spinning tops.

What is angular velocity?

Angular velocity is the measure of the rate at which an object rotates around an axis. It is typically measured in radians per second and is used to describe the speed and direction of rotational motion.

What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of rotational motion, while linear velocity is a measure of straight-line motion. Angular velocity is commonly used to describe the speed of objects that are rotating, while linear velocity is used to describe the speed of objects that are moving in a straight line.

How are torque and rotational motion related?

Torque is the force that causes an object to rotate around an axis. It is directly related to rotational motion because the greater the torque applied to an object, the faster it will rotate.

What is the difference between translational and rotational motion?

Translational motion is the movement of an object from one point to another in a straight line, while rotational motion is the movement of an object around an axis. Translational motion is typically seen in objects that are moving in a straight line, while rotational motion is seen in objects that are spinning or rotating around a fixed point.

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