Circular Motion Problem w/ Conservation of Energy

In summary, the physics teacher attempts to swing from a 24m rope, starting from rest with the rope horizontal. The rope will break if the tension force is twice the weight of the teacher. Using the conservation of energy, we can calculate the velocity for which the kinetic energy is twice the initial potential energy. However, to determine the height at which the rope breaks, we need to consider the centripetal force and the condition for the rope to break.
  • #1
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Homework Statement


Your favourite physics teacher who is late for class attempts to swing from the roof of a 24m long rope as shown in the picture. The teacher starts from rest (Ek=0) with the rope horizontal, but the rope will break if the tension force in it is twice the weight of the teacher. How high is the swinging physics teacher above the ground when the rope breaks?
(Hint: Use the conservation of energy)
CM2.png



Homework Equations


Ek=(1/2)mv^2
Eg=mgh
Fc=(mv^2)/r

The Attempt at a Solution


My diagram:
CM2-1.png

Eg = mgh
= m(9,8)(24)
= 235.2m
Ek = (1/2)mv^2
= mv^2
(because it says that the rope will break if the tension force in it is twice the weight of the teacher)
then i equate these.
235.2m = mv^2
235.2 = v^2
v = 15.3 m/s.
from here i have no idea what to do. i think i might have to use Fc=(mv^2)/r, but i not sure how.
thanks in advance for you help.




 
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  • #2
What you have calculated is the velocity for which the kinetic energy is twice the initial potential energy. It's not that useful or related to your problem.

You already mentioned Fc=mv^2/r. How does this play a role in your problem?
What supplies the centipetal force and what is the condition that the rope breaks?
 

1. What is circular motion and how does it relate to conservation of energy?

Circular motion is the movement of an object along a circular path. It relates to conservation of energy because the object's kinetic energy and potential energy are constantly changing as it moves around the circle, but the total energy remains constant.

2. What is the formula for calculating the kinetic energy of an object in circular motion?

The formula for calculating kinetic energy in circular motion is KE = 1/2 * m * v^2, where m is the mass of the object and v is its linear velocity.

3. How does the radius of the circular path affect the conservation of energy in circular motion?

The radius of the circular path affects the conservation of energy because it determines the object's speed and therefore its kinetic energy. A smaller radius will result in a higher speed and kinetic energy, while a larger radius will result in a lower speed and kinetic energy.

4. Can the total energy of an object in circular motion change?

No, the total energy of an object in circular motion remains constant due to the law of conservation of energy. This means that the object's kinetic energy and potential energy may change, but their sum will always be the same.

5. How can conservation of energy be used to solve circular motion problems?

Conservation of energy can be used to solve circular motion problems by setting the total initial energy equal to the total final energy and solving for the unknown variable, such as the object's speed or radius. This ensures that energy is conserved throughout the motion.

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