Circular motion , the loop the loop

In summary, the loop-the-loop machine has a radius of 18m and the minimum speed required to safely loop the loop is 30 m/s. The speed at the top will also be 30 m/s.
  • #1
NihalRi
134
12

Homework Statement


The loop-the-loop machine has radius R of 18m
(a) What is the minimum speed at which a cart must travel so that it will safety loop the loop
(b) what will the speed at the top be in this case

Homework Equations


Centipetal force = m*v^2/r
Kinetic and potential energies = (1/2) m*v^2 and mgh respectively

The Attempt at a Solution


(a) equating weight and centripetal force and then solving for v I got an answer for velocity of 13.2 but the actual answer is 30
(b) based on (a) calculate the velocity using energy equations
(1/2)m×v^2 = mgh + (1/2) m×v^2
 
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  • #2
NihalRi said:
(a) equating weight and centripetal force and then solving for v I got an answer for velocity of 13.2 but the actual answer is 30
I believe (a) is asking for the speed at the bottom. (Solve (b) first.)
 
  • #3
Doc Al said:
I believe (a) is asking for the speed at the bottom. (Solve (b) first.)
I get what it's asking just not how to get the answer
 
  • #4
You solved part (b).
 

What is circular motion?

Circular motion is a type of motion in which an object moves in a circular path around a central point. This can be achieved through the combination of a constant speed and a change in direction, or by a centripetal force that continuously pulls the object towards the center of the circle.

What is the loop the loop?

The loop the loop, also known as a vertical loop, is a type of circular motion in which an object travels through a vertical circular path. This is often seen in roller coasters, where the track forms a complete loop in the vertical plane.

What is the difference between centripetal and centrifugal force?

Centripetal force is a force that continuously pulls an object towards the center of a circular path, allowing it to maintain circular motion. Centrifugal force, on the other hand, is a fictitious force that appears to push an object away from the center of a circular path. It is actually a result of the object's inertia trying to keep it moving in a straight line.

What is the role of velocity in circular motion?

Velocity plays a crucial role in circular motion as it determines the speed at which an object moves along the circular path. It is also responsible for the direction of motion, as the object's velocity is constantly changing due to the change in direction in circular motion.

What are some real-life examples of circular motion and the loop the loop?

Some common examples of circular motion include the motion of planets around the sun, the rotation of a fan, or the motion of a car around a roundabout. The loop the loop can be seen in roller coasters, bobsled tracks, or even in the motion of a hula hoop around a person's waist.

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