Loop the loop problem with centripetal force

In summary, the problem involves a block of mass 5kg sliding along a frictionless loop-the-loop track with a radius of 2m. The first part asks for the resultant centripetal force acting on the block at point Q if it starts from rest at point P. The second part requires finding the height from the bottom of the loop at which the block should be released so that the force it exerts against the track at the top of the loop equals its weight. The third part asks for the difference between the force at the top and bottom of the loop. The relevant equations for solving these parts are conservation of energy and the formula for centripetal force, which uses mass, velocity, and radius. A free body diagram
  • #1
r19ecua
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Homework Statement


A small block of mass m = 5kg slides along the frictionless loop-the-loop track shown in the figure. R = 2m

a) If it starts from rest at P, what is the resultant centripetal force acting on it at Q?
b) At what height from the bottom of the loop should the block be released so that the force it exerts against the track at the top of the loop equals its weight?
c) What is the difference between the force at the top and the bottom?

Homework Equations


m*v^2/r
1/2mv^2f + mgyf = 1/2mv^2i + mgyi
This is as far as I know..

The Attempt at a Solution



Well I thought this was a simple conservation of energy problem, and then it HAD to involve centripetal force. Now I have no idea how to approach this problem :( This is a review problem, please help!
 
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  • #2
For part (a), using your conservation of energy formula will you the speed of the block at point Q. Once you get the speed at that point, your first equation gives you the resultant centripetal force at that point. So you have the correct relevant equations needed to solve part (a).

For part (b), draw a free body diagram at the point in question, and note all the forces acting on it. The sum of those forces in the centripetal direction is the net centripetal force in that direction. Then go back to your energy equation to solve. The solution to part c should follow.

I assume the figure which is not attached gives other numerical values so that you can numerically solve the problem.
 

1. What is a "loop the loop" problem with centripetal force?

A "loop the loop" problem with centripetal force is a physics problem that involves calculating the minimum speed at which an object must travel in a circular path without falling off. This type of problem is often used to understand the concept of centripetal force, which is the force that keeps an object moving in a circular motion.

2. How is centripetal force related to the "loop the loop" problem?

Centripetal force is the force that acts towards the center of a circle and keeps an object moving in a circular path. In the "loop the loop" problem, centripetal force is the force that prevents the object from falling off the loop as it moves through the curve.

3. What factors affect the minimum speed in a "loop the loop" problem?

The minimum speed in a "loop the loop" problem is affected by the radius of the loop, the mass of the object, and the force of gravity. A larger radius, lighter object, and smaller force of gravity will result in a lower minimum speed required to complete the loop without falling off.

4. How do you calculate the minimum speed in a "loop the loop" problem?

To calculate the minimum speed in a "loop the loop" problem, you can use the equation v = √(rg), where v is the minimum speed, r is the radius of the loop, and g is the acceleration due to gravity. This equation takes into account the factors that affect the minimum speed.

5. What are some real-life applications of the "loop the loop" problem with centripetal force?

The "loop the loop" problem with centripetal force has many real-life applications, such as designing roller coasters, calculating the minimum speed for a car to safely navigate a curved road, and understanding the forces acting on satellites in orbit. It is also used in sports, such as in gymnastics and snowboarding, to understand the forces involved in performing stunts and tricks.

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