Download Name Centripetal Forces in a Vertical Circle 1. A 0.6 kg marble is

Name _____________________________
Centripetal Forces in a Vertical Circle
1. A 0.6 kg marble is attached to a cord and swung in a VERTICAL circle of radius 1 meter at a constant 7.5 m/s. On the
diagrams below draw a free body diagram of the marble when it is at its lowest point, when it is at its highest point, and
when it is halfway from the bottom to the top.
A. When the object is at its lowest point what force provides the centripetal force? What direction does that force
point? Does that force have to do anything else? What?
B. When the object is at its lowest point is there any force acting opposite the centripetal force? What force?
C. Write a net force equation in the vertical direction. That net force has to equal the centripetal force. Find the
centripetal force. Find the tension in the string.
D. When the object is at its lowest point, what direction does Friction point? Does that affect centripetal force? Why or
why not? What does friction affect in this case?
E. A. When the object is at its highest point what force(s) provides the centripetal force? What direction do those
forces point?
F. Write a net force equation in the vertical direction. That net force has to equal the centripetal force. Find the
centripetal force. Find the tension in the string.
G. Find the velocity which would allow the Tension force to be zero. This is known as the critical velocity of the vertical
circle. Any slower and the object can’t stay in a vertical circle.
H. When the object is at its highest point, what direction does friction point? Does that affect centripetal force? Why or
why not? What does friction affect in this case?
I. When the object is half way between the highest and lowest point what force provides the centripetal force? What
direction does that force point? Does that force have to do anything else?
J. When the object is half way between the highest and lowest point is there any force acting opposite the centripetal
force?
K. Write a net force equation in the horizontal direction. That net force has to equal the centripetal force. Find the
centripetal force. Find the tension in the string.
L. When the object is half way between the highest and lowest point what direction does Friction point? Does that
affect centripetal force? Why or why not? What does friction affect in this case?
M. When the object is half way between the highest and lowest point what direction does gravity point? Does that
affect centripetal force? Why or why not? What does gravity affect in this case?
N. If the string is swung faster and faster, at what point on the circle do you think it will break? Why?
O. If the string has a maximum tension strength of 600 N, and what velocity will it break?
2. A roller coaster designer wants to put a loop in the coaster of radius p=24 meters. The roller coaster will have a mass
of 1500 kg when loaded with people.
a. Draw a free body diagram of the roller coaster car at its highest point on the loop.
b. What is the critical velocity the roller coaster would have to have at the top of the circle for car to not have to risk
falling out of a circular path? Is the mass of the rollercoaster important?
c. Draw a free body diagram of the roller coaster at its lowest point on the loop.
d. If the roller coaster is to have at least its critical velocity, how much normal force does the track need to be able to
provide at the lowest point? Is mass of the roller coaster important here?
4. An airplane stunt pilot wishes to fly in a vertical circle, of radius 3000 meters.
A. What is the minimum velocity the plane needs o make the loop?
B. If the plane is to maintain that speed throughout the entire loop, what maximum force will be acting on the plane’s
wings at the lowest point?