1 Youve taken your neighbors young child to the carnival to

1. You\'ve taken your neighbor\'s young child to the carnival to ride the rides. She wants to ride The Rocket. Eight rocket-shaped cars hang by chains from the outside edge of a large steel disk. A vertical axle through the center of the ride turns the disk, causing the cars to revolve in a circle. You\'ve just finished taking physics, so you decide to figure out the speed of the cars while you wait. You estimate that the disk is 5 m in diameter and the chains are 6 m long. The ride takes 10 s to reach full speed then the cars swing out until the chains are 20 from vertical. What is the cars’ speed?

a.) Draw a representational cartoon of the situation, including before and after if some kind of transformation takes place. Draw a physics representation of situation based on the cartoon representation. Choose and show coordinate axes. Record all quantities in appropriate places on the diagram and in a table. Identify symbolically all given and unknown quantities with appropriate variable names.

b.) State the general topic of physics needed to solve the problem. State all specific physics principles, concepts, laws, or theories needed. State any assumptions or simplifications you need to make. Construct a mathematical representation which is based on the physics principles and simplifying assumptions. Use algebra or other mathematical techniques to manipulate the equations to solve for your unknowns variables. Substitute numbers and units in for the variables you know. Use arithmetic to solve for your unknown quantities or numbers including units at every stage.

c.) Explain why your answer is a reasonable quantity or expression.

Thanks in advance!

Solution

R = 2.50 + 6 sin 20 = 4.55 m

horizontal force F_h = mg tan 20

F_h provides the centripetal force = m v² / R

m v² / R = m g tan 20

v = sqrt (R g tan 20) = sqrt (4.55 x 9.8 x tan 20)

v = 4.03 m/s