How Do Rollercoasters Use Circular Motion and Acceleration?

[helpme101]

Homework Statement

A rollercoaster consists of a 45 degree slope that is 100 m long followed by two loops which have radii of 40 m and 20 m respectively. If the rollercoaster accelerates down the initial slope due to gravity, determine:
a. The acceleration of the rollercoaster down the 45 degree slope.
b. The acceleration of the rollercoaster as it starts each loop. You can assume the speed of the roller coaster entering each loop is the same as the speed at the bottom of the initial slope.
c. The limit of the body's ability to withstand acceleration is approximately 5 g or 49.05ms^-2 is the roller coaster safe for the average person to ride?

Homework Equations

F=ma

The Attempt at a Solution

For part A: isn't the acceleration of the rollercoaster -9.81ms^-2? The start of the problem states that "if the rollercoaster accelerates down the initial slope due to gravity, determine..." If this isn't correct would I somehow use Newton's Second law, however I don't know the mass of the cart or the force.
For part B: I know that the two radii have a role on acceleration. Do I need to apply Newton's Second law?
For part C: would I be looking at the apparent weight? However, I'm not given the mass of the average person, so should I ask the professor for that??

 

[JBA]

This is a problem of strictly acceleration due to gravity relative to the slope of the ramp (think geometrically), the resulting velocity and centripetal acceleration in each loop.
F=ma is not relevant.. Your acceleration due to gravity is sqrt(9.81 * h) where h the the vertical distance of travel (again, think geometrically)

 

[ehild]

Your acceleration due to gravity is sqrt(9.81 * h) where h the the vertical distance of travel (again, think geometrically)

You statement is wrong. The expression in red is not acceleration.

 

[ehild]

Homework Statement

A rollercoaster consists of a 45 degree slope that is 100 m long followed by two loops which have radii of 40 m and 20 m respectively. If the rollercoaster accelerates down the initial slope due to gravity, determine:
a. The acceleration of the rollercoaster down the 45 degree slope.
b. The acceleration of the rollercoaster as it starts each loop. You can assume the speed of the roller coaster entering each loop is the same as the speed at the bottom of the initial slope.
c. The limit of the body's ability to withstand acceleration is approximately 5 g or 49.05ms^-2 is the roller coaster safe for the average person to ride?

Homework Equations

F=ma

The Attempt at a Solution

For part A: isn't the acceleration of the rollercoaster -9.81ms^-2? The start of the problem states that "if the rollercoaster accelerates down the initial slope due to gravity, determine..." If this isn't correct would I somehow use Newton's Second law, however I don't know the mass of the cart or the force.

No, the acceleration along a slope is less than g. Look at your Lecture Notes or Book, or see: http://hyperphysics.phy-astr.gsu.edu/hbase/mincl.html

For part B: I know that the two radii have a role on acceleration. Do I need to apply Newton's Second law?

You always can apply Newton's Second Law. What force should act to make a circle of given radius? What is the corresponding acceleration?

For part C: would I be looking at the apparent weight? However, I'm not given the mass of the average person, so should I ask the professor for that??

The problem asks if the accelerations in the loops are less or greater than 5g. It is not the apparent weight.

 

[JBA]

You statement is wrong. The expression in red is not acceleration.

Supid mistake, I apologize to all.