Applying Newton's Second Law - Example Problem 5.6-8

 

A passenger weighing 150 lb rides in a rollercoaster traveling at a constant 40 mph as it executes the loop shown. If the loop has a radius of 50 feet, determine the force exerted by the seat on the passenger at

1. the bottom of the loop,
2. half-way up the loop and
3. at the top of the loop.

 

 

Given:

• W = 150 lb
• v = 40 mph = 58.67 ft/s = constant
• ρ = 50 ft

 

Find:

• N_A
• N_B
• N_C

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

 

Draw 3 free-body diagrams of a single car. One for each position. Think about which coordinate system will be most advantageous to use.

 

 

 

 

Sum the forces in the n-direction to determine the normal force for each position.

 

N_A = lb  

 

 

 

N_B = lb   

 

 

 

N_C = lb