Circular motion: normal force on a loop

  • Thread starter Beth N
  • Start date
  • #1
41
4

Homework Statement


A 180lb pilot flies a verticle loop with radius 2000 ft at 350 mi/h. With what force does the seat fress upward against him at the bottom of the loop?
Problem 6.21
IMG_5728.JPG

Homework Equations


##F=ma##
##F_c=\frac {mv^2} {r} ##

The Attempt at a Solution


There seems to be a discrepancy in the answer key provided? On the first line the equation they came up is ## F= \frac {mv^2} {r} + mg## . But when the number was plugged in, it seems like they use the equation ##F= \frac {mv^2} {gr} + m ## Which equation is correct? My own answer corresponds with the first equation, which is why I get a different numerical answer.

Thank you!
 

Attachments

Answers and Replies

  • #2
20,844
4,543
Are you familiar with the difference between lb-force and lb-mass? What is the weight (in lb-force) of a body that has a mass of 180 lb-mass?
 
  • Like
Likes Beth N
  • #3
41
4
I'm more familiar with the unit with kilogram. But I guess the weight in lb-force would be mass in lb * 32.2 ft/second^2 ? (as opposed to 9.8 m/second^2 for kg). So the weight in lb-force of a body with mass 180 lb is 5796 lb? Still, I haven't quite understood the discrepancy in the answer key.
 
  • #4
41
4
Oh wait I get what you are saying now. 180-lb as indicated in the book's question is the weight (m*a), not the mass (m). I didn't realize that. Thank you!
 
  • #5
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,652
I'm more familiar with the unit with kilogram. But I guess the weight in lb-force would be mass in lb * 32.2 ft/second^2 ? (as opposed to 9.8 m/second^2 for kg). So the weight in lb-force of a body with mass 180 lb is 5796 lb? Still, I haven't quite understood the discrepancy in the answer key.
You really should use lb only for the mass unit and lbf for the force unit. The weight of a body with mass x lb in standard gravity is by definition x lbf, not 32.2x lbf. This is by definition of the pound force unit. There is also a similar kg related unit that sees very little use, kgf.
 
  • Like
Likes Beth N
  • #6
20,844
4,543
In Imperial units, the weight of 1 lb-mass is 1 lb-force. Crazy, huh? This all resolves itself when we specify that the mass to use in applying Newton's second law using Imperial units is the slug, which is the mass in lb-mass divided by 32.2.
 
  • Like
Likes Beth N
  • #7
PhanthomJay
Science Advisor
Homework Helper
Gold Member
7,165
507
Yes, but be sure you use the correct value for mass in the mv^2/r term!
Edit: oh already answered, I’m a bit late.
 
  • #8
PeterO
Homework Helper
2,426
48
I'm more familiar with the unit with kilogram. But I guess the weight in lb-force would be mass in lb * 32.2 ft/second^2 ? (as opposed to 9.8 m/second^2 for kg). So the weight in lb-force of a body with mass 180 lb is 5796 lb? Still, I haven't quite understood the discrepancy in the answer key.
I would convert the whole thing to kg and m/s, then when you get the final force, in newtons, convert that into imperial units of force.
 

Related Threads on Circular motion: normal force on a loop

  • Last Post
Replies
6
Views
5K
Replies
1
Views
2K
Replies
1
Views
10K
Replies
4
Views
19K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
3
Views
746
Replies
1
Views
4K
Replies
3
Views
3K
  • Last Post
Replies
5
Views
987
Top