• Support PF! Buy your school textbooks, materials and every day products Here!

Ball falling of a hemisphere

  • #1

Homework Statement


A ball with initial velocity 0 and mass m starts at the top of a hemisphere and begins to slid down the frictionless side. The radius of the hemisphere is r. At what angle does the ball fall off the hemisphere?


Homework Equations


mgsintheta, mgcostheta, fn
mv^2/r


The Attempt at a Solution


I guess that you can split mg into mgsin theta and mg cos theta and that one of them would create centripetal force. Then you can find where the centripetal force is 0 because there would be no normal force when the ball falls off? I'm not sure. Also, my teacher mentioned that there is a way to solve this with and without calculus.
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,315
1,005
Find the place (or time) at which the normal force becomes zero, if you constrain the ball is constrained to remain on the surface of the hemisphere.
 
  • #3
108
0
you can use energy to find theta, solve v then substitute into your force equation
 

Related Threads on Ball falling of a hemisphere

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
15
Views
517
  • Last Post
Replies
3
Views
5K
  • Last Post
6
Replies
139
Views
6K
Replies
5
Views
7K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
4
Views
3K
Replies
7
Views
554
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
5
Views
5K
Top