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

Force exerted on hemisphere

  • Thread starter Vibhor
  • Start date
  • #1
971
40

Homework Statement



?temp_hash=c5e575ffb27bf1584cb626211605385d.png


Homework Equations




The Attempt at a Solution



Using the fact that the sphere is in equilibrium in the 'y' direction , the force exerted by the floor N = 2mg .

Now , if I consider the lower hemisphere then , vertical force exerted by top hemisphere + weight of lower hemisphere = Normal reaction from the floor .

This means , vertical force exerted by top hemisphere on lower = mg

Should this be the total force exerted on the lower hemisphere ?

Thanks
 

Attachments

Last edited:

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,394
2,835
Yes, the sphere as a whole is "in equilibrium in the y direction" since the center of mass of the sphere has no acceleration.

However, does the center of mass of the lower hemisphere have any acceleration?
 
  • #3
971
40
However, does the center of mass of the lower hemisphere have any acceleration?
It has centripetal acceleration ω2r ( r=3R/8) directed towards the center of the sphere i.e in +y direction (upwards)

Taking + y to be upwards , 2mg - mg +R = mω2r , gives R = 5mg/8 downwards i.e option A)

Is that ok ??
 
  • #4
TSny
Homework Helper
Gold Member
12,394
2,835
It has centripetal acceleration ω2r ( r=3R/8) directed towards the center of the sphere i.e in +y direction (upwards)

Taking + y to be upwards , 2mg - mg +R = mω2r , gives R = 5mg/8 downwards i.e option A)

Is that ok ??
Yes, I believe that's all correct.
 
  • #5
971
40
Yes, I believe that's all correct.
Thank you :smile:
 
Last edited:

Related Threads on Force exerted on hemisphere

Replies
6
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
18
Views
837
  • Last Post
Replies
1
Views
294
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
8
Views
3K
Top