Ball rolling down incline

  • Thread starter df102015
  • Start date
  • #1
27
1

Homework Statement


upload_2016-5-11_17-21-27.png

The image above shows a basketball (a thin spherical shell I=⅔ mR^2) rolling don an incline of height 8.4 m. If the ball is already rolling with an initial linear speed of 3.0 m/s then what will be the final linear speed when it rolls off the incline?

Homework Equations


I = 2/3 m R^2
KE = 1/2 m v^2 + 1/2 I ω^2
ω = v / R
PE = m g h

The Attempt at a Solution


I know that i am missing some equations but honestly i don't know where to start other than substituting for ω and I.

KE = 1/2 m v^2 + 1/2 (2/3 m R^2) [(v / R)^2]

i do not think that i need the potential energy equation, but i mentioned it just incase. Also, how do i cancel out the mass and radius since they are not given in the problem?
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,963
3,320
You have all the equations. You just need the concept. Is anything conserved in this problem?
 
  • Like
Likes df102015
  • #3
27
1
You have all the equations. You just need the concept. Is anything conserved in this problem?
Energy, so would i set KE=PE ?
 
  • #4
TSny
Homework Helper
Gold Member
12,963
3,320
Energy, yes. But there is no law that says that KE should always equal PE. What about total mechanical energy: E = KE + PE? What can you say about E as the ball rolls down the slope?
 
  • Like
Likes df102015
  • #5
Hint:
Total Initial Energy = Total final energy
(As the ball rolls without slipping no heat is lost due to friction)
 
  • Like
Likes df102015
  • #6
27
1
Okay so would i use the equation that i have already set up? ...
KE = 1/2 m v^2 + 1/2 (2/3 m R^2) [(v / R)^2]
And would i add PE (mgh) and set equal to ME?
 
  • #7
27
1
Hint:
Total Initial Energy = Total final energy
(As the ball rolls without slipping no heat is lost due to friction)
But how do i set the equations up so that the variables i need cancel and everything else remains?
 
  • #8
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,574
6,448
But how do i set the equations up so that the variables i need cancel and everything else remains?
Do what you proposed in post #6 (add in PE), write the KE+PE expressions for each of the starting and ending circumstances, and set them equal.
 
  • Like
Likes df102015
  • #9
27
1
Do what you proposed in post #6 (add in PE), write the KE+PE expressions for each of the starting and ending circumstances, and set them equal.
Okay i think i have it...
1/2 m Vinitial^2 + 1/2 (2/3 m R^2) [(Vinitial / R)^2] + m g h = 1/2 m Vfinal^2 + 1/2 (2/3 m R^2) [(Vfinal / R)^2]

Is this correct?
 
  • #10
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,574
6,448
Okay i think i have it...
1/2 m Vinitial^2 + 1/2 (2/3 m R^2) [(Vinitial / R)^2] + m g h = 1/2 m Vfinal^2 + 1/2 (2/3 m R^2) [(Vfinal / R)^2]

Is this correct?
Yes.
 
  • Like
Likes df102015
  • #11
27
1

Related Threads on Ball rolling down incline

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
9K
Replies
4
Views
1K
  • Last Post
Replies
1
Views
12K
  • Last Post
Replies
2
Views
12K
Replies
3
Views
3K
Replies
11
Views
1K
Replies
3
Views
823
Replies
18
Views
3K
Replies
2
Views
3K
Top