Horizontal velocity over an uneven surface

  • #1
71
2

Homework Statement


A small ball of m=1kg at height hp = 8m at point p, is given an initial horizontal speed vp = 10 m/s. It slides over an uneven frictionless surface. What is speed vq of the ball at height hq = 3m at point q?
upload_2014-12-24_11-9-4.png


Homework Equations


Ui + KEi = Uf + KEf

The Attempt at a Solution


I figured out how to find the velocity at point q, but when I first did the problem, I thought that the horizontal velocity wouldn't change because there is no horizontal force acting on the ball. The surface is frictionless, so going back to kinematics, if you throw a ball at an angle, the horizontal velocity doesn't change because gravity only acts downward, so I thought it would remain at 10 m/s. But the speed actually increased to 14 m/s after I solved it using the total energy equation.
Why was my first way wrong?
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
14,131
3,547
In this case the ball isn't falling, but sliding. The surface exercises a normal force on the ball that is directed perpendicular to the surface (hence the name normal). That normal force has a non-zero horizontal component, so it increases v when the ball goes down, and it slows the thing down when going uphill. Roller coaster physics !

(Of course, at Q the normal force is straight up again).
 
  • Like
Likes rasen58
  • #3
71
2
Oh I see! I forgot about the normal force here. Thanks!
 

Related Threads on Horizontal velocity over an uneven surface

Replies
1
Views
2K
Replies
14
Views
811
Replies
4
Views
5K
Replies
10
Views
2K
  • Last Post
Replies
5
Views
3K
Replies
6
Views
2K
Replies
1
Views
4K
Replies
4
Views
2K
Top