# Calculate the force of ball on an incline leaning on a wall

1. Jun 23, 2015

### Amit86

Hi all,

I'm working on a problem from the Feynman exercise book, and have been racking my brains for an answer, so would really appreciate some help here. The problem seems simple enough:

A ball with a 3cm radius, weighing 1kg rests on an inclined plane (angle alpha) and also touches a vertical wall. Neglect friction.

(see attached diagram)

What is the force of the ball acting on the wall (Fw)?

The answers in the back gives
Fw= tan(alpha) kg.wt

I got the force due to gravity acting down the plane, Fr = 9.81.sin(alpha). The horizontal component of this force, which to my mind is the force acting on the wall, is

Frhor=9.81* sin(alpha)cos(alpha)

What am I missing here?!!!

Thanks!

Amit

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2. Jun 23, 2015

### SammyS

Staff Emeritus
Hello Amit86. Welcome to PF !

The only forces acting on the ball are gravity, and the two forces supplied by the two surfaces. Right ?

Can the vertical wall counteract the force gravity exerts on the ball?

3. Jun 23, 2015

### Amit86

Hi, Sammy. That's correct.

4. Jun 23, 2015

### SammyS

Staff Emeritus
There are two questions I asked.

5. Jun 23, 2015

### Amit86

I imagine the vertical wall can counteract the force

6. Jun 23, 2015

### SammyS

Staff Emeritus
(By the way, there is a "Reply" feature in the lower right-hand corner of the message screen that's helpful with dialogue.)

Can the vertical surface produce a force on the ball that has a vertical component?

(There's no friction.)

7. Jun 23, 2015

### Amit86

As far as I can tell, I don't think it can. "both surfaces have negligible friction"

8. Jun 23, 2015

### SammyS

Staff Emeritus
Right.

Therefore, only the incline can provide a force which has the vertical component necessary to counter act the gravitational force. Right?

9. Jun 23, 2015

### Amit86

I suppose that's true.

10. Jun 23, 2015

### HallsofIvy

You say things like "I imagine", "as far as I can tell", and "I suppose". Do you know in what direction gravity acts? Do you know in which direction the force from the wall acts?

11. Jun 23, 2015

### Amit86

Of course I do; check the diagram. I am looking for some insight into where the tan(alpha) comes from. I've provided all the information given in the question, I need to get some sense of how to proceed with a solution, and would appreciate constructive advice.

12. Jun 23, 2015

### SammyS

Staff Emeritus
This should help you to find the vertical force the incline needs to exert on the ball.

13. Jun 23, 2015

### Amit86

okay thanks!

14. Jun 23, 2015

### Amit86

Ok so I think I've got then...

The vertical component of the reaction force of the plane = the total gravitational force (i.e 9.81 x 1kg), so the horizontal component of reaction force of the plane would be 9.81*tan alpha Newtons or

Fw= tan(alpha) kg wt

15. Jun 23, 2015

### SammyS

Staff Emeritus
Correct !

Notice that this vertical force is greater than the vertical force that the incline exerts for the case when the ball is allowed to roll.

Last edited: Jun 23, 2015