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

[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

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

What am I missing here?!

Thanks!

Amit

 

[SammyS]

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

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

What am I missing here?!

Thanks!

Amit

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?

 

[Amit86]

Hi, Sammy. That's correct.

 

[SammyS]

Hi, Sammy. That's correct.

There are two questions I asked.

 

[Amit86]

I imagine the vertical wall can counteract the force

 

[SammyS]

I imagine the vertical wall can counteract the force

(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.)

 

[Amit86]

(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.)

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

 

[SammyS]

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

Right.

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

 

[Amit86]

Right.

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

I suppose that's true.

 

[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?

 

[Amit86]

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?

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.

 

[SammyS]

Right.

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

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

 

[Amit86]

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

okay thanks!

 

[Amit86]

okay thanks!

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

Thanks for your help!

 

[SammyS]

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

Thanks for your help!

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.