Determining Acceleration for Block A to Avoid Falling from Cart

[Mehta29]

Umm...I having trouble with the concept of acceleration and friction i guess...or something...

What acceleration must a cart have in order that the block A will not fall the coefficient of static friction between the block and the cart is μ , how would the behavior of the blokc be described by an observer on the cart?

I'm not sure if you guys can envision the problem but its a big box on "wheels" with a small box sort of attached to it



and i don't know how to answer either of the questions really

I know in the x direction u have Fn and in the y direction u have mg acting downwards and friction acting upwards...

Would Fn = (m1+m2)a and Ff - Mg= (m1+m2)a? or would u set Ff = mg?

Yea I'm drawing blanks up to here...

any help would be appreciated...thanksss

 

[Doc Al]

To solve this problem, start by identifying the vertical and horizontal forces acting on the small block. Then apply Newton's 2nd law to the small block for each direction. Hint: What direction is the acceleration?

 

[Mehta29]

okay i understand the acceleration part...a = g/μ...was just a little confused because the normal force had no force acting in the opposite direction...but how would it look to an observer? wouldn't it just remain stationary and look like it was a part of the cart?

 

[Pythagorean]

I know in the x direction u have Fn and in the y direction u have mg acting downwards and friction acting upwards...

I don't think friction acts upward in this case. The normal force acts upward, countering the gravitational force (and any other down forces there may be) on the object.

Now, the friction force acts in opposition to motion, and it is Mu*Fn (where Mu is the coefficient of friction and Fn is the normal force)

This is assuming that the surface the block is resting on is flat with respect to the Earth.

 

[Doc Al]

okay i understand the acceleration part...a = g/μ...was just a little confused because the normal force had no force acting in the opposite direction...but how would it look to an observer? wouldn't it just remain stationary and look like it was a part of the cart?

Huh?

Perhaps I'm thinking of a different problem. I imagine that the small block is on the front surface (vertical surface) of the cart, held there by friction. Is that correct?

If so: What forces act on the block? What direction is its acceleration?

If the block doesn't slip down it will move along with the cart.