A Block Slides Down an Inclined Plane

[jumbogala]

Homework Statement

A block slides down an inclined plane with friction. It is sliding at a constant speed. The only forces acting on the block are its weight and contact forces due to the incline. The inclined plane is stationary.

The inclined plane is a wedge that is highest on the left (eg. you would slide down towards the right). That is the way the block is sliding.

Which way does the force exerted by the block on the inclined plane point?

Homework Equations

The Attempt at a Solution

Well, I think there's a friction force pointing along the inclined plane towards the upper left and a normal force 90 degrees to the inclined plane pointing down. Adding these gives one force, pointing towards the left (straight to the left).

But apparently the answer is straight down (like along the y axis). I don't understand why, can anyone help?

 

[Doc Al]

Well, I think there's a friction force pointing along the inclined plane towards the upper left and a normal force 90 degrees to the inclined plane pointing down.

First consider forces acting on the block. Which way does friction and the normal force act on the block? What's the net force on the block?

 

[jumbogala]

The normal force acting on the block would be 90 degrees to the surface of the inclined plane, in a northwest direction.

The friction acting on the block would be opposite the block's motion, so it would be in a northeast direction parallel to the inclined plane.

Wouldn't the forces acting on the inclined plane, from the block, be the same as these but in the opposite direction?

 

[Doc Al]

The normal force acting on the block would be 90 degrees to the surface of the inclined plane, in a northwest direction.

The friction acting on the block would be opposite the block's motion, so it would be in a northeast direction parallel to the inclined plane.

I'm not sure how you are defining east and west, but OK. (Is the block sliding southeast or southwest?)

Wouldn't the forces acting on the inclined plane, from the block, be the same as these but in the opposite direction?

Absolutely.

 

[jumbogala]

I am defining east and west so that the block is sliding southeast.

Ok, so now if I add up two vectors, one in a southeast direction (but still 90 degrees to the surface of the inclined plane). And another in southwest direction (but still parallel to the inclined plane), the vector points straight down.

Which is the answer!

Thank you!

 

[Doc Al]

Excellent.

Another way to see it is this: We know that the net force on the block is zero, since it moves with constant velocity. The only forces on it are the force of the inclined plane and the force of gravity. Since gravity acts straight down, the inclined plane force must act straight up. Therefore, from Newton's 3rd law, the force of the block on the inclined plane must act straight down.