Question

An object of mass m is at rest at the top of a smooth slope of height h and length L. The coefficient of kinetic friction between the object and the surface, μk, is small enough that the object will slide down the slope if given a very small push to get it started.

Answer 1

Find an expression for the object's speed at the bottom of the slope.
Express your answer in terms of the variables m, μk, L, h, and appropriate constants.

Answer 2

Hi! This has one big similarity to the problem we just worked on. You want to find the acceleration in a particular direction. But now that direction is down-the-hill. Like,

So you have to find the net force!

What is the ONLY force in action here?

Answer 3

umm in not sure

Answer 4

Hint: you're experiencing this force right now.

Answer 5

Okay, it's not the only force... But it's a big one.

Answer 6

fg

Answer 7

Yep, force due to gravity. The other force is the normal force from the ramp onto the object. This keep the object from falling through the ramp :P

Answer 8

So!

Now you have to split gravitational force up into the \(x\) and \(y\), where the \(x\0 and \(y\) are like what I drew in the picture.

and, don't actually bother with the \(y\), because it is cancelled out by this normal force. Normal force is perpendicular to the surface and just counteracts gravity so that the object is supported.

Answer 9

Hint: knowing the proportions of some hidden triangles might help.

Let me draw a better picture.

Answer 10

The dotted line is one way to represent the force. But, instead, I split it up into two components.

Answer 11

I added a line to make a triangle! You can use another, too... But, anyway... This is a similar triangle to what the ramp is.