Basics: Object on Incline, Forces (Im Hopeless) Help

[MourningTide]

Homework Statement

Object weighing 100 grams is on a surface which is inclined to an angle where the mass just overcame the coefficient of friction (which is unknown) and started sliding down. Angle was measured to be 21 degrees to the horizontal.

What I want to know is would the mass have a constant velocity, thus acceleration of 0?
Why?

Also is this right in resolving the problem into x and y components:
x-component = mgsintheta - mumgcostheta (where mu = coefficient of friction)
y-component = None, as the object does not move in directions perpendicular to the plane.


Would greatly appreciate help, stressed out and struggling all day...

 

[bob1182006]

yes, the block is first at rest so v=0, and when it JUST slips and starts to slide down it isn't accelerating because the angle is measured as low as possible so that the object just overcomes the coefficient of friction.

your x component is right but for your y you should have N-mgcostheta or mgcostheta-N depending on how you setup your coordinates.

 

[MourningTide]

Ok thank you very much !

Now is it possible to calculate the value of the coefficient of friction without using tan theta?
Resolving the situation into x and y components, and assuming gravity to be 9.8m/s^2,

m*a = (mgsintheta) - (mumgcostheta)
m = 0.1kg
a = 0
theta = 21 degrees

0 = 0.3512 - (mu * 0.9114)

How do I go from here?

Sorry to be a pain...

 

[bob1182006]

well if you solve 0=mgsintheta-mumgcostheta you get mu=tantheta.

You can also continue it numerically how you have it. just solve for mu in 0=.3512-.9114mu which is the same as taking tan theta.

I don't think there's a way to solve for mu without dealing with angle's since the coefficient of friction depends on the angle at which the object begins to slip or slides at a constant velocity.

 

[Artaxerxes]

http://www.pha.jhu.edu/~broholm/l10/node2.html

If you use LaTeX the text will be more legible. It's easy, and it's fun.

Some remarks...

If you choose x to be parallel and y perpendicular to the incline:

$$F_x = mg \sin \theta - \mu F_N$$

$$F_y = F_N - mg \cos \theta$$

If no motion in the y direction $$F_y = 0$$

If the coefficient of friction is the same whether the object is at rest or in motion there will be no acceleration and $$F_x = 0$$.

But if the friction is lower when the object is in motion there will be an acceleration.