Help with Inclinded Plane Problem

[buttretler]

Hello Everyone!

Homework Statement

I'm having trouble with this problem. I'm sapose to figure out at what angle a 5 kg block beings to slide with a static coefficient of 0.4.

3. The Attempt at a Solution [/b

So far I've been working it out through trigonometry and I've gotten that ... mu = mgcos(theta)/mgsin(theta) = cos/sin = tan(theta)

therefore that 0.4 =tan(theta)
(theta) = tan^-1(0.4)
(theta) = 21.8 degrees

so the box would slide at roughly 22 degrees.

I must of done something wrong but seems to make sense to me, theirs got to be more to it than this. can anyone help?

 

[Doc Al]

Looks good to me. I agree with your answer.

 

[buttretler]

Really? I just can't seem to understand why the weight of the block is irrelavent. The fact that the staic friction is 0.4 would mean that the angle at which something slides on a plane with always be 22 degrees, like if it were 10 kg or 15kj, would the angle always be 22? I just can't wrap my head around it.

 

[Doc Al]

Really? I just can't seem to understand why the weight of the block is irrelavent. The fact that the staic friction is 0.4 would mean that the angle at which something slides on a plane with always be 22 degrees, like if it were 10 kg or 15kj, would the angle always be 22?

Yep. The mass is irrelevant.

I just can't wrap my head around it.

You are balancing the gravitational force acting down the plane with the maximum static friction acting up the plane. Since both are proportional to the mass, the mass doesn't matter.

 

[rwisz]

Hi there,

It looks like you have the right idea! You correctly used the equation for the coefficient of friction (mu) and solved for the angle (theta) at which the block begins to slide. Your calculations are also correct, so there may not be any errors in your work.

One thing to consider is the units of measurement you are using. Make sure that all your values are in the correct units (e.g. kilograms for mass, meters for distance) to ensure accurate calculations. Also, double check your calculations to make sure you are using the correct values for gravity (9.8 m/s^2) and the weight of the block (mg).

Additionally, it may be helpful to draw a free-body diagram to visualize the forces acting on the block and to make sure you are considering all the relevant forces. You can also try solving the problem using other methods, such as using the equation for the angle of inclination (theta = arctan(mu)) or using the formula for the maximum angle of inclination (theta = arctan(mu) - arctan(mu_s)).

I hope this helps! Keep up the good work and don't hesitate to ask for further clarification or assistance if needed. Good luck!