Physics help!!

Question

Hey I'm i have a physics test in a few days and am really not understanding coefficients of friction and those type of questions. I'll give you an example of what I'm dealing with.. 

 

1) what is the acceleration of a 220kg mass sitting on a 37 degree slope of the coefficient of friction between the object and the ramp is 0.37?

 

thanks for your time!

Answer 1

Begin with the basic formula for Newton's Second Law"

 

a = F(the net force)/m (mass)

 

I'll assume you can draw the situation showing all the forces that combine to equal the net force acting on the object:  normal force, gravitational force, and friction.

 

The components of the gravitational force (mg) are mg(sinΘ) and mg(cosΘ).  They replace the weight, so we can now ignore that.  The normal force N must be equal to mg(cosΘ), since the object is not floating away or falling through the inclined plane.

 

The friction force is by definition, the normal force x the coefficient of friction μ, which is given as 0.37

 

or mg(cosΘ)μ

 

We also have the force pushing the object downwards, which is mg(sinΘ).

 

Now we have the net force:  mg(sinΘ) -  mg(cosΘ)μ

 

a = [ mg(sinΘ) - mg(cosΘ)μ]/m

 

Simplifying:

 

a = [mg(sinΘ) - (cosΘ)μ]/m

 

Cancelling m

 

a = gsinΘ - cosΘμ

 

Now plug in values:

 

 a = 9.8 m/s² [0.6018-(0.7986)(0.37)]

 

a =3.0 m/s²   Render a with two significant figures because of the 9.8 gravitational constant. (ANSWER)