Forces of 2 dimensional motion w/friction

[Kenny_Mack]

i'm studying for a test and this question came up. i need all the help i can get.

A small mass m is set on the surface of a sphere. If the coefficient of static friction is (greek letter for coefficient of friction) = .6 at what angle would the mass start sliding?

 

[mrjeffy321]

it will start to slide when the force parralell to the surface pulling it down is equal to the force of friction.

parrallell force = mg * sin(angle)
force of friction = mg * cos(angle) * coefficient of friction

a nice trick for these types of problems is to know that is you have the coefficient of friction and you want to find the angle at which it wil slide, then use tan^-1(coefficient) = angle,
if you have the angle and you want the coefficient of friction that will cause it to start to slide at that angle, use tan(angle) = coefficient

 

[thepatientmental]

To answer this question, we need to consider the forces acting on the mass. In this case, there are two main forces: the normal force, which is perpendicular to the surface of the sphere, and the force of friction, which is parallel to the surface.

The normal force is equal to the weight of the mass, which is given by Fg = mg, where g is the acceleration due to gravity (9.8 m/s^2).

The force of friction is given by Ff = μN, where μ is the coefficient of friction and N is the normal force. In this case, μ = 0.6 and N = mg. So, Ff = 0.6mg.

Now, we need to consider the forces in the horizontal and vertical directions. In the vertical direction, the forces are balanced since the mass is not moving up or down. So, we can focus on the horizontal direction.

In the horizontal direction, we have the force of friction acting in the opposite direction of motion (since the mass is on the verge of sliding) and the component of the weight of the mass acting in the direction of motion.

Using trigonometry, we can determine that the angle between the weight and the horizontal direction is θ = tan^-1(0.6). So, the angle at which the mass will start sliding is approximately 31.8 degrees.

It's also important to note that this angle may change if the mass or the coefficient of friction changes. So, it's important to understand the concept and be able to apply it to different scenarios. I hope this helps with your test preparation. Good luck!