Solving the Force on a 2kg Object on an Inclined Plane

[brake4country]

Homework Statement

A 2 kg object is placed on a plane inclined at an angle of 30 degrees. If the coefficient of static friction is 1, and the coefficient of kinetic friction is 0.1, what is the net force on the block?

Homework Equations

F = ma

The Attempt at a Solution

I made a FBD with a force table of the following: F_n, w, and F_f. My acceleration along the x is -4.1 m/s² and F_n = +17.3 N.

My confusion is the question of the sum of the forces. If I add up all the forces along the x and the y, I get a net sum of -25.6 N. The correct answer is 2.7N. Help please!

 

[Nathanael]

I don't understand how the 'correct' answer is possible. I don't agree with your answer either, so please show your work.

Firstly, how did you get F_n=17.3?

 

[brake4country]

Ok. I did this problem over again slowly. I made a force table. I have normal force, weight, and force of friction. I have +17.3 for the normal force in the y direction by mg cos θ); weight is w_x = -10 N and x_y = -17. N. My force of friction is μF_n = (0.1)(17.3) = 1.73 N.

My net force is perpendicular to the incline = 1.73 N. What am I doing wrong here?

 

[Nathanael]

Oh, I see. You're using g=10m/s/s

Have you checked if the object will even accelerate?

 

[brake4country]

Yes, acceleration is -4.1 m/s². I calculated this using F_x=ma_x

 

[Nathanael]

But you used the coefficient of kinetic friction which assumes the block does slide. You need to check if the block will even slide in the first place using static friction.

 

[brake4country]

Oh I see. So the key to this problem is determining the normal force? Even if I calculated the normal force, how do I determine if the object is stationary or moving?

 

[Nathanael]

The normal force balances the component of gravity perpendicular to the surface. The object will be stationary if the component of gravity parallel to the surface is less than the maximum force of static friction.

 

[brake4country]

Ok. So if F parallel = -10 N and the F_s=17.3, then the block will be stationary? Are we comparing +/- signs here or just considering magnitude of forces?

 

[brake4country]

How best to approach a problem that involves both static and kinetic friction? Should I always test out the static frictional force first? For example, if the acceleration turns out to be positive (contrary to my diagram), should I assume that it is stationary? I hope that makes sense.

 

[Nathanael]

Ok. So if F parallel = -10 N and the F_s=17.3, then the block will be stationary?

Yep

Are we comparing +/- signs here or just considering magnitude of forces?

You can just compare magnitudes. The force of static friction will naturally have the opposite sign (because it opposes the force trying to make it to slide). It wouldn't make much sense for the friction to help accelerate the object, friction opposes the motion of the object.

How best to approach a problem that involves both static and kinetic friction? Should I always test out the static frictional force first?

Well it depends on the problem. The key thing about this problem is that it says "an object is placed on incline." So you should check static friction first because the object starts out at rest. If the problem said, "someone slides an object down an incline ... " then you would not need to check the static friction because the object would already be sliding.

For example, if the acceleration turns out to be positive (contrary to my diagram), should I assume that it is stationary? I hope that makes sense.

You would just need to compare magnitudes. Which direction is positive and which is negative is completely arbitrary. The friction will oppose the motion of the object regardless of how you set up your coordinates.

 

[brake4country]

Thank you!