How Does Horizontal Force Balance with Friction on an Inclined Plane?

[ngorecki]

A 2.00 kg block is held in equilibrium on an incline of angle θ = 55° by a horizontal force, F. If the coefficient of static friction between block and incline is µ s = 0.300, determine
(a) the minimum value of F and
(b) the normal force of the incline on the block.

F = ma
Mu = Ff/Fn

I am having trouble starting out. I don't know what the initial equation should be. Could i get some hints?

 

[Flipmeister]

Always, always, always start with a free-body diagram. Have you done that yet?

 

[ngorecki]

I have done that.
And i changed gravity into the x and y components.
I am not sure what to solve for first/how to solve for it

 

[Flipmeister]

The object is in equilibrium, so the net force in the x direction equals zero and the net force in the y direction equals 0. Now solve for that force F in the x and y direction to find its components.

 

[Nickie]

Sure, let's break down the problem and see if we can figure out the initial equations.

First, we know that the block is in equilibrium, which means that the forces acting on it must be balanced. This means that the sum of the forces in the horizontal and vertical directions must equal zero.

In the horizontal direction, we have the force F pushing the block up the incline, and the force of friction, Ff, pushing the block down the incline. Since the block is not moving horizontally, the horizontal forces must balance each other out. This can be written as:

F - Ff = 0

Next, in the vertical direction, we have the force of gravity pulling the block down the incline, and the normal force, Fn, pushing the block up the incline. Since the block is not moving vertically, the vertical forces must also balance each other out. This can be written as:

mg - Fn = 0

We also know that the coefficient of static friction, µs, is equal to the ratio of the force of friction to the normal force. This can be written as:

µs = Ff/Fn

We can use this equation to solve for the force of friction, Ff, by rearranging it to:

Ff = µsFn

Now, we have three equations and three unknowns (F, Fn, and Ff). We can use algebra to solve for these unknowns.

For part (a), we are trying to find the minimum value of F. This means that we want to find the value of F that just barely keeps the block in equilibrium. In other words, the force of friction, Ff, must be at its maximum value, which is equal to µsFn. We can substitute this into our first equation to get:

F - µsFn = 0

Solving for F, we get:

F = µsFn

For part (b), we are trying to find the normal force, Fn. We can use the second equation we wrote earlier and solve for Fn:

mg - Fn = 0

Fn = mg

So, the normal force is equal to the weight of the block, mg.

I hope this helps you get started! Remember, when solving problems like this, it's important to identify all the known values and use equations that relate those values to each other. Good luck!