What are the magnitude and direction of the friction force?

[skysunsand]

Homework Statement

A 200N block is on a 35 degree incline with a frictionless, massless pulley and a weight on the other side, Fw= 220. The system is in equilibrium.
What are the magnitude and direction of the frictional force on the 200N block?

Homework Equations

and

The Attempt at a Solution

Ft1 + Ft2 = Fw , so Ft1 and Ft2 are 220N

Fn= 20.4 sin 35 * 9.8 = 112.4

I guess Fw-Fn = Ff, but I don't understand why. Is that always true?
So the answer here would be 108 in regard to the magnitude, though the book wants 105. I guess that's a rounding thing? And it says down the incline, but why?

 

[gneill]

Homework Statement

A 200N block is on a 35 degree incline with a frictionless, massless pulley and a weight on the other side, Fw= 220. The system is in equilibrium.
What are the magnitude and direction of the frictional force on the 200N block?

Homework Equations

and

The Attempt at a Solution

Ft1 + Ft2 = Fw , so Ft1 and Ft2 are 220N

What are Ft1 and Ft2? The tensions in the string segments? If so, they do not sum to the weight of the hanging mass. If the pulley is massless and frictionless then they must be the same, yes. If the system is static (in equilibrium) then the tension will be equal to the weight of the hanging mass (as you've written).

Also, if the system is in equilibrium, the net force downslope must equal the net force directed upslope.

Fn= 20.4 sin 35 * 9.8 = 112.4

What is Fn? It looks like it should be the component of the block's weight that is directed downslope. Is that right? If so, you could have just used the block's weight (200N) and multiplied by the sine of the angle. No need to convert to mass and then back again to weight. As it is you have a numerical error in the result. Check your calculations.

I guess Fw-Fn = Ff, but I don't understand why. Is that always true?

It's true in this case because the system is in equilibrium. Thus the net force acting along the direction of the slope is zero.

So the answer here would be 108 in regard to the magnitude, though the book wants 105. I guess that's a rounding thing? And it says down the incline, but why?

Check your math as mentioned above. Friction always opposes the motion or attempted motion. Here the block 'wants' to move upslope, so the friction opposes that attempt and thus directed downslope.

 

[skysunsand]

What are Ft1 and Ft2? The tensions in the string segments? If so, they do not sum to the weight of the hanging mass. If the pulley is massless and frictionless then they must be the same, yes. If the system is static (in equilibrium) then the tension will be equal to the weight of the hanging mass (as you've written).

Yeah, that was my failure to mention the pulley is massless and frictionless. I was never quite sure why they made a point to mention that. Thank you for clarifying that.

Also, if the system is in equilibrium, the net force downslope must equal the net force directed upslope.

What is Fn? It looks like it should be the component of the block's weight that is directed downslope. Is that right? If so, you could have just used the block's weight (200N) and multiplied by the sine of the angle. No need to convert to mass and then back again to weight. As it is you have a numerical error in the result. Check your calculations.

Fn is my notation for normal force. I checked my calculations per what you said about converting and I ended up with 114.7, which, when subtracted, does give me 105.3.

Check your math as mentioned above. Friction always opposes the motion or attempted motion. Here the block 'wants' to move upslope, so the friction opposes that attempt and thus directed downslope.

How would I know which way the block "wants" to move? Would I just have to look at it and realize that because the weight on the right side is heavier, the block is automatically going to want to move up the slope?

 

[gneill]

Fn is my notation for normal force. I checked my calculations per what you said about converting and I ended up with 114.7, which, when subtracted, does give me 105.3.

The normal force doesn't enter into this particular problem because the frictional force is what you will determine from the other forces (so you don't need the normal force to calculate it). What you want is the downlope component of the block's weight. Fortunately, that's what you calculated! (The normal force would be given by mg cos(θ) )

How would I know which way the block "wants" to move? Would I just have to look at it and realize that because the weight on the right side is heavier, the block is automatically going to want to move up the slope?

Yes, that or do some preliminary calculations to compare the forces acting on the block.

 

[asteriatic]

I would like to address a few things in your response. Firstly, the magnitude of the friction force is the force that opposes the motion of an object and is dependent on the coefficient of friction between the two surfaces in contact. In this scenario, since the system is in equilibrium, the magnitude of the friction force is equal to the weight of the block, which is 200N.

Secondly, the direction of the friction force is always opposite to the direction of motion or potential motion of the object. In this case, since the block is on an incline, the direction of the friction force would be down the incline, opposing the motion of the block.

Now, coming to your attempt at solving the problem, I would like to clarify a few things. Firstly, the equation Ft1 + Ft2 = Fw is not applicable in this scenario as there is no tension force acting on the block. The force acting on the block is its weight, Fw = 200N.

Secondly, the equation Fw-Fn = Ff is not always true. This equation is only applicable when the object is on a horizontal surface and is not in motion. In this scenario, the normal force, Fn, is not equal to the weight of the block, but rather a component of the weight acting perpendicular to the incline.

Finally, the reason why the book wants 105 for the magnitude of the friction force is most likely due to rounding. The actual value of the friction force in this scenario is 107.8N, but rounding it to the nearest integer would give 108N. Similarly, the direction of the friction force being down the incline is due to the convention of using positive directions as up the incline and negative directions as down the incline.

I hope this helps clarify any confusion and aids in your understanding of the concept of friction force. As a scientist, it is important to understand and apply the correct equations and concepts in order to accurately analyze and solve problems.