algebra precalculus – How can I find the minimum force to apply to a slippery block in a slope as it moves at a constant speed?

Here is the problem:

The figure shows a block above a slope. Find the minimum force to apply on the block for the mass body $ m = 2 , kg $ such that this body moves with a constant speed upward in the inclination. We know that the coefficient of friction between the surfaces is $ mu = 0.3 $ and the angle of inclination is $ alpha = 30 ^ { circ} $.

Sketch of the problem

The alternatives given on my book are:

$ begin {array} {ll}
1. & 21 , N \
2. & 23 , N \
3. & 18 , N \
4. & 20 , N \
5. & 2.2 , N \
end {array} $

I really need help with this problem. Initially, I thought I should break down the strength and weight. Which I supposed that from the figure the force is parallel to the floor which is the base of the inclination.

By doing this and considering that the coefficient of friction (which I assumed static), this would translate as follows:

$ F cos alpha – mu N = 0 $

The normal or the tilt reaction I found using this logic:

$ N- mg cos alpha – F sin alpha = $ 0

$ N = mg cos alpha + F sin alpha $

Insert this into the equation above:

$ F cos alpha – mu left (mg cos alpha + F sin alpha right) = 0 $

$ F cos alpha – mu mg cos alpha – mu F sin alpha = 0 $

$ F left ( cos alpha – mu sin alpha right) = mu mg cos alpha $

$ F = frac { mu mg cos alpha} { cos alpha – mu sin alpha} $

Therefore, inserting the given information would become:

$ F = frac { frac {3} {10} (2 times 10) cos 30 ^ { circ}} { cos 30 ^ { circ} – frac {3} {10} sin 30 ^ { circ}} $

$ F = frac { frac {6 sqrt {3}} {2}} {cos 30 ^ { circ} – frac {3} {10} sin 30 ^ { circ}} $

$ F = frac { frac {6 sqrt {3}} {2}} { frac { sqrt {3}} {2} – frac {3} {10} times frac {1} { 2}} $

Here is where simplification becomes ugly:

$ F = frac {3 sqrt {3}} { frac {10 sqrt {3} -3} {20}}

$ F = frac {60 sqrt {3}} {10 sqrt {3} -3} about $ 27.25

So in the end, I get this value for strength. But it is far from the answer. Can any one help me with that ?. What could I have done wrong? How could I simplify that? Can any one offer FBD help to solve this problem?

ai – Move Unity NavMeshAgent at a constant speed

My NavMeshAgent shifts randomly as it moves along its path. It appears to be slower when a path segment is shorter (between two waypoints / turns) or when there are many continuous sharp turns. I tried to change the acceleration and angular velocity but it did not work. I've also tried modifying agent.velocity and although I've set it to vectors of equal magnitude for each image, it still does not move at a constant speed. I've also checked if everything is on the same Y coordinates because my game is orthogonal.

tracing – Draws a rotating elipse moved from the origin, keeping the dimensions constant

I'm trying to draw an ellipse in a parametric plot, rotated at an angle and shifted with respect to the origin with respect to the center. I'm almost there, here is my current solution

x[Rx_, Ry_, Cx_, α_, θ_] := 
 Rx Cos[α] Cos[θ] [Minus] 
  Ry Sin[α] Sin[θ] + Cx
y[Rx_, Ry_, Cy_, α_, θ_] := 
 Rx Cos[α] Sin[θ] + Ry Sin[α] Cos[θ] + Cy

 ParametricPlot[{x[10, 5, 0, α, θ], 
   y[10, 5, 3, α, 0.2 π]}, {α, 0, 2 π}, 
  PlotRange -> All], {θ, 0, 2 π}] 

However, as you will see by rotating the ellipse, once moved by the origin, the effective radius settings of the ellipse will change – not what I want! I suspect that when the ellipse is rotated, the parameters $ R_ {x} $ and $ R_ {y} $ are in relation to the $ x-y $ axis and not with the geometry itself, thus effectively becomes a rotation function.

Can anybody see a way to keep the identical shape when rotated for any central position of the ellipse? There is a solution here, but the problem is that if we move the ellipse, it does not turn around the center of the ellipse, but around the origin.

My online store is offline and gives CACHEGROUP an undefined error class constant

I hope someone can help me here. I am not at all familiar with the technical problems of Magento. I'm getting a startup error from my site. Anyone of similar with this problem? I hope you can put me online!


Fatal error: undefined class constant 'CACHE_GROUP & # 39; in /home/deb126395/domains/ on line 1075

The whole function is a polynomial or a constant?

Let $ f $ to be an entire function. $$ A = {z in mathbb {C} | f ^ (n) (z) = 0 hspace {.2cm} for hspace {.2cm} some hspace {.2cm} positive hspace {.2cm} integer hspace {.2cm} n} $$ Next

  1. Yes $ A = mathbb {C} $ then $ f $ is a polynomial or constant function.
  2. Yes $ A $ is uncountable then $ f $ is a polynomial or a constant.

I'm not getting this problem.Please give some ideas

How to create the icon Constant Glow Effect Icon?

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how to create such a brilliant effect in an icon via the code ???

security – A more efficient way to block the constant barrage of xhr ad-tracking queries?

I currently have a set of dynamic rules configured to block various ad tracking sites with the help of uBlock Origin, which work with a steady stream of requests, as observed in the recorder. My question would be: is there a more efficient way to proceed?

From what I've understood, the dynamic rules replace the "My filter" rules, but they both correspond to the same thing. Is there a previous point where I could cut these requests, or a potential tip to let a request go, then block it for toll-free numbering? Or maybe even kill him on arrival, so to speak?

My apologies for the poorly worded question. English is my mother tongue, so I do not really have a valid excuse.

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security – Constant risk of waking up on the local network?

I have a small, low – power home server from an old laptop motherboard and I want to keep it all the time. I do this by asking an Arduino to send a packet of wakeup ping on LAN every minute. Since the Arduino is still on, if there was a power failure and power was restored, the Arduino would wake up my home server. Are there security risks or general risks with this approach?

sql – constant date in a mysql database

The title is the same as the one I put on Google, and "even with quotation marks", this engine does not help. I ask you humans :]
I come here to see how to modify / display the date
and according to that all good, but I had the idea to set the date of origin of a user and with the field type date / time, I can not vary with time.
How can you insert or fix a fixed date ?, View the day of the recording, new field new attribute in the BD? and as if, type of field etc …