How do I calculate the minimum force needed to prevent sliding due to friction?

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To calculate the minimum force needed to prevent the small cube from sliding, the weight of the small cube (39.2N) must be balanced by the frictional force, which is determined by the coefficient of static friction (0.71) and the normal force. The equation F = u * Fn is used, where Fn is the normal force acting on the small cube. The acceleration required to keep the small cube from falling is derived from the relationship mg = uma, leading to an acceleration of approximately 13.8 m/s². The total force P required to accelerate both cubes is then calculated as P = (mass of large cube + mass of small cube) * acceleration, resulting in a force of 400.2N. Understanding these relationships allows for the correct calculation of the necessary force to prevent sliding.
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Homework Statement


The drawing shows a large cube (m=25kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (m=4kg) is in contact with the fron surface of the large cube and will slide downward unless P is sufficiently large. The coefficient of static friction between the cubes is 0.71. What is the smallest magnitude that P can have in order to keep the small cube from sliding downwardsI know that the weight of the small cube is 39.2N. I also know that Fn is in the same direction as P. Past that, I'm confused. I have a equation: F=u*Fn, which is friction is equal to coef. of friction times normal force.

Can someone explain to me what to do next?
 
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11 views, 12 hours and no help... guess you guys can help me or even tell me what else I need to put down...
 
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On the small block, mass m, the downward force will be due to gravity mg.
The upward force will be due to friction and a normal force from the acceleration uma.
In order for the block not to fall uma=mg where u = 0.71
Once you have solved for a, ask yourself how much force it takes to give that much a to the whole system.
Tom
 
Ok. I have W of 4kg = 39.2N. In order for the block to not fall, friction has to be 39.2N.

mg=uma
4*9.8=.71*ma
39.2=.71*ma
ma=Fn=55.2N.

Where do I go from there? Can you at least tell me what m is supposed to be: 4kg or 25kg object?
 
How much mass are you pushing?
 
I am pushing 4kg to the right. Is that correct?
 
silvashadow said:
11 views, 12 hours and no help... guess you guys can help me or even tell me what else I need to put down...
we're not here to please you, be patient
 
With what are you pushing the 4kg?
 
You guys have been great. I've gotten help from my teacher and some fellow classmates. Guess this place just isn't good for those who seek help.
 
  • #10
Personally, I already know how to do the problem. I ask questions to try to guide you. Do you now understand the problem?
 
  • #11
friction of 4kg = weight of 4kg
friction = uFn
Ff=mg=uma
mg=uma
g=ua
9.8=.71a
a=13.8

P=ma=(mass of big + mass of small)*13.8=400.2N
 

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