Physics Homework Problem Newtons Laws of Motion

AI Thread Summary
A physics homework problem involves calculating the acceleration of an object under a force on a frictionless surface. The discussion highlights the use of Newton's second law, F=ma, and the law of cosines to resolve forces into a resultant force. Participants clarify that while the acceleration is given, the mass of the object is not, complicating the application of these laws. The Pythagorean theorem is identified as a special case of the law of cosines, aiding in visualizing the resultant force. Ultimately, understanding the components of the forces allows for solving the unknown acceleration and mass.
destro47
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I have this problem on a web assignment due on the 20th of this month. A few of the problems have completely blown my mind including the following:

A force F0 causes an acceleration of 18 m/s2 when it acts on an object of mass m sliding on a frictionless surface. Find the magnitude of the acceleration of the same object in the circumstances shown in each figure below




I know F=ma, but doesn't seem to be enough to solve this problem. I have also included a picture of the diagram which accompanied this problem. I would appreciate any help or guidance that could point me in the right direction.
04-24.gif
 
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You need to resolve the two forces into a single force.

Do this by drawing a diagram in which the two forces form two sides of a triangle. The third side represents the resultant force.

Since you know two of the side lengths, and also the angle which separates them, it is possible to calculate the magnitude of the third force using the cosine rule.
c^{2} = a^{2} + b^{2} - 2abCosC

It is also possible to determine the angle that the resultant force acts at by using the sine rule.
a/SinA = b/SinB = c/SinC
 
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If I think that I understand you correctly ur saying to use the law of cosines to find the magnitude of the resultant force graphically. That makes sense, but what I don't understand is how that would work. Only the acceleration is given, the magnitude of the force is not given in this problem. Also, the mass of the box is not given so how would the law of cosines be applicable here?
 
never mind...makes sense now. I feel like a total retard. I used Pythagorean theorum to solve part A. I just realized that the pythagorean theorum is becomes a special case of the law of cosines when angle C = 90*
 
Well for the first case you have all you need, you should be able to intuitively "see" the resultant force. Now take the component of each applied force in that direction, using this and the known force F_0 you can solve for the unknown acceleration.

Once you have the acceleration you can solve for mass m and use it in part b.Edit: I'm to slow. Glad you got it.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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