Problem solving with forces and friction.

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The discussion focuses on solving problems involving forces and friction in various scenarios. The first problem requires calculating the minimum perpendicular force needed to prevent a crate from sliding down a 35° incline, given the crate's weight and the coefficient of static friction. The second problem involves determining how long it takes to move a box of books across a floor under the influence of a downward force and kinetic friction. The third scenario examines a system of two masses connected by a string over a pulley, where the goal is to find the coefficient of kinetic friction affecting one of the masses. Participants emphasize the importance of understanding force resolution and friction calculations to approach these problems effectively.
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1.The coefficient of static friction between the m = 2.90 kg crate and the 35.0° incline of Figure P4.41 is 0.340. What minimum force vector F must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?


2.A box of books weighing 250 N is shoved across the floor of an apartment by a force of 360 N exerted downward at an angle of 34.9° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 3.80 m, starting from rest?


3.Objects with masses m1 = 8.0 kg and m2 = 4.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.30. If, when the system starts from rest, m2 falls 1.00 m in 1.70 s, determine the coefficient of kinetic friction between m1 and the table.




Desperately need help don't have a clue what to do.
 
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I'm afraid you need to attempt these yourself before you can receive help. I can't believe you have no clue what to do. Do you have class notes or a book reference from which to read about friction?
 
OK I looked and I managed to figure out the third one but I just can seems to figure out how to start 1 and 2 give me something to just start I don't want the answer that won't help me.
 
Basically for the first one you'll have to resolve the forces on the box, work out the friction and then see how much more force is required to make the friction equal the force resolved parallel to the plane.

Question 2 is similar and is mainly about resolving forces.
 
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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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