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  1. Determine the behavior of a box placed on a horizontal surface under the following conditions. Also, determine whether at least one of the following is not possible or can not be determined with the information given:

(a) µS < µK

(b) FK < FS

(c) FT < FS(MAX)

(d) FS < FS(MAX)

(e) FK > FS

(f) FK/Fn = µS

(g) FS/Fn < µS

(h) Will the 90 Nt box move if a horizontal force of 100 Nt is exerted against it?

(i)Will another box pulled with 200 Nt just begin to move with slow but constant speed,

if µK = .57?

(j) Will the box in above be able to move with a constant speed if µS = .57?

 

2. Know the relationships among variables in a problem where a box is pulled forward with slow but steady speed, using a rope which makes an angle theta with the horizontal.

    1. FK = ?
    2. Fn = ?
    3. FE = ? (an equation which incorporates µK)

 

 

  1. Write mathematical expressions for the variables in #2 above, for a box pushed forward from behind,

    2. with slow but steady speed, when the exertion is at an angle theta with the horizontal.

     

     

  2. If a box is placed on an inclined surface, and the box remains at rest,
    1. what is the mathematical expression for FK in terms of FP?
    2. what is the mathematical expression for Fn in terms of FN?
    3. what is the mathematical expression for FK in terms of angle theta?
    4. Can the coefficient of friction be determined at any angle?

 

 

    5. If the box in #4 begins to move with slow but steady speed,

    1. what is the net force responsible for this motion?
    2. what role does the weight of the box have on the coefficient of friction?
    3. what is the mathematical expression for Fn in terms of FWT?

 

    6. If FWT is given for a box on an incline, with the length of the inclined surface, the vertical height of the inclined end, and the coefficient of friction, determine whether the box will remain at rest or will begin to move. The relationship between what two terms must you establish? How does µK = FK/Fn transform into a formula having angle theta as a variable? How does the angle theta taken from the physical description of the incline compare with the angle theta determined from the formula above? What behavior can be predicted by comparing these two values of theta?

 

    7. If the incline in problem #6 is replaced with another having similar length but with a different coefficient of kinetic friction, what force must be exerted against the box to prevent it from accelerating down the incline?

 

    8. Compare the effort needed to move two objects by interpreting their respective coefficient of rolling friction.

 

    9. Express FNET for a body accelerating on an inclined surface, in terms of angle theta and other relevant force vectors.

 

    10. Express FNET for a body accelerating on a horizontal surface through the relationships among other relevant force vectors.

 

    11. Given the original and final velocities of a moving body, and the coefficient of kinetic friction, determine the acceleration and/or distance traveled.