回複：Can you show your work? Thank!

It is hard for me to type the nasty formula, but i will try.

Suppose you are pulling with a force F with an angle q (measured from horizontal). The the normal force N (or the supporting force from the surface) should be:

N = mg - F*sinq

Thus the friction force f is given by

f = N*mk = (mg - F*sinq)*mk

And if the object is moving with a constant speed, the force pulling forward ( F*cosq ) should be equal to the force pulling backward (the friction). Therefore

F*cosq=(mg - F*sinq)*mk

Solving for F, we have

F = mg*mk/(mk*sinq + cosq)

To find the minimum of F, we calculate

dF/dq = mg*mk*(mk*cosq - sinq)/(mk*sigq +cosq)^2

and let dF/dq=0, we have

(mk*cosq - sinq) = 0

This gives

tanq = mk

所有跟帖： 

• Thank you so much !! If I did not learn Calculus,how could I sol -pingshi- ♂ (0 bytes) () 10/02/2009 postreply 00:48:46

• 回複：Thank you so much !! If I did not learn Calculus,how could I -oldbookworm- ♂ (749 bytes) () 10/02/2009 postreply 21:47:15

• Thanks! I get your idea. -pingshi- ♂ (0 bytes) () 10/02/2009 postreply 23:54:18