1. A trunk that weighs 500 N isresting on a carpet. The coefficient of static fr

Question

1.      A trunk that weighs 500 N isresting on a carpet. The coefficient of static frictionbetween the trunk and the carpet is 0.40. The coefficient ofkinetic friction is 0.20.

a.       What horizontal forcepushing against the trunk would be required to start the trunkmoving?

b.     What horizontal force pushing on the trunk would be required tokeep it moving at a constant velocity?

c.       What force pushing againstthe trunk at an angle of 25 degrees below the horizontal would berequired to start the trunk moving?

d.     What force pushing against the trunk at an angle of 25 degreesbelow the horizontal would be required to keep it moving at aconstant velocity?

Explanation / Answer

let the force is F, we have: F-mgs = 0 F = mgs = 500N*0.40 = 200N the force required is 200N to start moving. b) after it start moving, the force required to moving atconstant speed (a=0) is F - mgk = 0 =>F = mgk = 500N*0.20 = 100N c) let it be F, Fcos(25) - [mg - F*sin(25)]*s = 0 =>Fcos(25) - mgs +Fsin(25)*s = 0 =>F = mgs / [cos(25) +sin(25)*s] = 185.994N d) let it be F, Fcos(25) - [mg - F*sin(25)]*k = 0 =>Fcos(25) - mgk +Fsin(25)*k = 0 =>F = mgk / [cos(25) +sin(25)*k] =92.997N let it be F, Fcos(25) - [mg - F*sin(25)]*k = 0 =>Fcos(25) - mgk +Fsin(25)*k = 0 =>F = mgk / [cos(25) +sin(25)*k] =92.997N

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