A 15 kg box rests on the floor. the coefficient for friction between the floor a

Question

A 15 kg box rests on the floor. the coefficient for friction between the floor and the box is .34. the box may be pushed with a force (F1) that is directed at an angle 28 degrees above the horizontal, or pulled with a force (F2) directed 28 degrees above the horizontal. the box is to be moved at a constant speed.

A) Determine the amount of force needed to move the box at constant speed in both cases.
B) Provide an explanation for why the force in one case is greater than the other. Be specific and complete.

Explanation / Answer

The mass of the block m = 15kg When it is push with an angle 28 deg From Newton's laws the net force Fnet = Fcos? - µ(mg + Fsin?) = 0 Fcos? = µ(mg + Fsin?) Fcos? - µFsin? = µmg F [ cos? - µsin?] = µmg therefore the applied force F = µmg / [ cos? - µsin?] = (0.34)(15)(9.8) / [ cos28 - (0.34)sin28] = 69 N When it is pull Fcos? = µ(mg - Fsin?) Fcos? + µFsin? = µmg F [ cos? + µsin?] = µmg therefore the applied force F = µmg / [ cos? + µsin?] = (0.34)(15)(9.8) / [ cos28 + (0.34)sin28] = 47.9 N Pulling

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