How much work would it take to push a # 8 kg # weight up a # 5 m # plane that is at an incline of # pi / 4 #?

1 Answer
Jan 13, 2017

Answer:

The work done against the force of gravity is 277 joules.

Explanation:

The reason work must be done in this situation is that an applied force must act against gravity.

Work done on against (or by) a force is defined by

#W=FDeltadcostheta#

where #theta# is the angle between the direction of travel of the object and the direction of the force being applied.

You need to notice that in a problem such as this, the angle of the incline (and therefore of #Deltad#) is stated with respect to the horizontal, but because gravity is a vertical force, the angle we use in the formula is not this angle, but rather, we use its compliment (#pi/2 - theta#), because #theta# must be measured with respect to #F_g#.

That said, this time, both angles would be #pi/4#, but in the future, if faced with this question, try to keep this in mind.

The work done is #W=F(Deltad)cos(pi/4) = (8)(9.8)(5)(sqrt2/2)=277 J#