How much work would it take to push a # 1 kg # weight up a # 9 m # plane that is at an incline of # (5pi) / 12 #?

1 Answer
Jan 20, 2016

Answer:

#W=PE = mgh= 1 kg xx 9.81 m/s^2xx8.69 m = 85.3 J#

Explanation:

The work done will be equivalent to potential energy gained as the object climbs incline of 9 m. So we need to calculate the side opposite the 75 degree angle. 75 degrees is steep angle indeed.

#5pi/12 =5xxcancel(180)/cancel(12) = 75 #
The gives you an idea of the incline steepness
graph{1.5x [-10, 10, -1, 5]}

The hypotenuse = 9m thus
#sin75 = (opp)/(hyp) = (opp)/9 #
# opp = 9 sin75 =m 8.69#
The work done is equivalent to potential energy gained
Thus#W=PE = mgh= 1 kg xx 9.81 m/s^2xx8.69 m = 85.3 J#