How much work does it take to lift a #180 kg # weight #3/2 m #?

Question

How much work does it take to lift a #180 kg    # weight #3/2 m    #?

Adrian Ayala · Accepted Answer

#2646J#

Work is equal to force times distance. Initially, you must apply a force upward on the weight equal to the gravitational force in order to overcome its gravitational pull:

#180kgxx9.8m/s^2#

#=1764kgm/s^2#

#=1764 N#

At this point, the weight is not moving, but there is a net force of zero acting on it. It is not rising or falling.

Then you move it up through a course of #3/2m#:

#1764Nxx3/2m#

#=2646N*m#

#=2646J#

#J# (joules) is the unit for work. 2646 is how much work is done to lift the weight by #3/2m#.

Another way to look at it is this: work is the measurement of the amount of energy that is converted from one form to another. Energy is a conserved quantity, which means that it can only be transferred from one form to another. It cannot be created or destroyed.

In this case as the weight is being lifted, the kinetic energy it gained from the force you exert on it, is converted to its gravitational potential energy. When it is at #3/2m# above the ground, it has a gravitational potential energy of #180kgxx9.8m/s^2xx3/2m=2646J# So its gravitational potential energy went from 0 at ground level to #2646N #at #3/2m#.

In conclusion, #2646J# of work is done on the #180kg# weight as you lift it #3/2m# above ground. :)

Charles Aeschliman · Answer

#2646# joules

Given that the weight is being raised, the overall work completed will be the box's increased gravitational potential energy. The gravitational potential energy can be found using this formula: #"GPE"=mgh# #m# is the mass of the object in kilograms #g# is the gravitational acceleration, which is around #9.8 \ "m/s"^2# #h# is the height in meters Thus, we obtain: #"GPE"=180 \ "kg"*9.8 \ "m/s"^2*1.5 \ "m"# #=2646 \ "J"#

Adam Arnold · Answer

undefined Work = Force × Distance × cos(θ)
Work = (180 kg) × (9.8 m/s²) × (3/2 m) × cos(0°)
Work = 2646 J (joules)