How much work would it take to push a # 6 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?

1 Answer
Apr 17, 2016

Answer:

#166.31Nm#

Explanation:

It is always good to start a mathematical model with certain assumptions. Here, we are ignoring air resistance, friction, and assuming that gravity is a constant #9.8m/s^2# downwards.

The force straight down with gravity is given by

#F=ma#

where #m# is the mass of #6kg# and #a# is acceleration of gravity, #9.8m/s^2#, so

#F_("vertical down")=6kg*9.8m/s^2=58.8N#.

But since the plane gets in the way and the mass cannot move straight down, it would have to move down the #pi/4# plane. Using trigonometry, this gives a force down the plane of

#F_("down plane")=58.8N*cos(pi/4)#
#=58.8cos45=41.578N#

In order to move up the plane, you need to exert a force equal to or greater than the force down the plane, which means

#F_("up plane")=41.578N#

Now, to find the work you use the equation

#W=Fd#,

where #F# is the force we have already found and #d# is the distance of #4m# up the plane, so

#W=41.578N*4m=166.31Nm#