# How much work does it take to push an object with a mass of #2 kg# up a #2 m# ramp, if the ramp has an incline of #(11pi)/12 # and a kinetic friction coefficient of #3 #?

##### 1 Answer

My calculator is in the degree mode, so I will convert

Note:

I prefer to use conservation of energy. The top of the ramp has gravitational potential energy of

In addition to that, work was done against the force of friction -- call it

So the sum is

Now I will calculate work using the force *distance method. (Because cos165 has a negative value, I will use cos15 instead of cos165 in the following steps.)

The force of friction from the work above is

Exerting that force over the 2 m length calculates to

There is also some work against gravity. The downslope component of the weight of that mass,

So the work of pushing against that force is

So the sum is

I hope this helps,

Steve