Work of pulling sleigh in the top of the hill including the friction

[Xaime]

What work must be done to pull a loaded sleigh (total weight of 10 kg ) on the top height H=10 m. Gradient of slope amounts 30 degrees. Coefficient of friction between the sleigh and the ground decreases linearly along the way from 0,5 at the food of the hill to 0,1 in the top.

The pararell compnent of gravitational force

F _{s}=mg \sin \alpha

and the force of friction

F _{T}=mg\cos\alpha \mu

My formula for elementary Work is

dW=mg(\sin\alpha+ \cos \alpha \mu) dx

Now I have problem with integrate this equation, that is with the linearly changing coefficient of friction.

 

[gneill]

What work must be done to pull a loaded sleigh (total weight of 10 kg ) on the top height H=10 m. Gradient of slope amounts 30 degrees. Coefficient of friction between the sleigh and the ground decreases linearly along the way from 0,5 at the food of the hill to 0,1 in the top.

The pararell compnent of gravitational force

F _{s}=mg \sin \alpha

and the force of friction

F _{T}=mg\cos\alpha \mu

My formula for elementary Work is

dW=mg(\sin\alpha+ \cos \alpha \mu) dx

Now I have problem with integrate this equation, that is with the linearly changing coefficient of friction.

Hi Xaime, Welcome to Physics Forums.

In future, please retain and use the Homework Posting Template that is provided when you start a new thread in the Homework sections of the Forums.

For your problem, you'll have to write an expression for the friction coefficient that varies appropriately with the position on the slope. So μ(x) = some function of x, where x is the distance along the slope.