# Math Help - weight increse over incline

1. ## weight increse over incline

A wagon with people weighs 2,850 pounds being pulled by a horse weighing 1700 pounds can be moved very easy on a flat surface but what is the weight load being put on the horse when he takes that same load up a 5 degree incline?

10 degree incline the same load would feel like ? pounds

20 degree incline the same load would feel like ? pounds

Thank you

2. Hello CarriageWhip

Welcome to Math Help Forum!
Originally Posted by CarriageWhip
A wagon with people weighs 2,850 pounds being pulled by a horse weighing 1700 pounds can be moved very easy on a flat surface but what is the weight load being put on the horse when he takes that same load up a 5 degree incline?

10 degree incline the same load would feel like ? pounds

20 degree incline the same load would feel like ? pounds

Thank you
The component of a vertical weight force, $W$, down a plane inclined at an angle $\alpha$ to the horizontal is $W\sin\alpha$.

So, if $\alpha = 0^o$, the component is $W\sin 0^o = 0$. In other words, there is zero component on a horizontal plane.

If $\alpha = 10^o, \sin10^o \approx 0.174$. So just over $17$% of the weight acts down the plane. If the weight is $2850$ lbs, this is about $495$ lbs.

$\sin20^o \approx 0.342$. So just over $34$% of the weight will act down a $20^o$ plane. In the case you quote, this is about $975$ lbs.

3. Thank you for the time to work with my problem. Next stupid question would be when you say "down the plane" is that mean pulling up hill or force put on a down hill and is there a difference?

4. Hello CarriageWhip
Originally Posted by CarriageWhip
Thank you for the time to work with my problem. Next stupid question would be when you say "down the plane" is that mean pulling up hill or force put on a down hill and is there a difference?
I'm sorry - I don't really understand your English. I have shown you how to calculate that part of the weight force that acts down the hill. So if there is no friction, this will be the force you'll have to exert up the hill to keep the wagon from rolling down.

5. I personally think for problems involving inclined planes, it is more convinient to choose the coordinate system axes with x along the incline and y perpendicular to it, than the "standard" horizontal & vertical axis. With these axes, you reperesent a force of magnitude $mg cos \theta$ along the negative y axis. And so the component of vertical weight force is $mg cos \theta$.