# 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.

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 $mg cos \theta$.