Forces acting on a truck on a slope

[bolzano95]

Homework Statement

The truck is on the slope 45 degrees and on it is acting a horizontal external force. How big is the force of the ground if the mass of the truck is 5000 kg and the truck is not sliding down the slope?

Homework Equations

First of all I drew myself a sketch. Then I asked myself: Which forces are acting on the selected body (=truck). My answer was
1. force of gravity (because of the Earth)
2. Force of the ground (because the truck is in touch with the ground)
3. External force.
Is there anything else that affects a body? In my opinion no.

$$\vec{F_{ground}} + \vec{F_{gravity}} + \vec{F_{external}} = 0$$
$$( F_{ground}sin\alpha, F_{ground}cos\alpha ) + ( 0, -mg ) + ( -F_{external}, 0 ) = ( 0, 0 )$$
$$F_{ground}sin\alpha = F_{external}$$
$$F_{ground}cos\alpha = mg$$ ... and from here I express equation for $$F_{ground}$$

 

[PhanthomJay]

Looks good!