3. consider a locomotive and the rest of a freight train to be a single object. suppose the locomotive is pulling the train up a hill. describe the action and reaction forces that cause the locomotive to move up the hill, such as the reaction force and gravity.

The friction force and the x component for the weight should be the reaction forces that are opposite and equal to the action force, which causes the locomotive to move up the hill if the velocity of the locomotive remains constant.  

Explanation:

When the locomotive starts to pull the train up, appears two reaction forces opposed to the action force in the direction of the move.

The first one is due to the friction between the wheels and the ground, it will be the friction force (Fr):

Fr = μ*Pₓ =μmg*sin(φ)        

where μ: friction dynamic coefficient, Pₓ: is the weight component in the x-axis, m: total mass = train's mass + locomotive's mass, g: gravity, and sin(φ): is the angle respect to the x-axis.              

And the second one is the x component for the weight (Wₓ):

Wₓ = mg*cos(φ)  

where cos(φ): is the angle respect to the y-axis.    

These two forces should be the same as the action force, which causes the locomotive to move up the hill if the velocity of the locomotive remains constant.          

Explanation:

Newton’s third law explains how every action has an equal but opposite reaction, meaning that forces comes in pairs. While the locomotive’s wheels are pushing back against the ground as the action force, the ground is producing a reaction force towards the locomotive, propelling it forward. Another pair of forces that act on the locomotive is gravity and normal force. While gravity is pulling the locomotive towards the ground, the normal force the ground exerts on the locomotive is why the locomotive doesn’t fall through the ground.

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