Direction of acceleration in projectile motion

[JesnieC]

Homework Statement

Why is acceleration taken to be -g in vertical projection even when the object is falling towards the ground?

Homework Equations

The Attempt at a Solution

I know acceleration is -g when the object is going upwards but why is it still -g when the object is reaching the ground? Isn't the object accelerating in the same direction as gravity?

 

[Peter G.]

Gravity is always pulling things down, towards the center of the earth, hence, it is always accelerating them downwards no matter whether an object is going up or down. The acceleration is -g throughout because conventionally we take the downward direction to be negative.

So the acceleration time graph for an object being thrown upwards and then falling back downwards would be a straight horizontal line at the negative 9.81 mark.

If you are familiar with Newton's Second Law of Motion, it says that the acceleration is always in the same direction to the resultant force. In the case of an object thrown upwards, ignoring air resistance, the only force acting is mg, downwards, so you can predict the direction of the acceleration.

Hope this helps.

 

[AlexChandler]

Homework Statement

Why is acceleration taken to be -g in vertical projection even when the object is falling towards the ground?

Yes, think of Newton's law as a vector equation

$$\vec F = m \vec a$$

This means that the net force and the acceleration are in the same direction. Remember that acceleration is the rate of change of an objects velocity. For example, if the velocity is increasing in the +x direction, then the acceleration is in the +x direction. If the velocity is decreasing in the +x direction, then the acceleration is in the -x direction.

Maybe it will help to think about a mass spring system with the equation

$$\vec F = - k \vec x = m \vec a$$

in one dimension. If you pull the mass to the right, and let go, it will move to the left towards the equilibrium position. When it passes the equilibrium position, it will still be moving towards the left, but its velocity will be decreasing. If an objects velocity is decreasing in a certain direction, then this means it is accelerating in the opposite direction. Similarly, if an objects velocity is increasing in a certain direction, the object is accelerating in that direction.

Think about the spring equation. Draw a diagram of the spring in every different position. Draw the position vector, the force vector, the velocity vector, and the acceleration vector of the mass at every position. I think this exercise will be helpful.

It may not seem intuitive at first, but with some practice, it will come to make sense.