# Question on Horizontal Acceleration

#### Lucretius

Be advised this is not a homework question, even though it is in regards to a physics book I purchased over the summer to get a headstart on my upcoming AP class.

I was reading the chapter about acceleration, and the book seems to state that there is no such thing as horizontal acceleration. It gives the example of a cannonball moving equal horizontal distances per time interval. I know vertical acceleration exists because of gravity, but is there really no such thing as horizontal acceleration? Am I simply misunderstanding the book?

Doesn't a cannonball undergo horizontal acceleration when it is being fired from a cannon? It goes from a state of rest to faster and faster state of motion because of being acted upon by a horizontal force, correct?

I tried to reason this out for a day or two, but it still makes no sense. Hopefully you guys can clear it up for me :)

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#### Doc Al

Mentor
What the book probably meant to say is that, ignoring air resistance, a projectile in motion is only acted on by the force of gravity and thus only accelerates in the vertical direction. The horizontal speed of a projectile doesn't change.

Of course, while it's being fired out of the cannon there is surely other forces acting on it that do produce a horizontal acceleration. (The exploding gunpowder!) But once the cannon ball leaves the cannon, it is a projectile.

#### pallidin

Without the introduction or presence of a continuing force, a horizontal object will not experience continued acceleration in the horizontal frame.
That the ejection of the "cannon ball" has acceleration is not in question. The question is whether or not, and to what extent, this accelertion can be maintained, and largely drops-off quickly(the acceleration potential) after exiting the confined environment of the "barrel"

#### Lucretius

Oh, so an object in motion stays in that motion unless acted upon by an outside force? Would I be correct in stating that Newton's First Law states that no horizontal acceleration exists (excluding every force but gravity here) because of inertia?

One last question: If I were to roll a ball across the ground (ignoring friction and air resistance) would the pull of gravity down on the ball cause it to decelerate in the horizontal direction? Or would it just keep going?

#### Doc Al

Mentor
Lucretius said:
Oh, so an object in motion stays in that motion unless acted upon by an outside force? Would I be correct in stating that Newton's First Law states that no horizontal acceleration exists (excluding every force but gravity here) because of inertia?
Newton's 1st law says that an object will keep moving in a straight line at constant speed unless acted upon by a net force. When the cannonball leaves the cannon, there is no horizontal force and thus no horizontal acceleration. (Gravity acts downward, so there is a vertical acceleration downward.)

One last question: If I were to roll a ball across the ground (ignoring friction and air resistance) would the pull of gravity down on the ball cause it to decelerate in the horizontal direction? Or would it just keep going?
Assuming the ground were perfectly horizontal, it would keep going, sliding along. Since the ball is supported by the ground, the net force is zero. No acceleration at all. (If the ground were slanted downward, then the ball would accelerate as it slid down the hill.)

#### Lucretius

So let me check my understanding. We will suppose again that the ball is rolling across the ground ignoring the friction and the air resistance.

The ball would keep going perfectly horizontal because there are no forces acting horizontally on the ball, giving it a net force of zero, which allows it to remain in the state of motion it is in.

I just find it so bizarre that the gravitational force does not slow something down horizontally. I would have thought that the pull of gravity on something vertically would slow it down horizontally, or is gravity's pull on the object cancelled out by the balance of forces exerted by the ball and the horizontal surface it rolls on, making the ball not feel the effects of gravity, and thusly allowing it to experience no deceleration.

Are friction and air resistance the only horizontal forces then acting upon objects?

I'm sorry if my incessant questioning is getting annoying!

#### krab

Lucretius said:
Are friction and air resistance the only horizontal forces then acting upon objects?
Yes. I was going to say more, but found I would just be repeating what Doc Al already said. So just read his posts again.

#### Doc Al

Mentor
Lucretius said:
The ball would keep going perfectly horizontal because there are no forces acting horizontally on the ball, giving it a net force of zero, which allows it to remain in the state of motion it is in.
Sounds good to me.

I just find it so bizarre that the gravitational force does not slow something down horizontally. I would have thought that the pull of gravity on something vertically would slow it down horizontally, or is gravity's pull on the object cancelled out by the balance of forces exerted by the ball and the horizontal surface it rolls on, making the ball not feel the effects of gravity, and thusly allowing it to experience no deceleration.
Since gravity only acts downward, it cannot accelerate an object horizonally (on a horizontal surface).

Are friction and air resistance the only horizontal forces then acting upon objects?
In your example of the rolling ball, yes. In general, no.

#### False Prophet

I imagined that the downward component due to gravity also must slow the ball down horizontal too, all other forces aside I realize it doesn't, but I wonder does the pull of gravity somehow increase the friction so while considering friction (not air resistance) would different ammounts of gravity pulling the ball down impact the horizontal vector by changing the friction force?

#### Doc Al

Mentor
Yes, I would think that a heavier ball would produce a greater amount of rolling friction (due to surface deformation).

#### Lucretius

A ha! It just came to me after re-reading your post Doc Al! My problem was picturing the situation like so: I imagined gravity was an invisible line going from the Earth's surface to the center. I also imagined that when an object slid across a horizontal surface, that gravity went from a vertical force, to one that reached the object at an angle, trying to pull it back to the position in which the gravitational point of attraction was vertical in comparison to the object.

I just realized that I didn't take into effect the fact that no matter WHERE something goes, gravity will always be a vertical effect. Gravity is never at a "side angle" to something, it's always acting in a directly vertical way. There therefore is no horizontal deceleration because gravity works at a right angle in comparison to the horizontal direction.

I get it now!!! Thank you guys.

#### Doc Al

Mentor
Lucretius said:
I just realized that I didn't take into effect the fact that no matter WHERE something goes, gravity will always be a vertical effect. Gravity is never at a "side angle" to something, it's always acting in a directly vertical way. There therefore is no horizontal deceleration because gravity works at a right angle in comparison to the horizontal direction.
Exactly! Now you've got it.

#### brahmaphysics

Though it commonly seems that there is horizantal acceleration but i think the book is correct if you consider the case on earth. remember no matter how much horizantal force you apply there will be gravity present. the resultant of the horizantal force you apply and gravity will result in a force not at all horizantal. so there w,d be no horizantal acceleration. however for huge forces the effect is negligible.

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