Well the subject line isn’t the best but what I’m trying to figure out is if an object accelerates instantaneously in this situation.
Say you throw a ball straight down. As soon as the ball leaves your hand, you are no longer adding force to the ball so it accelerates at only 9.81 m/s/s (the acceleration due to gravity). This is because all acceleration is caused by a force and with no force, there is no acceleration. Is the change in acceleration instantaneous from the point you release the ball to the point the ball accelerates at 9.81 m/s/s?
In a sidenote and for further reference, how do I super and/or subscript so I don’t have to write m/s/s anymore?
Figured out the subscript/superscript thing. I just didn’t feel like opening a new browser to search “About This Message Board”. But question numero uno still remains unanswered.
The short answer: Theoretically yes, practically no.
In other words: A change in acceleration can be instantaneous in theoretical terms (that is, the function a(t) needn’t be continuous), but in reality, as you release the ball you’re applying less and less force until the ball no longer touches your hand. It happens over a very short time, but it still causes a(t) to be continuous.
However, if you’re doing calculations about it, I’d treat it as discontinuous/instantaneous.
And I had answered your other question, but I previewed and you’ve answered it yourself.
No. The force of gravity acts on the ball whether you hold it or let it go, and this has a relatively constant value. When you hold the ball, the value is the same but is balanced by the force on your hand – the ball doesn’t move but has two equal, balanced forces acting on it in different directions. When you let it go, it still has the same gravitational force acting on it. There is no change in the gravitational constant.
I understand fully that the gravity is constantly accelerating the ball downwards (or to the center of the Earth anyway). But when you throw the ball, say you hypothetically accelerate it an extra 10 m/s[sup]2[/sup]. Thus, the ball is considered to be travelling downwards at 19.81 m/s[sup]2[/sup]. As soon as you release the ball, though, is the change from 19.81 to 9.81 instant or gradual? That was essentially what my question is.
When you accelerate the ball downwards, the extra force you are adding on it is accelerating at 19.81m/s[sup]2[/sup], once that force is no longer applied, it only accelerates at 9.81m/s[sup]2[/sup]; however, it still takes on the velocity right before the force was no longer applied and then accelerates downwards from there at 9.81m/s[sup]2[/sup]. An analogy of your thought experiment would be a rocket, once it runs out of fuel the acceleration instantly becomes negative, it is slowing down, however, it takes time for the velocity to actually start being negative - the change in acceleration is instantaneous.
The ball is accelerating the whole time you are in the process of throwing it. When it leaves your hand you have imposed upon it a via this acceleration an initial velocity of v[sub]0[/sub]. This initial velocity now adds to the velocity imparted by continuing gravitational acceleration. V = v[sub]0[/sub] + ½ g*t[sup]2[/sup]
Sorry. Rereading your OP, I see I did not say anything you didn’t already know. Sorry.
When your hand adds a force to the ball, either to balance gravity or add additional acceleration; then this force is discontinued, the acceleratin will change, as you say, but not instantaneously. In practice, you cannot discharge the force of the hand instantaneously. Quickly, you start to let go, then let go more, then let go fully over a short time, but Newton’s second law still applies.
I agree with the good doctor. An acceleration graph may look discontinuous, but in reality, acceleration must always be continuous (as must be velocity).
I’m wrong. In practice you cannot completely discharge a force instantaneously. No matter how fast the force disappears there still is an extremelly small time interval in which the amount of force being applied is changing, you cannot have the change in force as instantaneous and therefor the change in acceleration can’t be either. Refer to LazarusLong42’s post.
At first the ball is acc. at the acc.you provide to it since you are holding it, g is not really important to the acc. here as you are counteracting it.
When you start to release it, the ball starts to come off your hand, the force you are applying diminishes and the ball NOW can actually acc. with gravity. As it leaves your hand then you have gravity working on it constantly to acc. it.
I think it’s also important to note that the velocity imparted by your hand is not constant. As your arm moves through its arc, it is accelerating and then decelerating through the force imparted by your muscles. If the arm ween’t decelerating, it would probably break your shoulder when it stopped suddenly.
On the downward stroke, at some point in the deceleration curve, the force of gravity exceeds that imparted by the hand and the ball leaves the hand.
Yay! If the good doctor is right, then I just found a valid argument for a question on my stupid test. I’d talk more about it but then this thread would end up in Great Debates or IMHO. So thanks for the help, my teacher is gonna get it on Monday.
