Choosing when intitial velocity is zero

[Mr Davis 97]

I have a quick question about when we can define the initial velocity to be zero. For example, in projectile motion problems, even though we know that projectile is originally at rest in a cannon, we assign the initial velocity to be some number that we can work with. However, for problems involving the work-energy theorem, no matter whether the ball has some measurable velocity at the beginning, on earth, we say that the initial velocity is zero in order to conclude that the work done is opposite that of gravity. Therefore, it seems that we pick and choose to define when velocity is zero. Why can we say it's zero in one type of problem (like work-energy theorem problems) but not other problems (liek projectile motion problems)?

 

[olivermsun]

A little clarification would be helpful. In the projectile motion problem, do you mean we give the initial velocity to be whatever velocity the projectile had when it left the barrel of the cannon? On the other hand, what kind of problem are you thinking of with the ball? Can you explain the example in some more detail?

 

[SteamKing]

I have a quick question about when we can define the initial velocity to be zero. For example, in projectile motion problems, even though we know that projectile is originally at rest in a cannon, we assign the initial velocity to be some number that we can work with.

That's not necessarily true. If a projectile is at rest in the cannon's bore before firing, it's going to stay there until the cannon is fired. But, the projectile resting comfortably inside the cannon is not what's interesting about this situation.

As the projectile leaves the muzzle of the cannon, it's going to be traveling at some definite velocity, having been accelerated by the expanding gases produced by the burning of the propellant with which the projectile is fired. After the projectile leaves the muzzle, the expanding gases from the propellant are no longer assumed to be accelerating the projectile, hence its instantaneous velocity at that time can be taken as a constant.

After that, gravity, air drag, etc., may or may not influence the motion of the projectile, as required by the problem statement.

While it is true that some problems have been simplified for teaching purposes, not everything about a given problem is necessarily made up.

 

[Dale]

However, for problems involving the work-energy theorem, no matter whether the ball has some measurable velocity at the beginning, on earth, we say that the initial velocity is zero in order to conclude that the work done is opposite that of gravity.

This is not always true in my experience. I have worked many such problems where the initial velocity was not zero.