Understanding the Center of Mass Acceleration in a Two-Body System

[kant]

Homework Statement

A cannonball is droped off a tower at a distence, but simultaneously a second cannonball is fired upward on the ground directly below it. What is the behavior ( movement ) of the center of mass acceration in such two body system.

Homework Equations

Newton s laws for systems

The Attempt at a Solution

A mass of distence d above the ground when droped, will have acceration g down ward. a second mass of the same multitude is fired from below to above, will have an acceration unknown to me. My attempt is that if i only known the acceration that initally impel the mass from the groud to above, i will be able to find the acceration of the center of mass.

Ma(cm) = m( 1)a( 1) + m(2)a( 2)

Where a( am) is a sub cm to donate the acceration of the center of mass.

a( 1) means a sub 1

I know that a(cm) is not downward

 

[neutrino]

a second mass of the same multitude is fired from below to above, will have an acceration unknown to me.

What are the forces that act on it?

 

[kant]

What are the forces that act on it?

Gravity, and and the initial forces that impel the cannon upward( such as throwing the cannon)

 

[neutrino]

Gravity is the only force which acts on it while it is in motion (assuming air-resistance is negligible). The problem asks you to study the motion of the CM after the cannon ball has been shot/thrown, therefore you need not take into consideration the initial forces.

 

[kant]

Gravity is the only force which acts on it while it is in motion (assuming air-resistance is negligible). The problem asks you to study the motion of the CM after the cannon ball has been shot/thrown, therefore you need not take into consideration the initial forces.

If that is the case, then the acceration of the cm is downward, but i know the answer is not just downward. It also goes up a bit, and then goes downward. What i don t know is why.

 

[Haywire]

What can you tell me about the initial velocity of the c.m.? Is it upward?

Nevertheless, as you calculated, the acceleration of the center of mass is always downward. It has to be, since the only external force acting on the system is gravity, which points always downwards.

 

[kant]

What can you tell me about the initial velocity of the c.m.? Is it upward?

Nevertheless, as you calculated, the acceleration of the center of mass is always downward. It has to be, since the only external force acting on the system is gravity, which points always downwards.

did you read my last post?

 

[neutrino]

It also goes up a bit, and then goes downward. What i don t know is why.

I think you are confusing the motion of the cm with that of the second ball. Where was the cm just before the the balls were dropped/shot? What was it's initial velocity? The acceleration is always towards the ground. (Essentially, this is what Haywire said, so (s)he must've read your post. )

 

[turdferguson]

Dont think of the position of the cm, just reason that the acceleration of a system's cm is the sum of the forces over the total mass. Each part is accelerating at g (projectile), so the cm is also accelerating at g

 

[tim_lou]

If that is the case, then the acceration of the cm is downward, but i know the answer is not just downward. It also goes up a bit, and then goes downward. What i don t know is why.

I think you are confused by the difference between acceleration and velocity. Sure, the ball goes up and then back down, but the acceleration is always the same, namely g. Since both balls accelerate at g, the acceleration for the cm must be g. (pointed downward)

(of course, this is neglecting the imperfection of the Earth's shape, Coriolis and Centrifugal force... also friction, quantum effects, relativistic effects and so on...)