Question

A) A same-size iron ball and wooden ball are dropped simultaneously from a tower and reach the ground at the same time. The iron ball has a greater momentum, Why?

b) The total momentum of a flock of identical birds could be zero only if the birds are flying in different directions. Why?

Answer 1

A) Because it has a greater mass

The momentum of an object is defined as:

`p=mv` (1)

where

m is its mass

v is its velocity

Two object dropped from the same height at the same time have same acceleration (g, acceleration of gravity, downward), so if we neglect air resistance, they will have same final velocity, according to the suvat equation:

`v^2-u^2=2as \rightarrow v = √(u^2+2as)`

where u = 0 is the initial velocity, a = g is the acceleration of gravity, s is the displacement (the height of the tower).

Therefore, the final velocity of the iron ball and of the wooden ball will be the same. However, the iron ball has a greater mass, so according to eq.(1), its momentum will be greater.

B) Because their momenta have opposite sign

The momentum is defined as

`p=mv`

where

m is the mass

v is the velocity

Velocity is a vector quantity, so momentum is a vector as well: this means that it has a direction.

Here we have a group of birds: if they are flying, this means that the magnitude of their momentum is not zero (because neither m nor v is zero). The only possibility for the total momentum to be zero is that their momenta are in opposite direction: that would mean that their momenta have opposite sign. In fact, if we consider two identical birds flying with same velocity in opposite directions, their total momentum will be:

`p= m v + m (-v) = mv - mv = 0`