# Question #88a84

##### 1 Answer

See below.

#### Explanation:

An example of an instance where an object might lose mass as it travels would be a rocket burning fuel. This is obviously on a much larger scale and a rocket has a thrust force to keeping it accelerating in the proper direction, but there are real world problems which have to take this factor of losing mass into account.

Density is given by ratio of mass to volume of an object (

I'm going to assume air resistance is negligible for now and examine which properties of the sphere's motion change.

If you halve the mass, of course the force of gravity acting on the object decreases.

#vecF_1=mg#

#vecF_2=(1/2m)g=>1/2vecF_1# Where

#g# is a constant, the free-fall or gravitational acceleration.

If you double the mass, the force of gravity acting on the object doubles.

Note that this does not affect the vertical acceleration of the object if air resistance is negligible.

If the object suddenly loses half of its mass, its momentum will be suddenly halved at that point also:

#vecp_1=mvecv#

#vecp_2=(1/2m)vecv=1/2vecp_1#

And it doubles if you double the mass.

Additionally, suddenly halving the mass also halves the kinetic energy of the object:

#K_1=1/2mv^2#

#K_2=1/2(1/2m)v^2=1/2K_1#

Again,

I believe a sphere specifically would have not only translational kinetic energy but rotational as well, because it would spin as it moves through the air.

#K_(rot)=Iomega^2#

Where

#omega=v_t/r#

and

#(2/3mr^2 # vs.#2/5mr^2)# .

In spite of all of this, if air resistance is ignored and this is treated as a simple projectile motion problem where there is no horizontal acceleration and the vertical acceleration is a constant

#Deltas=vecv_iDeltat+1/2vecaDeltat^2#

#vecv_f=vecv_i+vecaDeltat#

#(vecv_f)^2=(vecv_i)^2+2vecaDeltas#

If air resistance is not negligible, this does make a difference where mass is concerned, but I do not know enough about these effects at this point to teach someone else about them when the effect of the drag force acting on the object is not constant.

Great question! :)