Why is acceleration inversely proportional to mass?
acceleration equals to the force applied divided by mass
an object moving at a velocity of x carries the force of its mass times its speed.
when you apply a force onto an object, the increase in speed of it would be affected by its mass. Think of it this way: you apply some force onto an iron ball, and apply the same force on a plastic ball (they are of equal volume). Which one moves faster, and which one moves slower? The answer is obvious: the iron ball will accelerate slower and travel slower, while the plastic ball is faster.
The iron ball has a greater mass, so the force which makes it accelerate is deduced more. The plastic ball has a smaller mass, so the force applied is divided by a smaller number.
I hope this helps you a bit.
Assuming we're using
Say we wish to keep a force
The answer is: the object's acceleration must be halved.
We start with
and if we double the mass to
#2F = 2m*a#
This is an example of direct proportionality between
But we want to keep the force the same; we don't want
#F= 2m*1/2 a#
This is an example of inverse proportionality. When the force is taken as a constant, if mass doubles, acceleration must be halved.
You can also see the inverse relation between
#F=ma " "=>" "a=F/m" " <=>" "a=F(m^-1)#
#color(white)(F=ma) " "=>" "m=F/a" "<=>" "m=F(a^-1)#
It's now easy to see mathematically that