An Amusing Kinematic Fact
Most recent answer: 08/21/2012
Q:
if kinetic energy of two balls is same and having different mass and they offers sama retarding force than they covers same distance explain why?
- ashok goyat (age 17)
meham
- ashok goyat (age 17)
meham
A:
Hello Ashok,
I like this one, I haven't seen it before. It turns out that you don't need two different masses to determine the solution, one is sufficient. The distance traveled is independent of mass but depends only on the initial kinetic energy and the retarding force.
The premises are:
1: The two balls have the same amount of kinetic energy, i.e. KE = mv2/2.
2: There is a constant retarding force, with magnitude F. This means that the deceleration is a constant given by a = -F/m.
Now use the tried and true formulas x = xo + vo*t + a*t2/2 and v = vo + a*t. You know vo from the initial kinetic energy and mass so you can solve for t when the body stops. Plugging this value into the x formula you find the final value for x is independent of the mass. QED
LeeH
I like this one, I haven't seen it before. It turns out that you don't need two different masses to determine the solution, one is sufficient. The distance traveled is independent of mass but depends only on the initial kinetic energy and the retarding force.
The premises are:
1: The two balls have the same amount of kinetic energy, i.e. KE = mv2/2.
2: There is a constant retarding force, with magnitude F. This means that the deceleration is a constant given by a = -F/m.
Now use the tried and true formulas x = xo + vo*t + a*t2/2 and v = vo + a*t. You know vo from the initial kinetic energy and mass so you can solve for t when the body stops. Plugging this value into the x formula you find the final value for x is independent of the mass. QED
LeeH
(published on 08/21/2012)