Zachary W. answered • 08/27/19
I am a physicist that wants everyone to know physics!
Translational kinetic energy is expressed as: T = (1/2)mv2
In this equation, T is the kinetic energy, m is the mass of the object that is moving, and v is the magnitude of the moving object's velocity (or speed).
We have two cars and were given each car's speed, but we were not given the masses of the vehicles. So we will have these variables:
T1 = kinetic energy of car 1,
m1 = the mass of car 1,
v1 = 15 km/h, which is the speed of car 1,
T2 = kinetic energy of car 2,
m2 = the mass of car 2,
v2 = 30 km/h, which is the speed of car 2.
Because we do not know the masses of the two vehicles, we will have to keep the masses as unknown variables and compare their kinetic energies in terms of those variables.
The kinetic energy of car 1 can be expressed as:
T1 = (1/2)m1v12 = (1/2)m1(15 km/h)2 = (112.5 km2/h2)m1.
The kinetic energy of car 2 can be expressed as:
T2 = (1/2)m2v22 = (1/2)m2(30 km/h)2 = (450 km2/h2)m2.
Now, to compare the two kinetic energies, we will find their ratio:
T1/T2 = ((112.5 km2/h2)m1)/((450 km2/h2)m2) = 0.25 (m1/m2) = m1/(4m2).
So, the ratio of the kinetic energies gives:
T1/T2 = m1/(4m2).
Note: Below here is a special case of this problem, and is not the actual answer unless the two cars' masses were in fact the same.
An interesting special case might be whenever the cars have the same mass, or m1 = m2, which would give a kinetic energy ratio of:
T1/T2 = 1/4.
Which would mean:
T2 = 4T1.
