Question

two objects with masses 500 kg and 2000 kg are moving at the same speed. what is the ratio of the kinetic energy of the second object to the kinetic energy of the first object? group of answer choices

Answer 1

Use equation Ek = 0.5mv^2

where m is the mass of the object that is moving and v is it's velocity and Ek is it's kinetic energy.

Let's call the 500kg mass 'A'
And the 2000kg mass 'B'

Rearrange the kinetic energy equation above to make v the subject:

mv^2 = 2Ek
v^2 = 2Ek/m
v = sqrt(2Ek/m)

For object A:

v = sqrt(2Ek(A)/500)
v = sqrt(Ek(A)/250)

For object B:

v = sqrt(2Ek(B)/2000)
v = sqrt(Ek(B)/1000)

Both objects have equal velocity therefore their equations can be equated:

sqrt(Ek(A)/250) = sqrt(Ek(B)/1000)

Rearrange for Ek(B) / Ek(A) :

Ek(A)/250 = Ek(B)/1000
Ek(A) = Ek(B)/4
Ek(A) / Ek(B) = 1/4

Therefore Ek(B) / Ek(A) = 4

4 is the answer.