Question

Under what conditions will a moving 0.030 kg marble and a moving 2.43 kg rock have the same kinetic energy

Answer 1

To have the same kinetic energy the speed of the marble must be 9 times the speed of rock.

Step-by-step explanation:

The general formula of kinetic energy is given as follows:

`K.E = (1)/(2)mv^(2)`

where,

K.E = Kinetic Energy

m = mass of the object

v = speed of the object

So, for the marble and rock to have same kinetic energy, we can write:

`K.E_(marble) = K.E_(rock)\\\\(1)/(2)m_(marble)v_(marble)^(2) = (1)/(2)m_(rock)v_(rock)^(2)\\\\(0.03\ kg)v_(marble)^(2) = (2.43\ kg)v_(rock)^(2)\\\\taking\ square\ root\ on\ both\ sides:\\v_(marble) = \sqrt{(2.43\ kg)/(0.03\ kg)}v_(rock)\\\\v_(marble) = 9\ v_(rock)`

Hence, to have the same kinetic energy the speed of the marble must be 9 times the speed of rock.