Answer to Question #327596 in Mechanics | Relativity for soph

Question

A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have if it had …

… three times the mass and was moving with one-half the speed?

Answer 1

… twice the mass and was moving at the same speed?

Answer 2

… the same mass and was moving with twice the speed?

Answer 3

… one-half the mass and was moving with twice the speed?

Answer 4

… the same mass and was moving with one-half the speed?

Answer 1

The equation for kinetic energy:

$E=\frac{mv^2}{2}.$

If bicycle had three times the mass and was moving with one-half the speed?

$m'=3m,\space v'=\frac{v}{2}.$

$E'=\frac{m'v'^2}{2}=\frac{3mv^2}{2\cdot 4}=\frac{3}{4}E=\frac{3}{4}124=93\space J.$

Answer 1: 93 J

If bicycle had twice the mass and was moving at the same speed?

$m'=2m, \space v'=v.$

$E'=\frac{m'v'^2}{2}=\frac{2mv^2}{2}=2E=2\cdot124=248\space J.$

Answer 2: 248 J

If bicycle had the same mass and was moving with twice the speed?

$m'=m, \space v'=2v.$

$E'=\frac{m'v'^2}{2}=\frac{m\cdot 4v^2}{2}=4E=2\cdot124=496\space J.$

Answer 3: 496 J

If bicycle had one-half the mass and was moving with twice the speed?

$m'=\frac{m}{2}, \space v'=2v.$

$E'=\frac{m'v'^2}{2}=\frac{m\cdot 4v^2}{2\cdot 2}=2E=2\cdot124=248\space J.$

Answer 4: 248 J