Answer to Question #329010 in Mechanics | Relativity for soph

Question

A bicycle has a momentum of 24 kg m/s. What momentum would the bicycle have if it had…

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

Answer 1

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

Answer 2

… three times the 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 twice the speed?

Answer 5

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

Answer 1

The momentum equals:

$p=mv.$

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

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

$p'=m'v'=2mv=2p=2\cdot 24=48\space kg\cdot m/s.$

Answer 1: $48\space kg\cdot m/s.$

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

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

$p'=m\cdot v/2=p/2=24/2=12\space kg\cdot m/s.$

Answer 2: $12\space kg\cdot m/s.$

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

$m'=3m,\space v'=2v.$

$p'=3m\cdot 2v=6mv=6p=6\cdot 24=144\space kg\cdot m/s.$

Answer 3: $144\space kg\cdot m/s.$

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

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

$p'=(m/2)\cdot 2v=mv=p=24 \space kg \cdot m/s.$

Answer 4: $24 \space kg \cdot m/s.$

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

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

$p'=m\cdot 2v=2mv=2p=2\cdot 24=48 \space kg\cdot m/s.$

Answer 5: $48 \space kg\cdot m/s$

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

$m'=3m,\space v'=v/2.$

$p'=3m\cdot v/2=(3/2)mv=(3/2)p=(3/2)\cdot 24=36\space kg\cdot m/s$.

Answer 6: $36\space kg\cdot m/s$