A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
a) mp
b) p2/2m
c) mp/3
d) 1/2 mp2
c) mp/2
Hello, paulina,Originally Posted by paulina
$\displaystyle p=m\cdot v\ \Longrightarrow\ v=\frac{p}{m}$
The kinetic energy is $\displaystyle E_{kin}=\frac{1}{2}\cdot m\cdot v^2$. Plug in v into E and you'll get:
$\displaystyle E_{kin}=\frac{1}{2}\cdot m\cdot \left(\frac{p}{m}\right)^2$ = $\displaystyle \frac{p^2}{2m}$
So it's answer b)
Greetings
EB
Sloppy question $\displaystyle \bold{p}$ is a vector quantity, $\displaystyle KE$ is a scalar, but the wording seems to treat the two of them as if they are scalarsOriginally Posted by paulina
Also what is meant by $\displaystyle \bold{p}^2$ is not specified, presumably it means $\displaystyle |\bold{p}|^2$.
RonL
In Physics, $\displaystyle \bold{p}^2$ is defined to be the Euclidean dot product (unless otherwise stated), thus there is no ambiguity.Originally Posted by CaptainBlack
Note that the scalar vs. vector argument can be used to throw out answers a), c), and c) .
-Dan