Question #161974

A particle of mass m moves with momentum of magnitude p

A). Show that the kinetic energy of the particle is K = p^2 / 2m.

B). An object has a kinetic energy of 275J and a momentum of magnitude 25.0 kgm/s. Find the speed and mass of the object.


1
Expert's answer
2021-02-18T18:56:21-0500

A) By the definition of the linear momentum, we have:


p=mv.p=mv.

Then, we can write the kinetic energy of the particle as follows:


K=12mv2=12mmv2m=12(mv)2m=p22m.K=\dfrac{1}{2}mv^2=\dfrac{1}{2}\dfrac{m\cdot mv^2}{m}=\dfrac{1}{2}\dfrac{(mv)^2}{m}=\dfrac{p^2}{2m}.

B) Let's firs find the mass of the object from the formula:


K=p22m,K=\dfrac{p^2}{2m},m=p22K=(25.0 kgms)22275 J=1.14 kg.m=\dfrac{p^2}{2K}=\dfrac{(25.0\ \dfrac{kgm}{s})^2}{2\cdot275\ J}=1.14\ kg.

Finally, we can find the speed of the object from the definition of the linear momentum:


v=pm=25.0 kgms1.14 kg=22 ms.v=\dfrac{p}{m}=\dfrac{25.0\ \dfrac{kgm}{s}}{1.14\ kg}=22\ \dfrac{m}{s}.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS