Which has more kinetic energy-a light truck or a heavy truck both moving with the same momentum?

Answer 1

Well, a light truck has a mass : m

a heavy truck has a mass : M

where : M > m

so if the have the same momentum :

m.V = M.V'

M > m, then V > V'

Let's set values ; m = 4 ; M = 8

4V = 8V' >>>> V = 2V'

Kinetic energy :

4*V^2 / 2 = 2V^2 >>>> light truck

8*V^2 / 8 = V^2 >>>> heavy truck

interesting, the light truck has more kinetic energy

Answer 2

Given each truck has same momentum:

m1v1 = M2V2,

where m1, v1 are mass and velocity of LIGHT truck

where M2, V2 are mass and velocity of HEAVY truck.

V2 =(m1v1) / M2
So kinetic energy of heavy truck is (1/2) M2V2^2 =
(1/2) M2 [m1v1 / M2] ^2 simplified to [(1/2) (m1v1)^2] / M2

and you'll notice the bracketed numerator is the kinetic energy * of the light truck! So despite your intuition the light truck has the greater KE.

[Intuition might suggest a 10 lb weight would fall twice as fast as a 5 lb weight. Sometime you can't trust it.]

*Footnote/Amendment/SLIGHT CORRECTION: The bracketed quantity is m1 TIMES the KE of lighter truck; so the KE of heavier truck is
m1/M2 (which is less than 1)times the KE of the lighter truck. The original premise is OK; my supporting algebra could use closer perusal!

Answer 3

Well, the simple answer in this case is the best. The one with the most kinetic energy will require the most energy to stop (the heavy truck). Force = mass x acceleration, right?

Answer 4

The heavy truck will and here is why

kinetic energy
n. The energy possessed by a body because of its motion, equal to one half the mass of the body times the square of its speed.

Answer 5

Just Visit the site :
www.saketjain.com

Although this is not related to the answer but this site contains e-mail forwards, a very nice way to refresh your mood.

Contact Me at : [e-mail]