Conservation of Momentum and Kinetic Energy in Inelastic Collisions

[x86]

Homework Statement

A 50g object is moving east at 0.3 m/s. A 100g object is moving east as well at 0.25 m/s. These objects have an inelastic collision.

a) Find their final velocity
b) Find the kinetic energy lost

Homework Equations

P1 + P2 = P3 + P4 ; momentum is conserved
Ek = 1/2 mv^2

The Attempt at a Solution

So the only thing conserved is momentum

Please excuse me for not using units, it's too confusing to do that on a keyboard.

a) (0.3 * 50/1000 + 0.25 * 100/1000) / (150/1000) = vf = 4 / 15 m/s

b) Ek1 = 0.5 * (50/1000) * 0.3^2 + 0.5 * (100/1000) * 0.25^2 = 0.005375 J
Ek2 = 0.5 * (50/1000) * (4/15)^2 + 0.5 * (100/1000) * (4/15)^2= 0.00533333333J

Ek1 - Ek2 = 0.000042 J

Is this correct? Someone said that its Ek2 - Ek1 but that doesn't make sense to me, because then delta(Ek) would be negative and this is impossible. Also, 10 marbles - 3 marbles. 7 were lost

 

[Fightfish]

Strictly speaking, $\Delta E$ of the system is negative; there's nothing wrong with that. The negative sign corresponds to a loss of energy. $\Delta E$ is defined as $E_{f} - E_{i}$

If you want to phrase it in terms of energy lost, then simply take the absolute value when intepreting the answer. It's generally not good practice to nudge your answer into a positive value "by hand" as the sign carries physical meaning (and it also confuses you - subtract which from which?)

 

[x86]

Strictly speaking, $\Delta E$ of the system is negative; there's nothing wrong with that. The negative sign corresponds to a loss of energy. $\Delta E$ is defined as $E_{f} - E_{i}$

If you want to phrase it in terms of energy lost, then simply take the absolute value when intepreting the answer. It's generally not good practice to nudge your answer into a positive value "by hand" as the sign carries physical meaning (and it also confuses you - subtract which from which?)

Ah I see, but isn't Einitial - Efinal also correct?

 

[Fightfish]

It gives you the answer you wanted in this case, but I emphasize that understanding general principle(s) and idea(s) is more important. That is, it is perfectly fine to use so-called "shortcuts" like this while solving problems, but it is essential to know what exactly you are doing when you use them.

 

[x86]

It gives you the answer you wanted in this case, but I emphasize that understanding general principle(s) and idea(s) is more important. That is, it is perfectly fine to use so-called "shortcuts" like this while solving problems, but it is essential to know what exactly you are doing when you use them.

Okay, thank you for the advice. I think that I will try harder to understand the principals.