Calculating Final Energy of Stuck-Together Masses

[hodgepodge]

Homework Statement

A 2kg mass with KE=80 J strikes and sticks to an initially stationary 8kg mass. Calculate the final energy of the stuck-together masses.

Homework Equations

KE=1/2 x m x v squared

The Attempt at a Solution

i have no idea, any help would be appreciated

 

[rl.bhat]

Find the velocity of the 2 kg mass. then apply the law of conservation of momentum. Find the velocity of combined mass and hence the energy.

 

[hodgepodge]

found the velocity, but wat is the law of conservation of momentum? p=mv? if so, i then used K=(p squared)/(2m or m+m) and got 32 J

is that right?

 

[avenkat0]

p=mv where p is the linear momentum

the conservation of linear momentum says

where
u signifies vector velocity before the collision
v signifies vector velocity after the collision.

For an inelastic collision

 

[hodgepodge]

so since i have no epsillon it is inelastic? so i use the formula for inelastic collisions or p=mv?

 

[avenkat0]

whats your reasoning behind doing that?

Think about it like this, the first mass has kinetic energy initially.

now it strikes the second mass and they "stick together"... so in this process of sticking energy is lost to heat, bonding etc... but the momentum is conserved since there isn't a net external force on the system.
After they're are stuck they(m1+m2) start moving at a new velocity.
The question asks for the ENERGY in the final mass (m1+m2) after the collision

IF they stick together what kind of a collision is it? elastic or inelastic?

 

[hodgepodge]

inelastic, so i used that formula, and got final velocity of the entire mass to be 1.6886, then i put it into K=1/2 x m(total mass) x v(velocity of total mass) squared and fot 14.2568, am i even close?

 

[avenkat0]

you're close... can you write down exactly what you're doing so I know where you're going wrong

 

[hodgepodge]

K = 1/2 x m x v squared
80=.5 x 2 x v squared
v = 8.9443 m/s

m1 x v1i + m2 x v2i = (m1+m2)vf
2 x 8.443 + 8 x 0 = 2 + 8 x vf
16.886 = 10 x vf
vf = 1.6886 m/s

K = 1/2 x m x v squared
K = .5 x 10 x (1.6886) squared
K = 14.2568 J

 

[avenkat0]

v = 8.9443 m/s right... so
2 x 8.443? + 8 x 0 = 2 + 8 x vf

But everything else seems good.

 

[hodgepodge]

got 16.0001 J

Thank you so much!

 

[avenkat0]

No problem... anytime