Question

@Abhisar
A block of mass m = 4.4 kg slides from left to right across a frictionless surface with a speed 8.4 m/s It collides in a perfectly elastic collision with a second block of mass M that is at rest. After the collision, the 4.4-kg block reverses direction, and its new speed is 2.5 m/s What is V, the speed of the second block after the collision?

6.4 m/s
5.1 m/s
5.9 m/s
7.2 m/s

Answer 1

diagram:
https://patr1234-patr-pps.gradpoint.com/Resource/4332114,5F1,0,0,0,0,0/Assets/testitemimages/physics_a/momentum/phyinela-f117g1_r.jpg

Answer 2

Ok..let's see !

Answer 3

Have u tried it yourself ?

Answer 4

Ye I get stuck because there no mass for M so you can't get velocity

Answer 5

Any ideas?

Answer 6

one min !

Answer 7

Starting velocity of other block is rest so 0

Answer 8

K

Answer 9

So u tried to equate the initial kinetic energy with final kinetic energy. Can u write down the equations ?

Answer 10

I did m*v+m*v=m+m*v where its each mass of the block times its own velocity

Answer 11

it should be 4.4*8.4 = 4.4*-2.5 + MV

Answer 12

Now i can see the problem. There is no M given.

Answer 13

Exactly

Answer 14

Its elastic does that help

Answer 15

Actually we can calculate it, but first we will have to derive the equation for velocities by using conservation of kinetic energy and conservation of momentum

Answer 16

How

Answer 17

Let's denote the initial velocity by u, final velocities by v1 and v2.

Answer 18

\(\color{blue}{\text{Originally Posted by}}\) @Abhisar
Now for conservation of momentum,

\(\huge\tt mu = mv_1 + Mv_2\)

--> \(\huge\tt m(u-v_1) = Mv_2\)
\(\color{blue}{\text{End of Quote}}\)

Answer 19

Won't we still get that we cant solve since theres no mass or velocity

Answer 20

wait.....it's not done yet. Just tell me if u got the above modification ?

Answer 21

Yea but its still just 48=mv2

Answer 22

Now for conservation of kinetic energy

\(\huge\tt \frac{1}{2}mu^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2\)

-->\(\huge\tt m(u-v)(u+v) = mv_2^2\) by using \(\huge\tt (a-b)^2 = (a-b)(a+b)\)

Answer 23

Getting ?

Answer 24

What is a and b

Answer 25

The mathematical identity !

Answer 26

Like (a+b)^2 = a^2 + b^2 + 2ab

Answer 27

Im gettong 283=mv and still cant solve

Answer 28

There is also an identity (a-b)^2 = (a-b)(a+b)

Answer 29

Wait !!!!

Answer 30

We havn't derived the formula yet..you want me to directly give you the formula !

Answer 31

Plz

Answer 32

LOL !

Answer 33

Lol

Answer 34

LOL wait !

Answer 35

You still need to know mass M

Answer 36

Dang

Answer 37

is ur question seriously complete ?

Answer 38

Yea this is all the info

Answer 39

uh-oh !

Answer 40

@ganeshie8 may help you !