A 0.200 kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.100 kg, which is moving along the same line at a speed of 0.10 m/s. After the collision, both balls continue moving in the same, original direction. The speed of the 0.100 kg ball is 0.26 m/s. What is the new velocity of the 0.200 kg ball?
You can solve for that with the conservation of momentum equation (for motion along one axis only) but my question is how you do that?
Before impact
m = 0.200 kg
v = 0.30 m/s
p = 0.06
m = 0.100 kg
v = 0.10 m/s
p = 0.01
After impact
m = 0.200 kg
v = ?
m = 0.100 kg
v = 0.26 m/s
p = 0.026
Now, I'm a little confused on how to find the velocity should i use the same momentum but then although mass doesnt change that doesnt mean momentum doesnt change.
I tried that it’s not right
Ok, thanks a lot! Merry christmas and a happy almost new yr
To solve for the new velocity of the 0.200 kg ball after the collision, you can indeed use the conservation of momentum equation.
The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. In other words, the initial momentum of the system will be equal to the final momentum of the system.
Before the collision, the momentum of the system is:
total initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
= (0.200 kg * 0.30 m/s) + (0.100 kg * 0.10 m/s)
= 0.06 kg·m/s + 0.01 kg·m/s
= 0.07 kg·m/s
After the collision, the momentum of the system is:
total final momentum = (mass1 * velocity1') + (mass2 * velocity2')
Let's assign the new velocity of the 0.200 kg ball as velocity1' and the new velocity of the 0.100 kg ball as velocity2'.
Now, since both balls continue moving in the same, original direction, we know that velocity2' is given as 0.26 m/s.
Therefore, we can rewrite the equation for total final momentum as:
total final momentum = (0.200 kg * velocity1') + (0.100 kg * 0.26 m/s)
Now, since we have the total initial momentum and the total final momentum, we can set the two equal to each other and solve for velocity1':
0.07 kg·m/s = (0.200 kg * velocity1') + (0.100 kg * 0.26 m/s)
Simplifying the equation, we get:
0.07 kg·m/s = 0.200 kg·m/s + 0.026 kg·m/s
Combining like terms, we have:
0.07 kg·m/s = 0.226 kg·m/s
To isolate velocity1', we subtract 0.226 kg·m/s from both sides of the equation:
0.07 kg·m/s - 0.226 kg·m/s = 0.226 kg·m/s - 0.226 kg·m/s + 0.226 kg·m/s
-0.156 kg·m/s = 0
Finally, we solve for velocity1':
velocity1' = -0.156 kg·m/s / 0.200 kg
velocity1' = -0.78 m/s
Therefore, the new velocity of the 0.200 kg ball after the collision is -0.78 m/s. The negative sign indicates that the velocity is in the opposite direction of the original motion.
thanks! merry christmas
You are welcome. Happy New Year and Merry Christmas !
Original momentum = .06+.01 = .07
that is also the final momentum
.07 = .2*v + .026