2.)A 16 g mass is moving in the +x direction at 30 cm/s while a 4 g mass is moving in the -x direction at 50 cm/s. They collide head on and stick together. Find their velocity after the collision
To find the velocity of the masses after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is the product of its mass and velocity. We can calculate the momentum of the 16 g mass as (mass1 x velocity1) and the momentum of the 4 g mass as (mass2 x velocity2).
The initial total momentum before the collision can be calculated as:
Initial total momentum = (mass1 x velocity1) + (mass2 x velocity2)
Given:
mass1 = 16 g = 0.016 kg (since 1 g = 0.001 kg)
velocity1 = +30 cm/s (in the positive x-direction)
mass2 = 4 g = 0.004 kg
velocity2 = -50 cm/s (in the negative x-direction)
Substitute the given values into the equation for initial total momentum:
Initial total momentum = (0.016 kg x 30 cm/s) + (0.004 kg x -50 cm/s)
Now, we need to calculate the final velocity of the masses after the collision. Since the masses stick together, we can treat them as a single object with a combined mass. Let's call this combined mass as mf and the final velocity as vf.
Total momentum after the collision can be calculated as:
Total momentum after collision = mf x vf
Using the principle of conservation of momentum, we can say that the initial total momentum is equal to the total momentum after the collision. Therefore, we can set up the following equation:
(0.016 kg x 30 cm/s) + (0.004 kg x -50 cm/s) = mf x vf
Now, solve the equation to find the final velocity, vf.
(0.016 x 30) + (0.004 x -50) = mf x vf
(0.48) + (-0.2) = mf x vf
0.28 = mf x vf
We also know that the combined mass, mf, is the sum of the individual masses:
mf = mass1 + mass2
mf = 0.016 kg + 0.004 kg
mf = 0.02 kg
Substitute this value back into the equation:
0.28 = 0.02 kg x vf
Now, solve for vf:
vf = 0.28 / 0.02
vf = 14 m/s
Therefore, the velocity after the collision is 14 m/s.