A 2 kg ball of putty moving to the right at 3m/s has a head-on inelastic collision with a 1 kg ball of putty moving to the left at 3m/s. What is the final magnitude and direction of the velocity of the stuck together balls after the collision?
Linear momentum is conserved. Therefore
M1*V1 + M2*V2 = (M1 + M2)*Vfinal
2*3 -1*3 = (2 + 1)*Vfinal
Vfinal = 1 m/s
in the positive (right) direction
To find the final magnitude and direction of the velocity of the stuck together balls after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision. Mathematically, this can be expressed as:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
- m1 and m2 are the masses of the two objects (in this case, the two balls of putty)
- v1 and v2 are the velocities of the two objects before the collision
- vf is the velocity of the stuck together balls after the collision
Given:
- m1 = 2 kg (mass of the first ball of putty)
- v1 = 3 m/s (velocity of the first ball moving to the right)
- m2 = 1 kg (mass of the second ball of putty)
- v2 = -3 m/s (velocity of the second ball moving to the left; negative because it's in the opposite direction)
Plugging in the values, we get:
(2 kg * 3 m/s) + (1 kg * -3 m/s) = (2 kg + 1 kg) * vf
(6 kg·m/s - 3 kg·m/s) = 3 kg * vf
3 kg·m/s = 3 kg * vf
Simplifying the equation, we find:
vf = 3 kg·m/s / 3 kg
vf = 1 m/s
Therefore, the final magnitude of the velocity of the stuck together balls after the collision is 1 m/s.
Now, let's determine the direction. Since the first ball was originally moving to the right and the second ball was moving to the left, the net momentum after the collision is in the direction of the first ball. Therefore, the direction of the final velocity is to the right.
In conclusion, the final magnitude of the velocity of the stuck together balls after the collision is 1 m/s, and the direction is to the right.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. So, we can calculate the initial momentum of each ball:
Initial momentum of the 2 kg ball = mass x velocity = 2 kg x 3 m/s = 6 kg·m/s (to the right)
Initial momentum of the 1 kg ball = mass x velocity = 1 kg x (-3 m/s) = -3 kg·m/s (to the left)
Since momentum is a vector quantity, we take the positive direction as to the right and the negative direction as to the left.
Now, let's calculate the total initial momentum before the collision:
Total initial momentum = momentum of the 2 kg ball + momentum of the 1 kg ball
= 6 kg·m/s + (-3 kg·m/s)
= 3 kg·m/s (to the right)
According to the principle of conservation of momentum, the total momentum after the collision will be equal to the total initial momentum.
Since the balls stick together after the collision, they will move as a single object. Let's assume their final velocity is V (to be determined).
The final momentum of the stuck together balls will be the product of their total mass (2 kg + 1 kg = 3 kg) and their final velocity (V):
Final momentum of the stuck together balls = total mass x final velocity = 3 kg x V
According to the principle of conservation of momentum:
Total initial momentum = Total final momentum
Therefore,
3 kg·m/s (to the right) = 3 kg x V
Now, let's solve for V:
V = (3 kg·m/s) / 3 kg
V = 1 m/s
Hence, the final magnitude of the velocity of the stuck together balls after the collision is 1 m/s. Since the initial velocities of the balls have opposite directions, the final direction of the stuck together balls after the collision will be to the right.