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?
Apply conservation of linear momentum.
2*3 - 1*3 = (2+1)*Vfinal
Momentum remains to the right, since the right-moving mass had more momentum.
To solve this problem, we can use the principles of conservation of momentum. The conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system.
First, let's determine the initial momentum of each ball before the collision. The momentum (p) of an object is equal to the product of its mass (m) and velocity (v). So for the 2 kg ball moving to the right at 3 m/s, its initial momentum is:
p1 = m1 * v1 = 2 kg * 3 m/s = 6 kg*m/s
Similarly, for the 1 kg ball moving to the left at 3 m/s, its initial momentum is:
p2 = m2 * v2 = 1 kg * (-3 m/s) = -3 kg*m/s
Since both balls are moving in opposite directions, we take the negative sign for the second momentum.
Now, let's find the total initial momentum before the collision:
p_initial = p1 + p2 = 6 kg*m/s + (-3 kg*m/s) = 3 kg*m/s
Next, we need to determine the final momentum of the stuck together balls after the inelastic collision. Since the balls stick together, they move as one object. Let's denote the final velocity of the stuck together balls as vf. To find the final momentum, we multiply the total mass (m_total) of the two balls (2 kg + 1 kg = 3 kg) by the final velocity (vf):
p_final = m_total * vf
According to the conservation of momentum, p_initial = p_final. Therefore:
3 kg*m/s = 3 kg * vf
Now, let's solve for vf:
vf = (3 kg*m/s) / 3 kg = 1 m/s
So, the final magnitude of the velocity of the stuck together balls after the collision is 1 m/s.
To determine the direction, we can observe that the 2 kg ball was initially moving to the right and the 1 kg ball was moving to the left. Since the total momentum is positive after the collision, we can conclude that the balls move to the right (opposite to the initial velocity of the 1 kg ball).
Therefore, the final direction of the velocity is to the right.