A ball with a mass of 0.5 kg is traveling at 25 m/s and collides with a ball at rest that has a mass of 2 kg. After the collision, both balls are traveling 5 m/s in the same direction. Was momentum conserved?
Well, it sounds like those two balls certainly had a wild collision! Now, let's talk about momentum conservation. In an isolated system like this, the total momentum before and after the collision should be the same if there are no external forces acting on the system.
To check if momentum was conserved, we need to consider the momentum of each ball before and after the collision.
Before the collision, the first ball has a momentum of (0.5 kg) * (25 m/s) = 12.5 kg*m/s, and the second ball is at rest, so its momentum is zero.
After the collision, both balls are moving at 5 m/s. So, the momentum of the first ball is (0.5 kg) * (5 m/s) = 2.5 kg*m/s, and the momentum of the second ball is (2 kg) * (5 m/s) = 10 kg*m/s.
Now, if we add up the momentum before the collision, we get 12.5 kg*m/s + 0 kg*m/s = 12.5 kg*m/s. If we add up the momentum after the collision, we get 2.5 kg*m/s + 10 kg*m/s = 12.5 kg*m/s.
So, we can see that the total momentum before the collision is equal to the total momentum after the collision, which means momentum was conserved! Those balls did quite a balancing act.
To determine if momentum was conserved, we need to calculate the total momentum before and after the collision.
The formula for momentum is:
Momentum (p) = mass (m) x velocity (v).
Let's calculate the total momentum before the collision:
Initial momentum (before collision) = (mass of ball 1 x velocity of ball 1) + (mass of ball 2 x velocity of ball 2)
Ball 1 (moving) = mass 1 x velocity 1 = 0.5 kg x 25 m/s = 12.5 kg·m/s
Ball 2 (at rest) = mass 2 x velocity 2 = 2 kg x 0 m/s = 0 kg·m/s
Total initial momentum = 12.5 kg·m/s + 0 kg·m/s = 12.5 kg·m/s.
Now, let's calculate the total momentum after the collision:
Total momentum (after collision) = (mass of ball 1 x velocity of ball 1) + (mass of ball 2 x velocity of ball 2)
Both balls are traveling at 5 m/s in the same direction, so:
Ball 1 (after collision) = mass 1 x velocity 1 = 0.5 kg x 5 m/s = 2.5 kg·m/s
Ball 2 (after collision) = mass 2 x velocity 2 = 2 kg x 5 m/s = 10 kg·m/s
Total final momentum = 2.5 kg·m/s + 10 kg·m/s = 12.5 kg·m/s.
The total initial momentum (before collision) was 12.5 kg·m/s, and the total final momentum (after collision) was also 12.5 kg·m/s.
Since the initial momentum is equal to the final momentum, we can conclude that the momentum was conserved in this collision.
To determine whether momentum was conserved in this collision, we need to calculate the momentum before and after the collision for both balls.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is calculated as:
p = m * v
For the first ball with a mass of 0.5 kg and a velocity of 25 m/s, the initial momentum is:
p1_initial = 0.5 kg * 25 m/s
For the second ball at rest with a mass of 2 kg, its initial momentum is:
p2_initial = 2 kg * 0 m/s (since it is at rest)
The total initial momentum of the system (both balls) is the sum of the individual momenta:
p_initial_total = p1_initial + p2_initial
Now let's calculate the final momentum after the collision. We are given that both balls are traveling with a velocity of 5 m/s in the same direction. Therefore, the final momentum for the first ball is:
p1_final = 0.5 kg * 5 m/s
For the second ball (which was initially at rest), its final momentum is:
p2_final = 2 kg * 5 m/s
The total final momentum of the system is the sum of the individual momenta:
p_final_total = p1_final + p2_final
Now, to determine if momentum was conserved, we need to compare the initial and final total momentum:
If p_initial_total = p_final_total, then momentum is conserved.
Let's calculate the values and check if momentum was conserved:
p_initial_total = (0.5 kg * 25 m/s) + (2 kg * 0 m/s)
p_initial_total = 12.5 kg·m/s
p_final_total = (0.5 kg * 5 m/s) + (2 kg * 5 m/s)
p_final_total = 10 kg·m/s
Since p_initial_total (12.5 kg·m/s) does not equal p_final_total (10 kg·m/s), the total momentum was not conserved in this collision.
Given:
M1 = 0.5kg, Vi = 25 m/s.
M2 = 2kg, V2 = 0.
V3 = 5 m/s = Velocity of M1 and M2 after colliding.
a. M1*V1 + M2*V2 = 0.5*25 + 2*0 = 12.5kg-m/s = Momentum before colliding.
b. M1*V3 + M2*V3 = Momentum after colliding.
If a and b are equal, momentum is conserved.