In a lab experiment, a student is trying to apply the conservation of momentum. Two identical balls, each with a mass of 1.0 kg, roll toward each other and collide. The velocity is measured before and after each collision. The collected data is shown below.

| | Initial Velocity Ball A (m/s) | Initial Velocity Ball B (m/s) | Final Velocity Ball A (m/s) | Final Velocity Ball B (m/s) |
| :------ | :-----------------------------: | :-----------------------------: | :---------------------------: | :---------------------------: |
| Trial 1 | +1.0 | -2.0 | -2.0 | -1.0 |
| Trial 2 | +0.5 | -1.5 | -0.5 | -0.5 |
| Trial 3 | +2.0 | +1.0 | +1.0 | -2.0 |
| Trial 4 | +0.5 | -1.0 | +1.5 | -1.5 |

Which trial shows the conservation of momentum in a closed system?
A. Trial 1
B. Trial 2
C. Trial 3
D. Trial 4

Calculate the initial and final momentum for each trial using p = m A ​ v A ​ + m B ​ v B ​ .
Compare the initial and final momentum for each trial.
Identify the trial where the initial momentum equals the final momentum.
Trial 2 shows the conservation of momentum: T r ia l 2 ​ .

Explanation

Understanding the Problem We are given a problem involving the conservation of momentum in a closed system. We have data from four trials where two identical balls collide, and we need to determine which trial demonstrates the conservation of momentum. The conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In simpler terms, the total momentum before a collision should be equal to the total momentum after the collision.

Setting up the Solution To solve this problem, we need to calculate the total initial momentum and the total final momentum for each trial. The momentum of an object is given by the product of its mass and velocity ( p = m v ). Since both balls have a mass of 1.0 kg, we can simplify the calculations. The total momentum for each trial is the sum of the individual momenta of the two balls.

Calculating Momenta for Each Trial Let's calculate the initial and final momenta for each trial:


Trial 1: Initial momentum: p ini t ia l ​ = ( 1.0 kg ) ( 1.0 m/s ) + ( 1.0 kg ) ( − 2.0 m/s ) = 1.0 − 2.0 = − 1.0 kg m/s Final momentum: p f ina l ​ = ( 1.0 kg ) ( − 2.0 m/s ) + ( 1.0 kg ) ( − 1.0 m/s ) = − 2.0 − 1.0 = − 3.0 kg m/s
Trial 2: Initial momentum: p ini t ia l ​ = ( 1.0 kg ) ( 0.5 m/s ) + ( 1.0 kg ) ( − 1.5 m/s ) = 0.5 − 1.5 = − 1.0 kg m/s Final momentum: p f ina l ​ = ( 1.0 kg ) ( − 0.5 m/s ) + ( 1.0 kg ) ( − 0.5 m/s ) = − 0.5 − 0.5 = − 1.0 kg m/s
Trial 3: Initial momentum: p ini t ia l ​ = ( 1.0 kg ) ( 2.0 m/s ) + ( 1.0 kg ) ( 1.0 m/s ) = 2.0 + 1.0 = 3.0 kg m/s Final momentum: p f ina l ​ = ( 1.0 kg ) ( 1.0 m/s ) + ( 1.0 kg ) ( − 2.0 m/s ) = 1.0 − 2.0 = − 1.0 kg m/s
Trial 4: Initial momentum: p ini t ia l ​ = ( 1.0 kg ) ( 0.5 m/s ) + ( 1.0 kg ) ( − 1.0 m/s ) = 0.5 − 1.0 = − 0.5 kg m/s Final momentum: p f ina l ​ = ( 1.0 kg ) ( 1.5 m/s ) + ( 1.0 kg ) ( − 1.5 m/s ) = 1.5 − 1.5 = 0.0 kg m/s

Comparing Initial and Final Momenta Now, let's compare the initial and final momenta for each trial to see which one conserves momentum:


Trial 1: Initial momentum (-1.0 kg m/s)  = Final momentum (-3.0 kg m/s)
Trial 2: Initial momentum (-1.0 kg m/s) = Final momentum (-1.0 kg m/s)
Trial 3: Initial momentum (3.0 kg m/s)  = Final momentum (-1.0 kg m/s)
Trial 4: Initial momentum (-0.5 kg m/s)  = Final momentum (0.0 kg m/s)

From the above comparisons, we can see that only Trial 2 has the same initial and final momentum.

Conclusion Therefore, Trial 2 demonstrates the conservation of momentum in a closed system.

Examples
The principle of conservation of momentum is crucial in many real-world applications, such as designing safer vehicles. When a car crashes, engineers use the conservation of momentum to predict the motion of the car and its occupants, helping them design safety features like airbags and seatbelts that minimize injuries. Similarly, in sports like billiards or bowling, understanding momentum transfer helps players predict the motion of balls after collisions, improving their performance. Even in space travel, the conservation of momentum is used to calculate the trajectories of spacecraft and the effects of rocket propulsion.

Answered by GinnyAnswer | 2025-07-03

Trial 2 demonstrates conservation of momentum, as the total initial momentum (-1.0 kg m/s) equals the total final momentum (-1.0 kg m/s). Other trials do not satisfy this condition. Therefore, the correct answer is Trial 2.
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Answered by Anonymous | 2025-07-04