A student used a spreadsheet to model the conservation of momentum. (a) State the principle of conservation of momentum. (b) The spreadsheet modelled an elastic collision between object A and object B. Before collision object A object B After collision The spreadsheet shows the initial values and final values when the student tested the model. A B C D E 1 Initial values 2 mass / kg 3 0.85 1.70 0.85 1.70 4 magnitude of velocity / m/s 5 1.30 0.98 0.54 6 angle of velocity to x direction (i) Deduce whether the values show an elastic collision... (ii) Deduce whether the values show the conservation of momentum...

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A student used a spreadsheet to model the conservation of momentum - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 4

Question 14

A student used a spreadsheet to model the conservation of momentum. (a) State the principle of conservation of momentum. (b) The spreadsheet modelled an elastic co... show full transcript

Worked Solution & Example Answer:A student used a spreadsheet to model the conservation of momentum - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 4

Step 1

State the principle of conservation of momentum.

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Answer

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. This implies that the momentum before an interaction is equal to the momentum after the interaction.

Step 2

Deduce whether the values show an elastic collision.

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Answer

To determine if the collision is elastic, we can check if the kinetic energy before and after the collision is conserved.

Calculation of Kinetic Energy Before the Collision:

For object A:

$E_k = \frac{1}{2} mv^2 = \frac{1}{2} (0.85 \text{ kg}) (1.30 \text{ m/s})^2 = 0.72 \text{ J}$
For object B:

$E_k = \frac{1}{2} mv^2 = \frac{1}{2} (1.70 \text{ kg}) (0.85 \text{ m/s})^2 = 0.48 \text{ J}$
Total Kinetic Energy Before:

$E_k (before) = 0.72 + 0.48 = 1.20 \text{ J}$

Calculation of Kinetic Energy After the Collision:

For object A:

$E_k = \frac{1}{2} (0.85 \text{ kg}) (0.98 \text{ m/s})^2 = 0.41 \text{ J}$
For object B:

$E_k = \frac{1}{2} (1.70 \text{ kg}) (0.54 \text{ m/s})^2 = 0.25 \text{ J}$
Total Kinetic Energy After:

$E_k (after) = 0.41 + 0.25 = 0.66 \text{ J}$

Conclusion:

Since the total kinetic energy before (1.20 J) is not equal to the total kinetic energy after (0.66 J), the values show that the collision is not elastic.

Step 3

Deduce whether the values show the conservation of momentum.

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Answer

To check for conservation of momentum, we will calculate the momenta of the objects before and after the collision.

Calculation of Momentum Before the Collision:

For object A:

$p_A = m_A \cdot v_A = 0.85 \text{ kg} \cdot 1.30 \text{ m/s} = 1.11 \text{ kg m/s}$
For object B:

$p_B = m_B \cdot v_B = 1.70 \text{ kg} \cdot 0.85 \text{ m/s} = 1.45 \text{ kg m/s}$
Total Momentum Before:

$p_{total} (before) = p_A + p_B = 1.11 + 1.45 = 2.56 \text{ kg m/s}$

Calculation of Momentum After the Collision:

For object A:

$p_A' = m_A \cdot v_A' = 0.85 \text{ kg} \cdot 0.98 \text{ m/s} = 0.83 \text{ kg m/s}$
For object B:

$p_B' = m_B \cdot v_B' = 1.70 \text{ kg} \cdot 0.54 \text{ m/s} = 0.92 \text{ kg m/s}$
Total Momentum After:

$p_{total} (after) = p_A' + p_B' = 0.83 + 0.92 = 1.75 \text{ kg m/s}$

Conclusion:

Since the total momentum before (2.56 kg m/s) is not equal to the total momentum after (1.75 kg m/s), the values do not show conservation of momentum.

A student used a spreadsheet to model the conservation of momentum - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 4

Worked Solution & Example Answer:A student used a spreadsheet to model the conservation of momentum - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 4

State the principle of conservation of momentum.

Deduce whether the values show an elastic collision.

Calculation of Kinetic Energy Before the Collision:

Calculation of Kinetic Energy After the Collision:

Conclusion:

Deduce whether the values show the conservation of momentum.

Calculation of Momentum Before the Collision:

Calculation of Momentum After the Collision:

Conclusion:

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