4.1 State the principle of conservation of momentum in words. The rocket is travelling vertically upwards at a constant speed $v$ when an internal explosion causes A to move DOWNWARDS at a speed $\frac{1}{3} v$. Ignore ALL external forces on the rocket: 4.2 Calculate the velocity of B in terms of $v$ immediately after the internal explosion. The graph below shows the average force exerted by A on B during the internal explosion as a function of time. 4.3 Name the physical quantity represented by the area under the graph. 4.4 Redraw the graph in your ANSWER BOOK. On the same set of axes, sketch the graph of average force that B exerts on A as a function of time.

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4.1 State the principle of conservation of momentum in words - NSC Physical Sciences - Question 4 - 2021 - Paper 1

Question 4

4.1 State the principle of conservation of momentum in words. The rocket is travelling vertically upwards at a constant speed $v$ when an internal explosion causes ... show full transcript

Worked Solution & Example Answer:4.1 State the principle of conservation of momentum in words - NSC Physical Sciences - Question 4 - 2021 - Paper 1

Step 1

State the principle of conservation of momentum in words.

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Answer

The principle of conservation of momentum states that the total (linear) momentum of an isolated or closed system remains constant. In simpler terms, the momentum before an event (like a collision) must equal the momentum after the event, provided no external forces are acting on the system.

Step 2

Calculate the velocity of B in terms of v immediately after the internal explosion.

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Answer

To solve this, we use the conservation of momentum:

Before explosion, momentum: $p_{initial} = (m_A + m_B) v = (3m + 2m)v = 5mv$

After explosion, momentum: $p_{final} = m_A v_A' + m_B v_B' = 3m(-\frac{1}{3}v) + 2m v_B'$

Setting the initial momentum equal to the final momentum: $5mv = 3m(-\frac{1}{3}v) + 2m v_B'$

o Multiplying through by $\frac{1}{m}$ gives: $5 = -1 + 2 \frac{v_B'}{v}$

o Rearranging this, we find: $2 \frac{v_B'}{v} = 6$ $v_B' = 3v$

Thus, the velocity of B immediately after the explosion is $3v$ downwards.

Step 3

Name the physical quantity represented by the area under the graph.

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Answer

The area under the graph represents impulse. Impulse is the change in momentum of an object when a force is applied over a period of time.

Step 4

Redraw the graph in your ANSWER BOOK.

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To sketch the graph of the average force that B exerts on A as a function of time, we note that this force will have an equal magnitude but opposite direction compared to the force that A exerts on B, due to Newton's Third Law. Therefore, the graph will mirror the original one, where the average force exerted by B on A is in the opposite direction. The areas under the curves will be equal, illustrating equal and opposite impulses.

4.1 State the principle of conservation of momentum in words - NSC Physical Sciences - Question 4 - 2021 - Paper 1

Worked Solution & Example Answer:4.1 State the principle of conservation of momentum in words - NSC Physical Sciences - Question 4 - 2021 - Paper 1

State the principle of conservation of momentum in words.

Calculate the velocity of B in terms of v immediately after the internal explosion.

Name the physical quantity represented by the area under the graph.

Redraw the graph in your ANSWER BOOK.

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