Grade 12 Physical Sciences · Mechanics · Draw momentum vector diagrams

Draw momentum vector diagrams Grade 12

Draw arrows for the initial momentum, final momentum and change in momentum, including when an object bounces back, for example a ball that hits a wall with 4 kg·m/s and rebounds with 3 kg·m/s has Δp = 7 kg·m/s away from the wall.

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Practice · NavyBlue · 2 marks

A trolley of mass

0, 8

kg moves to the left at

2, 5

m·s

^{- 1}

. Friction slows it down to

1, 0

m·s

^{- 1}

, still moving to the left. Take left as positive.

(b) Draw a vector diagram showing

p_{i}

p_{f}

and

Δ p

for the trolley.(2)

Work it out on paper first. Then mark yourself with the memo, one tick at a time.

More questions: draw momentum vector diagrams

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3. Practice · NavyBlue · 3 marks
A soccer ball of mass $0, 45$ kg rolls east at $8$ m·s $^{- 1}$ . A player kicks it and it moves west at $12$ m·s $^{- 1}$ . Take east as positive.
(c) Draw a vector diagram, roughly to scale, that shows the initial momentum, the final momentum and the change in momentum of the ball.(3)
Show the memo (3 ticks)Memo
1. ✓
  Initial momentum arrow $p_{i}$ : arrow pointing east, length representing $3, 60$ kg·m·s $^{- 1}$
  1 mark · Draw momentum vector diagrams
2. ✓
  Final momentum arrow $p_{f}$ : arrow pointing west, $1, 5$ times as long as $p_{i}$ ( $5, 40$ kg·m·s $^{- 1}$ )
  1 mark · Draw momentum vector diagrams
3. ✓
  Change in momentum arrow $Δ p$ : arrow pointing west, $2, 5$ times as long as $p_{i}$ ( $9, 00$ kg·m·s $^{- 1}$ ), so that $p_{i} + Δ p = p_{f}$
  1 mark · Draw momentum vector diagrams
4. Practice · NavyBlue · 2 marks
A tennis ball of mass $60$ g falls vertically and hits the court at $9$ m·s $^{- 1}$ . It bounces straight up and leaves the court at $7$ m·s $^{- 1}$ . Take upward as positive.
(b) Draw a labelled vector diagram showing $p_{i}$ , $p_{f}$ and $Δ p$ for the bounce.(2)
Show the memo (2 ticks)Memo
1. ✓
  Initial and final momentum arrows $p_{i}$ : downward arrow ( $0, 54$ kg·m·s $^{- 1}$ ); $p_{f}$ : shorter upward arrow ( $0, 42$ kg·m·s $^{- 1}$ )
  1 mark · Draw momentum vector diagrams
2. ✓
  Change in momentum arrow $Δ p$ : upward arrow, longest of the three ( $0, 96$ kg·m·s $^{- 1}$ )
  1 mark · Draw momentum vector diagrams
5. Practice · NavyBlue · 2 marks
A ball of mass $0, 25$ kg moves to the right and hits a wall. The vector diagram shows its initial momentum $p_{i}$ and its final momentum $p_{f}$ , drawn to scale on a grid in which one square represents $0, 5$ kg·m·s $^{- 1}$ . The ball is in contact with the wall for $0, 04$ s. Take right as positive.
(c) Draw the change in momentum vector, to the same scale, and write down its magnitude and direction.(2)
Show the memo (2 ticks)Memo
1. ✓
  Arrow and scale $Δ p = p_{f} - p_{i}$ : an arrow $10$ squares long pointing left (from the head of $p_{i}$ to the head of $p_{f}$ when they share a tail)
  1 mark · Draw momentum vector diagrams
2. ✓
  Value $Δ p = 10 \times 0, 5 = 5, 0$ kg·m·s $^{- 1}$ to the left
  1 mark · Draw momentum vector diagrams
6. Practice · NavyBlue · 2 marks
A car of mass $1200$ kg travels north. The driver speeds up from $10$ m·s $^{- 1}$ to $16$ m·s $^{- 1}$ . Take north as positive.
(b) Draw a vector diagram, roughly to scale, showing the initial momentum, the final momentum and the change in momentum of the car.(2)
Show the memo (2 ticks)Memo
1. ✓
  Initial and final momentum arrows $p_{i}$ ( $12000$ kg·m·s $^{- 1}$ ) and $p_{f}$ ( $19200$ kg·m·s $^{- 1}$ ): both arrows point north, $p_{f}$ is $1, 6$ times as long as $p_{i}$
  1 mark · Draw momentum vector diagrams
2. ✓
  Change in momentum arrow $Δ p$ : arrow pointing north ( $7200$ kg·m·s $^{- 1}$ ), $0, 6$ times the length of $p_{i}$ ; $p_{i} + Δ p = p_{f}$
  1 mark · Draw momentum vector diagrams

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