Paper 2 resources - Science Doctor - Free Printable

Here are the solutions to the problems on Newton's Second Law worksheet.

Basic

1. Units and Symbols Table

| Term | Symbol | Unit |
| :--- | :---: | :--- |
| Acceleration | $a$ | $\text{m/s}^2$ |
| Force | $F$ | $\text{N}$ (Newtons) |
| Mass | $m$ | $\text{kg}$ |

2. Equation Triangle
* Top section: Force ($F$)
* Bottom left section: Mass ($m$)
* Bottom right section: Acceleration ($a$)

3. Work out force ($F = m \times a$)
* a. $4\,\text{kg} \times 2\,\text{m/s}^2 = \mathbf{8\,N}$
* b. $150\,\text{kg} \times 3\,\text{m/s}^2 = \mathbf{450\,N}$
* c. $20\,\text{kg} \times 2.7\,\text{m/s}^2 = \mathbf{54\,N}$
* d. $500\,\text{kg} \times 5\,\text{m/s}^2 = \mathbf{2500\,N}$

4. $66\,\text{kg} \times 2\,\text{m/s}^2 = \mathbf{132\,N}$

5. $1000\,\text{kg} \times 9.8\,\text{m/s}^2 = \mathbf{9800\,N}$

6. $50\,\text{kg} \times 5\,\text{m/s}^2 = \mathbf{250\,N}$

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Medium

7. Rearranging Equations
* mass = Force / acceleration ($m = F/a$)
* acceleration = Force / mass ($a = F/m$)

8. Work out mass ($m = F / a$)
* a. $12 / 5 = \mathbf{2.4\,kg}$
* b. $200 / 25 = \mathbf{8\,kg}$
* c. $3 / 15 = \mathbf{0.2\,kg}$
* d. $3 / 0.5 = \mathbf{6\,kg}$

9. Work out acceleration ($a = F / m$)
* a. $20 / 5 = \mathbf{4\,m/s^2}$
* b. $7 / 14 = \mathbf{0.5\,m/s^2}$
* c. $2000 / 1250 = \mathbf{1.6\,m/s^2}$
* d. $0.75 / 0.45 = \mathbf{1.67\,m/s^2}$ (rounded)

10. $500\,\text{N} / 50\,\text{kg} = \mathbf{10\,m/s^2}$

11. $250\,\text{N} / 5\,\text{m/s}^2 = \mathbf{50\,kg}$

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Hard

12. First, convert grams to kilograms: $500\,\text{g} / 1000 = 0.5\,\text{kg}$.
Then calculate acceleration: $20\,\text{N} / 0.5\,\text{kg} = \mathbf{40\,m/s^2}$

13.
* a) Resultant Force: Subtract friction from the pulling force. $40\,\text{N} - 8\,\text{N} = \mathbf{32\,N}$
* b) Acceleration: Convert mass first ($200\,\text{g} = 0.2\,\text{kg}$). Then divide force by mass: $32\,\text{N} / 0.2\,\text{kg} = \mathbf{160\,m/s^2}$

14.
* Net Force: Gravity pulls down, air resistance pushes up.
* Weight of object: $0.3\,\text{kg} \times 9.8\,\text{m/s}^2 = 2.94\,\text{N}$.
* Net Force: $2.94\,\text{N} (\text{down}) - 1.5\,\text{N} (\text{up}) = \mathbf{1.44\,N}$
* Acceleration: $1.44\,\text{N} / 0.3\,\text{kg} = \mathbf{4.8\,m/s^2}$

15.
* Total Mass: Add the person and the sled together. $60\,\text{kg} + 15\,\text{kg} = 75\,\text{kg}$.
* Acceleration: $300\,\text{N} / 75\,\text{kg} = \mathbf{4\,m/s^2}$