Newtons Second Law of Motion (F = ma) Worksheet - Free Printable

Here are the step-by-step solutions for each problem on the worksheet. I have checked the calculations to ensure they are correct.

1. Water-filled Balloon

* Given: Mass ($m$) = $2\text{ kg}$, Acceleration ($a$) = $3\text{ m/s}^2$.
* Formula: $F = m \times a$
* Calculation: $2 \times 3 = 6$
* Answer: The force is $6\text{ N}$.

2. Gymnast and Mat

* Given: Force ($F$) = $10\text{ N}$, Acceleration ($a$) = $20\text{ m/s}^2$.
* Formula: $m = F / a$
* Calculation: $10 / 20 = 0.5$
* Answer: The mass of the mat is $0.5\text{ kg}$.

3. Loaded Coal Cart

* Given: Total Mass ($m$) = $300\text{ kg} + 20,000\text{ kg} = 20,300\text{ kg}$, Force ($F$) = $15,000\text{ N}$.
* Formula: $a = F / m$
* Calculation: $15,000 / 20,300 \approx 0.74$
* Answer: The wagon's acceleration is approximately $0.74\text{ m/s}^2$.

4. Theme Park Ride Carriage

* Given: Mass ($m$) = $1000\text{ kg}$, Acceleration ($a$) = $0.5\text{ m/s}^2$.
* Formula: $F = m \times a$
* Calculation: $1000 \times 0.5 = 500$
* Answer: The force required is $500\text{ N}$.

5. Football Kick

* Given: Force ($F$) = $7.5\text{ N}$, Acceleration ($a$) = $12\text{ m/s}^2$.
* Formula: $m = F / a$
* Calculation: $7.5 / 12 = 0.625$
* Answer: The mass of the football is $0.625\text{ kg}$.

6. Spring Gun Launching Ball

* Given: Mass ($m$) = $5\text{ N} / 0.95\text{ m/s}^2$ (Note: The problem lists "5 N" under mass, but Newtons are force. However, looking at the calculation provided in the image key, it treats 5 as the mass value directly or there is a typo in the question setup. Let's look at the calculation shown: $a = 5\text{ N} / 0.95\text{ kg}$. This implies the "5 N" was actually meant to be the Force, and we need to find acceleration, OR the mass is 0.95kg and Force is 5N. Let's re-read carefully.
* *Correction based on standard physics problems:* Usually, you are given Mass and Force to find Acceleration.
* Text says: "A spring gun... launch a 0.95 kg ball with a force of 5N."
* So, $m = 0.95\text{ kg}$, $F = 5\text{ N}$.
* Formula: $a = F / m$
* Calculation: $5 / 0.95 \approx 5.26$
* *Wait, looking at the image's own answer key logic:* The image text for #6 says "mass of 5 N" which is physically incorrect units, but the calculation box shows `a = 5 N / 0.95 kg`. This confirms $F=5$ and $m=0.95$.
* Calculation: $5 / 0.95 = 5.263...$
* *Note on the Image Key:* The image key has a typo/error in the final line for #6. It writes `a = 100 kg/1` which belongs to problem #9. The actual calculation for #6 should be $5.26\text{ m/s}^2$. However, if we strictly follow the visual pattern of the other answers, let's just solve it correctly.
* Correct Calculation: $5 / 0.95 = \mathbf{5.26\text{ m/s}^2}$.

7. Tractor Pulling Trailer

* Given: Mass ($m$) = $2400\text{ kg}$, Acceleration ($a$) = $4\text{ m/s}^2$.
* Formula: $F = m \times a$
* Calculation: $2400 \times 4 = 9600$
* Answer: The force required is $9600\text{ N}$ (or $9.6\text{ kN}$).

8. Canoeist Paddling

* Given: Force ($F$) = $5000\text{ N}$, Acceleration ($a$) = $10\text{ m/s}^2$.
* Formula: $m = F / a$
* Calculation: $5000 / 10 = 500$
* Answer: The mass of the canoe(s) is $500\text{ kg}$.

9. Satellite in Space

* Given: Mass ($m$) = $1000\text{ kg}$, Acceleration ($a$) = $0.1\text{ m/s}^2$.
* Formula: $F = m \times a$
* Calculation: $1000 \times 0.1 = 100$
* Answer: The rocket must exert $100\text{ N}$ of thrust.

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Final Answer:
1. 6 N
2. 0.5 kg
3. 0.74 m/s²
4. 500 N
5. 0.625 kg
6. 5.26 m/s²
7. 9600 N
8. 500 kg
9. 100 N