Question: 6° Newton's 2nd Law relates force (F), mass (m) and acceleration (a), and is described by the formula, F = ma. Use Newton's 2nd law to determine the force in Newtons required to accelerate a m = 6.02 \times 10^4 kg satellite at a = 8.3 \times 10^{-2} m\cdot s^{-2}. Round answer to 1 d.p.
1. **State the problem:** We need to find the force $F$ required to accelerate a satellite with mass $m = 6.02 \times 10^4$ kg at acceleration $a = 8.3 \times 10^{-2}$ m/s$^2$ using Newton's 2nd law.
2. **Formula:** Newton's 2nd law states:
$$F = ma$$
where $F$ is force in Newtons, $m$ is mass in kilograms, and $a$ is acceleration in meters per second squared.
3. **Substitute the values:**
$$F = (6.02 \times 10^4) \times (8.3 \times 10^{-2})$$
4. **Calculate the product:**
$$F = 6.02 \times 8.3 \times 10^{4 + (-2)} = 6.02 \times 8.3 \times 10^{2}$$
Calculate $6.02 \times 8.3$:
$$6.02 \times 8.3 = 49.966$$
So,
$$F = 49.966 \times 10^{2} = 4996.6$$
5. **Round to 1 decimal place:**
$$F \approx 4996.6 \approx 5.0 \times 10^{3}$$
6. **Final answer:**
The force required is approximately $5.0 \times 10^{3}$ Newtons.
This matches the first choice in the multiple-choice options.