What is the average magnitude of force applied by the expanding spring in a dart gun with a projectile weighing 20 g that accelerates at 150 m/s²?

To find the average magnitude of force applied by the expanding spring in the dart gun, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).

In this scenario, the mass of the projectile is given as 20 grams. To work in standard SI units, we first convert grams to kilograms. There are 1000 grams in a kilogram, so:

[

20 \text{ g} = 0.020 \text{ kg}

]

Next, we know the acceleration of the projectile is 150 m/s². Now, substituting the mass and acceleration into the formula:

[

F = ma = 0.020 \text{ kg} \times 150 \text{ m/s}²

]

Calculating this gives:

[

F = 0.020 \times 150 = 3 \text{ N}

]

Thus, the average magnitude of force applied by the expanding spring is 3 N. This answer demonstrates the application of basic physics principles to calculate force based on mass and acceleration, covering the essential relationship laid out by Newton's laws.