What is the average force a 0.200 kg dart applies to a block during impact when fired horizontally?

To determine the average force that a 0.200 kg dart applies to a block during impact when fired horizontally, we first need to consider the relationship between mass, acceleration, and force as described by Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = ma).

Assuming the dart is fired at a certain speed and comes to a stop upon impacting the block, we first need to know its initial velocity. However, since the question does not provide an exact speed, let's assume a reasonable initial speed for a dart, for instance, 16.0 m/s, which is typical for a dart fired from a common pneumatic launcher.

1. Calculate the momentum of the dart before impact:

Momentum (p) = mass (m) × velocity (v)

p = 0.200 kg × 16.0 m/s = 3.2 kg·m/s

2. Assume the time duration of the impact (Δt):

For a typical dart impact, this could be quite short. If we assume, for example, that the impact lasts around 0.1 seconds, we can calculate the average force during this time.