Question 200: Laws of Motion

Question

A machine gun fires bullets of mass $$30 \mathrm{~g}$$ with velocity of $$1000 \mathrm{~m} / \mathrm{s}$$. The man holding the gun can exert a maximum force of $$300 \mathrm{~N}$$ on it. How many bullets can he fire per second at most?

Accepted Answer

To determine how many bullets the man can fire per second without exceeding the maximum force he can exert, we need to compute the force applied due to the momentum change of the bullets being fired.
The momentum $ p $ of a single bullet is given by:
$$ p = m \cdot v $$
where $ m $ is the mass of the bullet and $ v $ is the velocity of the bullet. Here, $ m = 30 	ext{ g} = 0.03 	ext{ kg} $ (since $ 1 	ext{ g} = 0.001 	ext{ kg} $) and $ v = 1000 	ext{ m/s} $.
Now we calculate the momentum of a single bullet:
$$ p = 0.03 	ext{ kg} \cdot 1000 	ext{ m/s} = 30 	ext{ kg} \cdot	ext{m/s} $$
The rate of change of momentum gives us the force exerted by the bullets being fired. If $ F $ is the force and $ n $ is the number of bullets fired per second, the force is equal to the rate of change of momentum:
$$ F = n \cdot \frac{\Delta p}{\Delta t} $$
Since $ \Delta p $ is the change in momentum per bullet and $ \Delta t = 1 $ second (because $ n $ is measured in bullets per second), the force exerted by $ n $ bullets is:
$$ F = n \cdot \frac{30 	ext{ kg} \cdot 	ext{m/s}}{1 	ext{ s}} = n \cdot 30 	ext{ N} $$
We know the man can exert a maximum force of $ F_{\max} = 300 	ext{ N} $. Therefore, the maximum number of bullets ($ n_{\max} $) that can be fired per second without exceeding the maximum force is obtained by equating the two:
$$ 300 	ext{ N} = n_{\max} \cdot 30 	ext{ N} $$
Solving for $ n_{\max} $:
$$ n_{\max} = \frac{300 	ext{ N}}{30 	ext{ N/bullet}} = 10 	ext{ bullets/s} $$
Thus, the man can fire at most 10 bullets per second. Hence, the correct answer is:
$$ 	extbf{Option C: 10} $$

Answer

3

Answer

6

Answer

10

Answer

9

Laws of Motion

A machine gun fires bullets of mass $30 \mathrm{~g} with velocity of 1000 \mathrm{~m} / \mathrm{s}. The man holding the gun can exert a maximum force of 300 \mathrm{~N}$ on it. How many bullets can he fire per second at most?

Choose the correct answer: