In what distance can a 25 gram bullet traveling at 250m/s be stopped by force of 5000N?
In what distance can a 25 gram bullet traveling at 250m/s be stopped by force of 5000N?
force*distance= 1/2 m*v^2
To determine the distance at which a 25 gram bullet traveling at 250 m/s can be stopped by a force of 5000N, we can use the concept of impulse.
Impulse can be calculated using the equation:
Impulse = Force × Time
In this case, we want to find the time it takes for the bullet to stop, so we rearrange the formula:
Time = Impulse / Force
Next, we need to calculate the impulse acting on the bullet. Impulse is calculated using the equation:
Impulse = Change in momentum
Momentum is calculated using the equation:
Momentum = Mass × Velocity
Given the mass of the bullet (25 grams) and its velocity (250 m/s), we can calculate the initial momentum.
Initial Momentum = Mass × Initial Velocity
Now, since the bullet comes to a stop, the final velocity is 0 m/s and the momentum is:
Final Momentum = Mass × Final Velocity
However, since the mass of the bullet remains the same throughout (25 grams), the initial and final momenta have the same value. Therefore, the change in momentum is:
Change in Momentum = Final Momentum - Initial Momentum
= 0 - (Mass × Initial Velocity)
= - Mass × Initial Velocity
Now, we have all the information we need to calculate the time it takes for the bullet to stop:
Time = Impulse / Force
= (Change in Momentum) / Force
= (- Mass × Initial Velocity) / Force
Now we can substitute the given values into the equation:
Time = (-0.025 kg × 250 m/s) / 5000 N
= -1.25 N·s / 5000 N
= -0.00025 s
The negative sign indicates that the time is in the opposite direction to the initial motion of the bullet.
Finally, to find the distance the bullet travels within this time, we can use the equation:
Distance = Velocity × Time
Substituting the values:
Distance = 250 m/s × (-0.00025 s)
= -0.0625 m
Therefore, the bullet can be stopped within a distance of 0.0625 meters or 6.25 centimeters.