A 15 g bullet is fired from a rifle, it takes 2.50×10^-3 s for the bullet to travel the length of the barrel, and it exits with the speed of 715 m/s. Assuming that the acceleration of the bullet is constant, find the average net force exerted on the bullet
We can use the formula:
average net force = (mass of the bullet) x (change in velocity) / (time taken)
The change in velocity is the final velocity (715 m/s) minus the initial velocity (which is 0 m/s because the bullet starts at rest in the barrel):
change in velocity = 715 m/s - 0 m/s = 715 m/s
Substituting the given values into the formula:
average net force = (0.015 kg) x (715 m/s) / (2.50×10^-3 s) = 429,000 N
Therefore, the average net force exerted on the bullet is 429,000 N.
To find the average net force exerted on the bullet, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the object's mass (m) multiplied by its acceleration (a):
F = m * a
In this case, the mass of the bullet (m) is given as 15 grams, which we'll need to convert to kilograms before plugging it into the formula.
mass (m) = 15 g = 15 × 10^(-3) kg = 0.015 kg
The acceleration (a) can be determined using the formula for average acceleration:
a = (v - u) / t
where v is the final velocity, u is the initial velocity, and t is the time taken for the motion. From the given information, we know that the bullet exits the barrel with a velocity of 715 m/s and it takes 2.50 × 10^(-3) s to travel the length of the barrel.
Let's calculate the acceleration:
a = (v - u) / t
a = (715 m/s - 0 m/s) / 2.50 × 10^(-3) s
a = 286,000 m/s^2
Now we can substitute the values of mass (m) and acceleration (a) into the formula for force (F):
F = m * a
F = 0.015 kg * 286,000 m/s^2
F ≈ 4,290 N
Therefore, the average net force exerted on the bullet is approximately 4,290 Newtons (N).
To find the average net force exerted on the bullet, we can use Newton's second law of motion, which states that the net force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Given:
- Mass of the bullet (m) = 15 g = 0.015 kg
- Time taken for the bullet to travel the length of the barrel (Δt) = 2.50×10^-3 s
- Final speed of the bullet (v) = 715 m/s
First, we need to calculate the acceleration of the bullet using the formula:
acceleration (a) = (final velocity - initial velocity) / time
Since the initial velocity of the bullet is 0 m/s (as it starts from rest inside the rifle), the formula becomes:
a = v / t
Substituting the given values:
a = 715 m/s / 2.50×10^-3 s
Now, let's calculate the acceleration:
a = 2.86×10^5 m/s^2
Now, we can calculate the net force (F) using Newton's second law of motion:
F = m * a
Substituting the given values:
F = 0.015 kg * 2.86×10^5 m/s^2
Now, we can calculate the average net force exerted on the bullet:
F ≈ 4290 N
Therefore, the average net force exerted on the bullet is approximately 4290 Newtons.