A 12.0g bullet is accelerating from rest to a speed of 700m/s as it travels 20.0cm in a gun barrel. How large is it's accelerating force ?
sol
To find the accelerating force acting on the bullet, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is:
F = m * a
Given:
Mass of the bullet (m) = 12.0g = 0.012 kg (since 1 g = 0.012 kg)
Speed of the bullet (v) = 700 m/s
Distance traveled (s) = 20.0 cm = 0.20 m (since 1 cm = 0.01 m)
First, let's calculate the acceleration (a) of the bullet using the formula:
v^2 = u^2 + 2as
Where:
u = initial velocity = 0 m/s (since the bullet starts from rest)
Rearranging the equation, we can solve for acceleration:
a = (v^2 - u^2) / 2s
Substituting the values:
a = (700^2 - 0^2) / (2 * 0.20)
a = 49,000 / 0.40
a = 122,500 m/s^2
Now that we have the acceleration, we can calculate the force (F) using Newton's second law:
F = m * a
Substituting the values:
F = 0.012 * 122,500
F = 1,470 N
Therefore, the accelerating force acting on the bullet is 1,470 Newtons.