A bullet of mass 3.0g moving at 350m/s hits a tree and penetrates through a distance
of 12 cm before coming to rest. Determine the retarding force exerted on the bullet
To determine the retarding force exerted on the bullet, you can use Newton's second law of motion, which states that force is equal to the mass of an object multiplied by its acceleration. In this case, since the bullet comes to rest, its final velocity is 0 m/s, so its initial velocity is 350 m/s. The acceleration can be calculated using the equation of motion, assuming constant deceleration:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s)
u = initial velocity (350 m/s)
a = acceleration
s = displacement (12 cm = 0.12 m)
Now, rearranging the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (0^2 - (350^2)) / (2 x 0.12)
Evaluate the expression:
a = -3052083.33 m/s^2
Since the acceleration is negative, it indicates that the bullet experienced deceleration or retardation. Finally, using Newton's second law, you can calculate the force:
Force = mass x acceleration
Converting the mass of the bullet from grams to kilograms (1 g = 0.001 kg):
mass = 3.0 g = 3.0 x 0.001 kg = 0.003 kg
Force = 0.003 kg x (-3052083.33 m/s^2)
Evaluate the expression:
Force ≈ -9156.25 Newtons
Therefore, the retarding force exerted on the bullet is approximately -9156.25 N. The negative sign signifies that the force is acting in the opposite direction to the motion of the bullet.