A bullet of mass ,0.006kg traveling at 180m/s penetrates deeply into the target and it is brought to rest in 0.01seconds. Calculate; (I) force exerted on the target
To calculate the force exerted on the target, we can use the formula:
Force = change in momentum / time
The change in momentum can be calculated using the initial and final velocities of the bullet:
change in momentum = mass * (final velocity - initial velocity)
final velocity of the bullet is 0 m/s (since it stops after penetrating the target)
change in momentum = 0.006 kg * (0 m/s - 180 m/s) = -1.08 kg m/s
The negative sign indicates that the momentum of the bullet has decreased (since it is moving in the opposite direction).
Now we can substitute these values into the formula for force:
Force = change in momentum / time = (-1.08 kg m/s) / (0.01 s) = -108 N
The negative sign indicates that the force was exerted in the opposite direction to the initial motion of the bullet (i.e. towards the shooter). This is known as a "reactive force" and is equal in magnitude but opposite in direction to the "action force" exerted by the bullet on the target.
To calculate the force exerted on the target by the bullet, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt). The momentum (p) is the product of mass (m) and velocity (v).
Given:
Mass of the bullet (m): 0.006 kg
Initial velocity of the bullet (v): 180 m/s
Time taken to come to rest (Δt): 0.01 s
First, we need to calculate the initial momentum (p₁) of the bullet:
p₁ = m * v
p₁ = 0.006 kg * 180 m/s
p₁ = 1.08 kg·m/s
Next, we calculate the change in momentum (Δp):
Δp = p₂ - p₁
Since the bullet comes to rest, the final momentum (p₂) is zero.
Δp = 0 - 1.08 kg·m/s
Δp = -1.08 kg·m/s
Finally, we can calculate the force exerted on the target using Newton's second law:
F = Δp / Δt
F = -1.08 kg·m/s / 0.01 s
F = -108 N
Therefore, the force exerted on the target by the bullet is -108 N, where the negative sign indicates that the force is in the opposite direction of the bullet's initial motion.