The late news reports the story of a shooting in the city. Investigators think that they have recovered the weapon and they run ballistics tests on the pistol at the firing range. If a 0.050-kg bullet were fired from the handgun with a speed of 400 m/s and it traveled 0.080 m into the target before coming to rest, what force did the bullet exert on the target?
momentum = 0.05*400
time in corpse = 0.08 m / 400
force = change in momentum / time = 0.05 * 400 / (0.08/400)
= (0.05/0.08) * 400^2 = 100,000 Newtons ---- Good grief !
To calculate the force exerted by the bullet on the target, we can use the equation:
Force = Change in momentum / Time
First, we need to calculate the momentum of the bullet. The momentum (p) of an object can be calculated using the equation:
Momentum = Mass × Velocity
Given:
Mass of the bullet (m) = 0.050 kg
Velocity of the bullet (v) = 400 m/s
Momentum (p) = 0.050 kg × 400 m/s
p = 20 kg·m/s
Next, we need to calculate the change in momentum. The change in momentum (∆p) can be calculated using the equation:
∆p = Final Momentum - Initial Momentum
The initial momentum is zero because the bullet is initially at rest inside the gun. Therefore:
∆p = Final Momentum - 0
∆p = 20 kg·m/s - 0
∆p = 20 kg·m/s
Now, we need to calculate the time (t) it takes for the bullet to come to rest. Since the distance traveled by the bullet is given as 0.080 m, we can use the formula:
Distance = 0.5 × Acceleration × Time^2
Rearranging the formula, we get:
Time = √(2 × Distance / Acceleration)
Assuming the acceleration to be constant, we can use the acceleration due to gravity (9.8 m/s^2).
Time = √(2 × 0.080 m / 9.8 m/s^2)
t = √(0.01632 / 9.8)
t = √0.0016653
t ≈ 0.0408 s
Now we can calculate the force using the equation:
Force = ∆p / t
Force = 20 kg·m/s / 0.0408 s
Force ≈ 490.20 Newtons
Therefore, the force exerted by the bullet on the target is approximately 490.20 Newtons.