Answer:
Step-by-step explanation:
To calculate the force exerted on the bullet by the target, we can use the equation:
Force = Change in momentum / Time
First, we need to calculate the momentum of the bullet before it hits the target. The momentum of an object is given by the equation:
Momentum = Mass × Velocity
Given that the mass of the bullet is 40g (or 0.04kg) and the velocity is 300m/s, we can calculate the initial momentum of the bullet:
Initial momentum = 0.04kg × 300m/s = 12 kg·m/s
Next, we need to calculate the change in momentum. Since the bullet comes to rest after penetrating a distance of 20cm (or 0.2m), its final momentum is zero. Therefore, the change in momentum is:
Change in momentum = Final momentum - Initial momentum
= 0 - 12 kg·m/s
= -12 kg·m/s
Now, we need to consider the time it takes for the bullet to come to rest. Since the bullet is brought to rest by the target, we can assume that the deceleration is constant. To calculate the time taken, we can use the equation:
Distance = Initial velocity × Time + (1/2) × Acceleration × Time^2
In this case, the initial velocity is 300m/s, the distance is 0.2m, and the acceleration is unknown. Solving the equation for time, we get:
0.2m = 300m/s × Time + (1/2) × Acceleration × Time^2
Since the bullet comes to rest, we can assume that the final velocity is zero. Rearranging the equation and substituting the final velocity as zero, we get:
Acceleration × Time^2 - 300m/s × Time + 0.2m = 0
Now, we can solve this quadratic equation to find the value of time. Once we have the time, we can calculate the force using the equation mentioned earlier.
Please note that the actual force exerted on the bullet by the target would depend on various factors, such as the deformation of the bullet and the target, the nature of the materials involved, and the contact area. This calculation assumes ideal conditions and simplifications for educational purposes.