For a ballistics study a 1.9 gram bullet is fired into soft wood at 380 meters/sec and penetrates 15 cm.
a.) find the retarding force (resistance) in N.
b.) the time needed to stop the bullet in sec.
c. acceleration of the bullet in meters/sec.
a) initial kinetic energy = (force) x (penetration distance)
Solve for the force, F = .
Use kg and meters for doing the calculation.
b) Vaverage * time = (Vo/2)*time = 0.15 m
Solve for the stopping time.
Vo is the initial velocity, 380 m/s
c) a = F/m = Vo/(stopping time)
(You should get the same answer wither way)
f=2.41N
To find the answers to these questions, we can use the equations of motion and the concepts of work and energy.
a.) To find the retarding force (resistance), we need to use the concept of work done against friction. The work done against friction can be calculated by the formula:
Work = Force × Distance
In this case, the work done against friction is equal to the change in kinetic energy of the bullet. The change in kinetic energy can be calculated as:
Change in kinetic energy = 0.5 × mass × (final velocity^2 - initial velocity^2)
Plugging in the values:
Change in kinetic energy = 0.5 × 0.0019 kg × ((0 m/s)^2 - (380 m/s)^2)
Now, we can equate this change in kinetic energy to the work done against friction:
Change in kinetic energy = Work done against friction
0.5 × 0.0019 kg × ((0 m/s)^2 - (380 m/s)^2) = Force × Distance
Plugging in the values:
0.5 × 0.0019 kg × (-144400 m^2/s^2) = Force × 0.15 m
Solving for the force:
Force = (0.5 × 0.0019 kg × (-144400 m^2/s^2)) / 0.15 m
b.) To find the time needed to stop the bullet, we can use the concept of deceleration. Deceleration is the rate at which velocity decreases. We can calculate the deceleration using the formula:
Deceleration = (Final velocity - Initial velocity) / Time
In this case, the final velocity is 0 m/s (since the bullet stops) and the initial velocity is 380 m/s.
Setting the equation for deceleration:
Deceleration = (0 m/s - 380 m/s) / Time
Solving for time:
Time = (Final velocity - Initial velocity) / Deceleration
Time = (0 m/s - 380 m/s) / Deceleration
c.) To find the acceleration of the bullet, we start with the equation of motion:
Final velocity^2 = Initial velocity^2 + 2 × Acceleration × Distance
In this case, the final velocity is 0 m/s (since the bullet stops), the initial velocity is 380 m/s, and the distance is 0.15 m (penetration distance).
Plugging in the values:
0 m/s^2 = (380 m/s)^2 + 2 × Acceleration × 0.15 m
Solving for acceleration:
Acceleration = (0 m/s^2 - (380 m/s)^2) / (2 × 0.15 m)
To find the answers to these questions, we'll need to use the principles of Newton's laws of motion. Let's go through the process step by step:
a.) To find the retarding force acting on the bullet as it penetrates the wood, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the bullet is decelerating, so the force will oppose its motion. Therefore, the retarding force can be calculated as:
F = m * a
Given:
mass (m) = 1.9 grams = 0.0019 kg (since 1 gram = 0.001 kg)
acceleration (a) = ?
Since the bullet is decelerating, we can consider the change in velocity (-380 m/s) as the acceleration.
Let's substitute the given values:
F = 0.0019 kg * (-380 m/s)
F = -0.722 N (rounded to three decimal places)
b.) To find the time needed to stop the bullet, we can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s, since the bullet comes to a stop)
u = initial velocity (380 m/s)
a = acceleration (calculated as -380 m/s)
t = time taken
Rearranging the equation:
t = (v - u) / a
Substituting the values:
t = (0 m/s - 380 m/s) / -380 m/s
t = 1 s
Therefore, the time needed to stop the bullet is 1 second.
c.) To calculate the acceleration of the bullet, we need to use the equation:
a = (v - u) / t
Given:
v = final velocity (0 m/s)
u = initial velocity (380 m/s)
t = time taken (1 s)
Substituting the values:
a = (0 m/s - 380 m/s) / 1 s
a = -380 m/s^2
Therefore, the acceleration of the bullet is -380 meters per second squared.