A bullet of mass 0.02kg is fired at a speed of 500m/s towards a fixed wooden block of thickness 10cm. The bullet penetrates the block and emerges with a speed of 200m/s.
a) Find the average retarding force on the bullet when it is passing through the block.
b) Estimate the time required for the bullet to pass through the block.
c) If the block is not present, how long does the bullet take to travel the same distance?
a)
mass, m = 0.02 kg
Distance, S = 10 cm = 0.01 m
initial velocity, u = 500 m/s
final velocity, v = 200 m/s
Acceleration = (v²-u²)/2S m/s²
b)
v=u+at
solve for t.
c)
Time to travel 10 cm without resistance,
t0 = S/u
please help me to solve this question.
To find the average retarding force on the bullet while passing through the block, we can use Newton's second law of motion. The formula is F = m * a, where F is the force, m is the mass, and a is the acceleration.
a) First, let's find the acceleration of the bullet while passing through the block. We can use the formula v^2 = u^2 + 2as, where v is the final velocity (200 m/s), u is the initial velocity (500 m/s), a is the acceleration, and s is the distance traveled through the block (which is the thickness of the block).
Given:
Initial velocity (u) = 500 m/s
Final velocity (v) = 200 m/s
Distance traveled (s) = thickness of block = 10 cm = 0.1 m
Using the formula, we can rearrange it to find the acceleration:
a = (v^2 - u^2) / (2 * s)
Substituting the values:
a = (200^2 - 500^2) / (2 * 0.1)
Calculating the acceleration gives us:
a = (-300,000) / (0.2)
a = -1,500,000 m/s^2
Now that we have the acceleration, we can find the average retarding force using Newton's second law:
F = m * a
Given:
Mass of the bullet (m) = 0.02 kg
Acceleration (a) = -1,500,000 m/s^2
Substituting the values:
F = 0.02 * (-1,500,000)
F = -30,000 N
Therefore, the average retarding force on the bullet when it is passing through the block is 30,000 N (in the opposite direction of the bullet's motion).
b) To estimate the time required for the bullet to pass through the block, we can use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given:
Initial velocity (u) = 500 m/s
Final velocity (v) = 200 m/s
Acceleration (a) = -1,500,000 m/s^2
Rearranging the formula, we get:
t = (v - u) / a
Substituting the values:
t = (200 - 500) / (-1,500,000)
Calculating the time gives us:
t = -300 / (-1,500,000)
t = 0.0002 seconds (or 0.2 milliseconds)
Therefore, it would take approximately 0.2 milliseconds for the bullet to pass through the block.
c) If the block is not present, the bullet will not experience any retarding force and will continue to travel with its initial velocity. Therefore, the time it takes for the bullet to travel the same distance would be the distance divided by the initial velocity.
Given:
Initial velocity (u) = 500 m/s
Distance = thickness of block = 10 cm = 0.1 m
Using the formula:
t = distance / velocity
Substituting the values:
t = 0.1 / 500
t = 0.0002 seconds (or 0.2 milliseconds)
Therefore, if the block is not present, it would take approximately 0.2 milliseconds for the bullet to travel the same distance.