A bullet of mass 12 g is fired horizontally into a fixed wooden block with a speed of 20m/s. The bullet is brought to rest in the block in 0.1 seconds by a costant resistance. Calculate the
(i) magnitude of the resistance
(ii) distance moved by the bullet in the wood.
impulse=changemomentum
force*.1=.012*20
solve for resistance force.
distance: average velocity is 10m/s, in .1 sec
distance=avgvelociyt*time=1meter
great! Thank you bobpursley
Sorry to ask 20 x0.1 is it not 2
To solve this problem, we can use the principles of conservation of momentum and Newton's second law of motion.
(i) Magnitude of the resistance:
First, let's find the initial momentum of the bullet before it hits the wooden block. The formula for momentum is given by: momentum = mass x velocity.
Mass of the bullet = 12 g = 0.012 kg (converted to kilograms)
Velocity of the bullet = 20 m/s
Initial momentum of the bullet = (mass x velocity) = (0.012 kg) x (20 m/s) = 0.24 kg·m/s
Since the bullet is brought to rest quickly by a constant resistance force, we can assume that the change in momentum of the bullet is also equal to the impulse exerted by the resistance force.
Impulse = change in momentum = final momentum - initial momentum
Since the bullet is brought to rest, the final momentum is zero.
Impulse = 0 - 0.24 kg·m/s = -0.24 kg·m/s
The impulse can also be written as the product of the resistance force and the time taken:
Impulse = force x time
-0.24 kg·m/s = force x 0.1 s
Solving for the force:
force = (-0.24 kg·m/s) / (0.1 s)
force = -2.4 N
Since the resistance force cannot be negative (it acts in the opposite direction to the bullet's motion), we take the magnitude of the force as:
Magnitude of the resistance force = |-2.4 N| = 2.4 N
Therefore, the magnitude of the resistance is 2.4 N.
(ii) Distance moved by the bullet in the wood:
To calculate the distance moved by the bullet in the wood, we can use the formula for distance traveled under constant acceleration:
Distance = initial velocity x time + (1/2) x acceleration x time^2
Since the bullet comes to rest, the final velocity is zero.
Initial velocity of the bullet = 20 m/s
Time taken to come to rest = 0.1 s
Using the formula:
Distance = (20 m/s) x (0.1 s) + (1/2) x (acceleration) x (0.1 s)^2
Since the bullet comes to rest in the block, the final velocity is zero. Using the formula for final velocity:
Final velocity = initial velocity + acceleration x time
0 m/s = 20 m/s + (acceleration) x (0.1 s)
(acceleration) x (0.1 s) = -20 m/s
acceleration = -200 m/s^2 (negative since it opposes the bullet's motion)
Now we can substitute the values into the distance formula:
Distance = (20 m/s) x (0.1 s) + (1/2) x (-200 m/s^2) x (0.1 s)^2
Simplifying:
Distance = 2 m + (-0.01 m)
Distance = 1.99 m
Therefore, the distance moved by the bullet in the wood is approximately 1.99 meters.