A 20-g bullet is fired horizontally into a 980 g block of wood suspended by a long cord. The bullet sticks in the block and causes the block to swing 15 cm above its initial level.
a) What is the momentum of the bullet before it hit the block?
b) Determine the velocity of the bullet, u, before it hit the block.
c) If the bullet-block system oscillates continuously, what would be the values of T, f, and
w, if the length of the cord is 1.96 m?
To find the answers to the questions, we need to apply the principles of conservation of momentum and energy.
a) To calculate the momentum of the bullet before it hits the block, we can use the equation:
Momentum = mass x velocity
Given:
Mass of the bullet = 20 g = 0.02 kg (since 1 g = 0.001 kg)
Velocity of the bullet before it hits the block = ?
Momentum = ?
Since the bullet is fired horizontally and sticks in the block, the bullet and the block will move together after the collision. Therefore, the momentum of the bullet before it hits the block is equal to the momentum of the bullet-block system after the collision.
So, the momentum of the bullet before it hits the block is equal to the momentum of the bullet-block system after the collision.
b) To find the velocity of the bullet, u, before it hits the block, we can use the equation:
Momentum = mass x velocity
Given:
Mass of the bullet = 20 g = 0.02 kg
Velocity of the bullet before it hits the block = u (unknown)
Momentum = momentum of the bullet before it hits the block = ?
From the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision. Since the block is initially at rest, the momentum before the collision is only due to the bullet, and after the collision, the momentum is due to the bullet-block system.
Therefore, we can set up the following equation:
Bullet momentum before collision = Bullet-block momentum after collision
(0.02 kg) x u = (0.02 kg + 0.98 kg) x v, where v is the velocity of the bullet-block system after the collision.
c) To find the values of T (period), f (frequency), and w (angular frequency) if the length of the cord is 1.96 m, we need to use the principles of simple harmonic motion.
The period T of an oscillating system is given by the equation:
T = 2π √(l / g)
where l is the length of the cord and g is the acceleration due to gravity.
Given:
Length of the cord l = 1.96 m
Acceleration due to gravity g = 9.8 m/s^2
Using these values in the equation, we can find the period T of the oscillating system.
The frequency f of the system is the reciprocal of the period, so we can find it by calculating:
f = 1 / T
Finally, the angular frequency w is given by:
w = 2πf
Using the calculated value of f, we can find w.
By following these steps, you will be able to find the answers to the given questions about momentum and oscillations.
you know the height it went, what PE does it have, At the bottom when starting, it had that KE. From that, determine the velocity of block/bullet at impact.
now use conservation of momentum at impact
(M+m)V= momentumbullet
and now determine velocity bullet
Momentumbullet=m*v
c. I am not certain what your w means, angular momentum, or angular freq.
for T, T=2PI sqrt(length/g)
f= 1/T