A 5 gram bullet is fired horizontally and hits an 8 kilogram block of wood (initially at rest) which can move freely. The wood and the bullet move with a velocity of 0.50 m/s after impact. What is the initial velocity of the bullet?
momentum is conserved
Mb * Vi = (Mb + Mw) * Vf
Vi = (.005 + 8) * 0.50 / .005
To find the initial velocity of the bullet, we can use the principle of conservation of linear momentum.
The formula for linear momentum is:
p = mv
Where p is the momentum, m is the mass, and v is the velocity.
Before the impact, the bullet has a mass of 5 grams, which is equal to 0.005 kilograms. Let's call its initial velocity Vb.
The wood block has a mass of 8 kilograms and is initially at rest.
After the impact, both the bullet and the wood block move with a velocity of 0.50 m/s. Let's call their final velocity Vf.
According to the principle of conservation of linear momentum, the total momentum before the impact is equal to the total momentum after the impact. Therefore:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Where m1 and m2 are the masses of the bullet and the wood block respectively, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities.
Plugging in the values we have:
(0.005 kg * Vb) + (8 kg * 0 m/s) = (0.005 kg * 0.50 m/s) + (8 kg * 0.50 m/s)
Simplifying the equation:
0.005 kg * Vb = 4 kg * 0.50 m/s
0.005 kg * Vb = 2 kg*m/s
Vb = (2 kg*m/s) / (0.005 kg)
Vb = 400 m/s
Therefore, the initial velocity of the bullet is 400 m/s.
To find the initial velocity of the bullet, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity. Let's denote the initial velocity of the bullet as v_b, and the final velocity of the bullet and the wood as v_f. The mass of the bullet is 5 grams, which is equivalent to 0.005 kilograms, and the mass of the wood is 8 kilograms.
Before the collision:
The momentum of the bullet is given by p_b = m_b * v_b, where p_b is the momentum of the bullet, m_b is the mass of the bullet, and v_b is the initial velocity of the bullet.
The momentum of the wood is given by p_w = m_w * 0, where p_w is the momentum of the wood, and m_w is the mass of the wood. Since the wood is initially at rest, its initial velocity is 0.
After the collision:
The momentum of the bullet and the wood is given by p_f = (m_b + m_w) * v_f, where p_f is the total momentum of the bullet and the wood after the collision, and v_f is the final velocity of the bullet and the wood.
Since momentum is conserved, we can set the initial momentum equal to the final momentum:
p_b + p_w = p_f
m_b * v_b + m_w * 0 = (m_b + m_w) * v_f
0.005 kg * v_b + 8 kg * 0 = (0.005 kg + 8 kg) * 0.50 m/s
0.005 kg * v_b = 8.0025 kg * m/s - 0 kg * m/s
0.005 kg * v_b = 8.0025 kg * m/s
v_b = (8.0025 kg * m/s) / 0.005 kg
v_b = 1600.5 m/s
Therefore, the initial velocity of the bullet is approximately 1600.5 m/s.