A 14 g bullet is fired into a 120 g wooden
block initially at rest on a horizontal surface.
The acceleration of gravity is 9.8 m/s^2
.
After impact, the block slides 6.97 m before coming to rest.If the coefficient of friction between block
and surface is 0.568 , what was the speed of
the bullet immediately before impact?
To find the speed of the bullet immediately before impact, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.
In this case, the initial momentum of the bullet-block system before the impact is zero since the wooden block is initially at rest. Therefore, the total momentum after the impact should also be zero because the block comes to rest after sliding.
Let's denote the velocity of the bullet before impact as v. The momentum of the bullet can be calculated using the formula:
Momentum = mass * velocity
The momentum of the bullet before impact is given by:
Momentum_bullet = mass_bullet * velocity_bullet = 0.014 kg * v
The momentum of the block after impact is given by:
Momentum_block = mass_block * velocity_block = 0.120 kg * 0 (since the block comes to rest)
According to the law of conservation of momentum:
Momentum_bullet + Momentum_block = 0
0.014 kg * v + 0.120 kg * 0 = 0
0.014 kg * v = 0
Therefore, the speed of the bullet immediately before impact is 0 m/s, indicating that the bullet is not moving.
It's worth noting that in reality, the bullet would lose some of its kinetic energy when hitting the block, but for this question, it seems as though the bullet does not have any initial speed.
To find the speed of the bullet immediately before impact, we can use the conservation of linear momentum.
Step 1: Find the initial momentum of the bullet and block system.
The initial momentum of the system before impact can be calculated using the formula:
P_initial = m_bullet * v_bullet_initial
where m_bullet is the mass of the bullet and v_bullet_initial is the initial velocity of the bullet.
Since the block is initially at rest, its initial momentum is zero.
Step 2: Find the final momentum of the bullet and block system.
After impact, the bullet and block move together. We can calculate their final momentum using the formula:
P_final = (m_block + m_bullet) * v_final
where m_block is the mass of the wooden block, m_bullet is the mass of the bullet, and v_final is the final velocity of the bullet and block together.
Step 3: Apply the conservation of linear momentum.
According to the conservation of linear momentum, the initial momentum equals the final momentum.
Therefore, we can set up the equation:
P_initial = P_final
m_bullet * v_bullet_initial = (m_block + m_bullet) * v_final
Step 4: Substitute the given values and solve for v_bullet_initial.
Let's substitute the given values:
m_bullet = 14 g = 0.014 kg (convert grams to kilograms)
m_block = 120 g = 0.120 kg (convert grams to kilograms)
v_final = 0 (since the block comes to rest)
0.014 kg * v_bullet_initial = (0.120 kg + 0.014 kg) * 0
0.014 kg * v_bullet_initial = 0
Therefore, the speed of the bullet immediately before impact is 0 m/s.