A 50.0 g bullet strikes a 7.00 kg stationary wooden block. If the bullet becomes embedded in the block, and the block with the embedded bullet moves off at a velocity of 5.00 m/s, what was the initial velocity of the bullet?
conserve momentum:
.050v + 7.00(0) = 5.00(.050+7.00)
v = 705 m/s
To find the initial velocity of the bullet, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The total initial momentum is given by the product of the mass and initial velocity of the bullet. Let's call the initial velocity of the bullet "v". The total initial momentum is then (50.0 g) * v.
The total final momentum is given by the product of the mass and final velocity of the block with the embedded bullet. Let's call the final velocity of the block "V". The total final momentum is then (7.00 kg + 50.0 g) * V.
Since we know that the total momentum before the collision is equal to the total momentum after the collision, we can set up the equation:
(50.0 g) * v = (7.00 kg + 50.0 g) * 5.00 m/s
Now, let's solve for the initial velocity of the bullet, v:
(50.0 g) * v = (7.00 kg + 50.0 g) * 5.00 m/s
(0.050 kg) * v = (7.050 kg) * 5.00 m/s
v = [(7.050 kg) * 5.00 m/s] / (0.050 kg)
v = 5.65 m/s
Therefore, the initial velocity of the bullet was 5.65 m/s.
To find the initial velocity of the bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum p of an object is given by the product of its mass m and velocity v: p = m * v.
Let's denote the initial velocity of the bullet as v1 and the final velocity of the block with the embedded bullet as v2. The mass of the bullet is 50.0 g, which is equivalent to 0.050 kg. The mass of the wooden block is 7.00 kg.
Before the collision, only the bullet is in motion, so the total initial momentum is given by: p_initial = m_bullet * v1.
After the collision, the bullet becomes embedded in the block, and they move off together with a final velocity of 5.00 m/s. Therefore, the total final momentum is given by: p_final = (m_bullet + m_block) * v2.
According to the principle of conservation of momentum, p_initial = p_final. So, we have the equation: m_bullet * v1 = (m_bullet + m_block) * v2.
Plugging in the known values, we can solve for v1:
0.050 kg * v1 = (0.050 kg + 7.00 kg) * 5.00 m/s
v1 = (7.05 kg * 5.00 m/s) / 0.050 kg
v1 ≈ 705.00 m/s
Therefore, the initial velocity of the bullet was approximately 705.00 m/s.
.050v + 7.00(0) = 5.00(.050+7.00)
v = 705 m/s