In a police ballistics test, a 10.0-g bullet moving at 300 m/s is fired into a 1.00-kg block at rest. The bullet goes through the block almost instantaneously and emerges with 50.0% of its original speed. What is the speed of the block just after the bullet emerges
momentum lost=momentum block gained
10*150=1000V
solve for v.
To solve this problem, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Step 1: Calculate the momentum of the bullet before the collision:
Momentum = mass x velocity
M(bullet) = 10.0 g = 0.01 kg (convert grams to kilograms)
V(bullet) = 300 m/s
Momentum(bullet) = 0.01 kg x 300 m/s = 3 kg·m/s
Step 2: Calculate the momentum of the block before the collision:
M(block) = 1.00 kg (given)
V(block) = 0 m/s (at rest)
Momentum(block) = 1.00 kg x 0 m/s = 0 kg·m/s
Step 3: Calculate the momentum of the bullet after the collision:
V(bullet, final) = 50.0% of 300 m/s = 0.5 x 300 m/s = 150 m/s
Momentum(bullet, final) = 0.01 kg x 150 m/s = 1.5 kg·m/s
Step 4: Calculate the momentum of the block after the collision:
Let V(block, final) be the final velocity of the block after the collision.
According to the conservation of momentum principle, the total momentum before the collision (3 kg·m/s) should be equal to the total momentum after the collision.
Total momentum before = Total momentum after
Momentum(bullet) + Momentum(block) = Momentum(bullet, final) + Momentum(block, final)
Plugging in the values we calculated:
3 kg·m/s + 0 kg·m/s = 1.5 kg·m/s + M(block, final)
Simplifying the equation, we can find the final momentum of the block:
M(block, final) = 3 kg·m/s - 1.5 kg·m/s
M(block, final) = -1.5 kg·m/s (opposite direction of bullet)
Step 5: Calculate the speed of the block just after the bullet emerges:
The momentum of an object can be calculated using the formula:
Momentum = mass x velocity
Plugging in the values we have:
-1.5 kg·m/s = 1.00 kg x V(block, final)
Simplifying the equation to solve for V(block, final):
V(block, final) = -1.5 kg·m/s / 1.00 kg
V(block, final) = -1.5 m/s
Therefore, the speed of the block just after the bullet emerges is 1.5 m/s in the opposite direction of the bullet.
To find the speed of the block just after the bullet emerges, we can first calculate the final velocity of the bullet after passing through the block, and then use the principle of conservation of momentum to find the velocity of the block.
Let's break down the problem step by step:
1. Calculate the final velocity of the bullet:
The bullet goes through the block almost instantaneously and emerges with 50.0% of its original speed.
Given:
Initial speed of the bullet (v initial) = 300 m/s
Final speed of the bullet (v final) = 50.0% of the initial speed = 50.0 / 100 * 300 m/s = 150 m/s
2. Find the velocity of the block:
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Initially, the block is at rest, so its initial momentum is zero.
After the bullet passes through the block, both the bullet and the block move together.
Let's denote:
Mass of the bullet (m bullet) = 10.0 g = 0.01 kg
Mass of the block (m block) = 1.00 kg
Velocity of the block just after the bullet emerges = v block
Conservation of momentum equation: (m bullet * v bullet) + (m block * v block) = 0
Plugging in the given values, we get:
(0.01 kg * 150 m/s) + (1.00 kg * v block) = 0
Rearranging the equation to solve for v block:
v block = - (0.01 kg * 150 m/s) / (1.00 kg)
v block = -1.50 m/s (negative sign indicates the opposite direction of the bullet)
Therefore, the velocity of the block just after the bullet emerges is -1.50 m/s.