A 15-g bullet is fired horizontally into a 3.000-kg block of wood suspended by a long cord. The bullet sticks in the block. Compute the speed of the bullet if the impact causes the block to swing 10 cm above its initial level.

Initial Velocity of bullet=19.1m/s

Well, well, well! Looks like this bullet really got stuck in its tracks! Let's get playful with some physics calculations.

To find the speed of the bullet, we need to use the law of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.

The initial momentum is given by the formula: initial momentum = mass of bullet × initial velocity of bullet

The final momentum is given by the formula: final momentum = (mass of bullet + mass of block) × final velocity

Since the bullet gets stuck in the block, we know that the final velocity is zero. So, we can set the initial momentum equal to the final momentum and solve for the velocity of the bullet.

(15 g) × (19.1 m/s) = (15 g + 3 kg) × (0 m/s)

We need to convert grams to kilograms to keep things consistent:

(0.015 kg) × (19.1 m/s) = (0.015 kg + 3 kg) × (0 m/s)

Now we can solve for the initial velocity of the bullet:

(0.015 kg) × (19.1 m/s) = (3.015 kg) × (0 m/s)

And the velocity of the bullet is:

(0.015 kg) × (19.1 m/s) / (3.015 kg) = approximately 0.095 m/s

So, it seems like this bullet ended up losing a lot of its speed! I hope it didn't see that coming!

To solve this problem, we can use the principle of conservation of momentum.

Step 1: Let's first find the initial momentum of the bullet.
The mass of the bullet is 15 g, which is equal to 0.015 kg.
The initial velocity of the bullet is given as 19.1 m/s.
So the initial momentum of the bullet is:
Initial momentum of the bullet = Mass of the bullet * Initial velocity
Initial momentum of the bullet = 0.015 kg * 19.1 m/s

Step 2: Next, we find the mass of the block of wood.

The block of wood's mass is given as 3.000 kg.

Step 3: Now, let's calculate the final momentum of the bullet and the block after the bullet sticks in it.

Because the bullet sticks in the block, the final velocity of both the bullet and the block will be the same.

The final momentum of the bullet and the block is:
Final momentum = (Mass of the bullet + Mass of the block) * Final velocity

We can rearrange this equation to solve for the final velocity:
Final velocity = Final momentum / (Mass of the bullet + Mass of the block)

Step 4: Finally, let's calculate the final velocity.

We know the block swings up by 10 cm, which is equal to 0.1 m. This means the potential energy gained by the block is equal to the initial kinetic energy of the bullet.

Initial kinetic energy of the bullet = (1/2) * Mass of the bullet * (Initial velocity)^2
Potential energy gained by the block = Mass of the block * g * Height (where g is the acceleration due to gravity)

Since the bullet sticks in the block, the final kinetic energy of the bullet is zero.

Equating the initial kinetic energy of the bullet and the potential energy gained by the block:
(1/2) * Mass of the bullet * (Initial velocity)^2 = Mass of the block * g * Height

Substituting the values we know:
(1/2) * 0.015 kg * (19.1 m/s)^2 = 3.000 kg * 9.81 m/s^2 * 0.1 m

Now, we can solve this equation to find the final velocity of the bullet.

Following these steps should give you the speed of the bullet when the block swings up by 10 cm.

To solve this problem, we can use the principles of conservation of momentum and energy. Here's how you can calculate the speed of the bullet:

1. First, let's determine the initial momentum of the bullet and the block. Since the bullet is fired horizontally, its momentum can be calculated as the product of its mass and velocity:

Initial momentum of bullet = mass of bullet × velocity of bullet

The bullet has a mass of 15 g, which is 0.015 kg. The given initial velocity of the bullet is 19.1 m/s. Plugging in these values, we get:

Initial momentum of bullet = 0.015 kg × 19.1 m/s

2. Since the bullet sticks in the block, the final momentum of the bullet and the block (combined) is zero. This is due to the conservation of momentum principle.

Final momentum of bullet and block = 0

3. Now, let's consider the energy in the system before and after impact. Initially, the block is at rest, and there is no kinetic energy. After the impact, the block swings upward, reaching a maximum height of 10 cm (which is equivalent to 0.1 m). The energy lost by the bullet should be equal to the potential energy gained by the block during this upward swing.

Energy lost by bullet = Potential energy gained by block

The energy lost by the bullet is given by:

Energy lost by bullet = (1/2) × mass of bullet × (velocity of bullet)^2

4. The potential energy gained by the block is given by:

Potential energy gained by block = mass of block × g × height

The mass of the block is given as 3.000 kg, the acceleration due to gravity (g) is approximately 9.8 m/s^2, and the height is 0.1 m.

5. Equating the energy lost by the bullet and the potential energy gained by the block, we have:

(1/2) × mass of bullet × (velocity of bullet)^2 = mass of block × g × height

Plug in the values and solve for the velocity of the bullet:

(1/2) × 0.015 kg × (velocity of bullet)^2 = 3.000 kg × 9.8 m/s^2 × 0.1 m

Simplify the equation and solve for the velocity of the bullet.

Once you perform the calculation, you should find that the speed of the bullet is approximately 271.98 m/s.

Use the distance of upward swing to compute the velocity right after impact.

M (9.8 m/s^2)(0.1 m) = (1/2) M V^2
V = sqrt(2 g H) = 1.4 m/s

Now use conservation of momentum, applied to the bullet impact, for the bullet velocity, Vb.

m Vb = (M + m)*1.4 m/s
Vb = 1.4*(3.015/.015) = 281 m/s

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