Find the internal energy produced by a bullet of mass 10 g traveling horizontally at a speed of 10 × 10^2 m/s, which embedded itself in a wood of mass 9.9 × 10^2 g suspended freely by two strings.

To find the internal energy produced by the bullet, we first need to calculate the initial kinetic energy of the bullet before it embeds itself in the wood.

The initial kinetic energy of the bullet is given by:

KE = 0.5 * m * v^2

where m is the mass of the bullet and v is its velocity.

Given:
m = 10 g = 0.01 kg
v = 10 × 10^2 m/s = 1000 m/s

KE = 0.5 * 0.01 * (1000)^2
KE = 0.5 * 0.01 * 1000000
KE = 5000 J

Now, when the bullet embeds itself in the wood, the system will come to a stop due to the conservation of momentum. The final velocity of the system will be zero.

Let the final velocity of the system be v_f.

Using the conservation of momentum:

m1 * v1 = (m1 + m2) * v_f

where m1 is the mass of the bullet, m2 is the mass of the wood, and v1 is the initial velocity of the bullet.

0.01 * 1000 = (0.01 + 0.99) * v_f
10 = 1 * v_f
v_f = 10 m/s

Now, the internal energy produced by the bullet is the work done in bringing the system to a stop. This is given by:

Internal energy = KE_initial - KE_final
Internal energy = KE_initial - 0
Internal energy = 5000 J

Therefore, the internal energy produced by the bullet is 5000 J.

The internal energy produced by the bullet is equal to the kinetic energy of the bullet before it embedded itself in the wood. The kinetic energy of the bullet is given by:

```
Ek = (1/2) - m - v^2
```

where:

- Ek is the kinetic energy in joules
- m is the mass of the bullet in kilograms
- v is the velocity of the bullet in meters per second

Plugging in the given values, we get:

```
Ek = (1/2) - 0.01 kg - (10 × 10^2 m/s)^2 = 500 J
```

Therefore, the internal energy produced by the bullet is 500 J.