A 4.00g bullet, traveling horizontally with a velocity of magnitude 410m/s , is fired into a wooden block with mass of 0.780kg , initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 220m/s . The block slides a distance of 49.0cm along the surface from its initial position.

(a)What is the coefficient of kinetic friction between block and surface?

(b)What is the decrease in kinetic energy of the bullet?

(c)What is the kinetic energy of the block at the instant after the bullet passes through it?

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To solve this problem, we can use the principles of conservation of momentum and conservation of energy.

(a) To find the coefficient of kinetic friction between the block and surface, we can use the fact that the block slides a certain distance. The work done by friction can be calculated as the product of the force of friction, the displacement, and the coefficient of kinetic friction.

The work done by friction is equal to the decrease in kinetic energy of the block. So, we can set up the equation:

Work = Force of friction * displacement = change in kinetic energy of the block

The change in kinetic energy is given by the work-energy theorem as:

Change in kinetic energy = (final kinetic energy) - (initial kinetic energy)

Since the block is initially at rest, the initial kinetic energy of the block is zero. The final kinetic energy of the block can be calculated using:

Final kinetic energy = (1/2) * mass of the block * (final velocity)^2

We are given the mass of the block (0.780 kg) and the final velocity of the block (220 m/s). We also know the displacement of the block (49.0 cm = 0.49 m).

Therefore, we can use the equation:

Force of friction * displacement = (1/2) * mass of the block * (final velocity)^2

From this equation, we can solve for the coefficient of kinetic friction:

Coefficient of kinetic friction = (Force of friction) / (Normal force)

The normal force is the force exerted by the surface on the block and is equal in magnitude and opposite in direction to the force of gravity acting on the block. The force of gravity can be calculated as the product of the mass of the block and gravitational acceleration (9.8 m/s^2).

(b) To find the decrease in kinetic energy of the bullet, we can use the principle of conservation of mechanical energy. If we assume that there is no other external force acting on the bullet during its passage through the block, then the decrease in kinetic energy of the bullet is equal to the work done by the force of friction between the bullet and the block.

The decrease in kinetic energy of the bullet can be calculated using the equation:

Decrease in kinetic energy = (force of friction) * (distance traveled by bullet inside the block)

We are given the mass of the bullet (4.00 g = 0.00400 kg), the initial velocity of the bullet (410 m/s), and the final velocity of the bullet (220 m/s). The distance traveled by the bullet inside the block is not explicitly given, but it can be calculated using the displacement of the block (49.0 cm = 0.49 m).

(c) To find the kinetic energy of the block at the instant after the bullet passes through it, we can use the equation:

Kinetic energy = (1/2) * mass * (velocity)^2

We are given the mass of the block (0.780 kg) and the final velocity of the block (220 m/s).