what force is necessary to stop a 20 g bullet moving at 200 m/s as it penetrates a wood at a distance of 4 m?

A 300 g piano is being lifted at a steady speed from the ground level straight upward to an apartment 15 m above the ground. The crane that is doing the lifting produces a steady power of 500 watts. How much time does it take to lift the piano?

Your question is badly worded. 4 m is not the distance from which the bullet was fired. It is the distance over with the bullet's velocity is decelerated to zero.

Otherwise the question cannot be answered.

I will ignore your second question, which should have been posted separately.

All of the kinetic energy is converted to work penetrating the wood. (That work becomes heat)

Force*Distance = (initial kinetic energy)

Solve for the force. Make sure bullet mass is in kg

To determine the force necessary to stop a bullet, we need to apply the principle of impulse-momentum.

The impulse experienced by an object is equal to the change in momentum of that object. Momentum is calculated by multiplying mass by velocity: momentum = mass × velocity.

In this case, the bullet has a mass of 20 g, which is equal to 0.02 kg, and it's moving at a velocity of 200 m/s.

The initial momentum of the bullet before impact can be calculated as follows:
momentum_initial = mass × velocity = 0.02 kg × 200 m/s = 4 kg·m/s.

Now, we need to calculate the final momentum of the bullet, assuming it comes to rest after penetrating the wood. Since it's stopping, the final velocity is 0 m/s, so the final momentum is zero:
momentum_final = mass × 0 m/s = 0 kg·m/s.

The change in momentum is given by:
change_in_momentum = momentum_final - momentum_initial.

In this case, the change in momentum is:
change_in_momentum = 0 kg·m/s - 4 kg·m/s = -4 kg·m/s.

The negative sign indicates the opposite direction of the change in momentum, which represents the force acting in the opposite direction to stop the bullet. We can use Newton's second law of motion, which states that force is equal to the rate of change of momentum, to calculate the force.

Force = change_in_momentum ÷ time.

To determine the time it takes for the bullet to stop, we need to divide the distance traveled by the velocity:
time = distance ÷ velocity = 4 m ÷ 200 m/s = 0.02 s.

Now we can calculate the force required to stop the bullet using the equation above:
force = (-4 kg·m/s) ÷ (0.02 s) = -200 N.

Therefore, the force necessary to stop the 20 g bullet moving at 200 m/s as it penetrates the wood at a distance of 4 m is 200 Newtons in the opposite direction of motion.