a 3.0-g bullet traveling at 350-m/s hits a tree and slows down ununiformly to a stop while penetrating a distance of 12-cm into the trees trunk. what was the force exerted on the bullet to bring it to a rest?

Force x (penetration distance) = inital kinetic energy = (1/2) M V^2.

Convert m to kg and the penetration distance to meters before doing the calculation, to get the force in Newtons.

To determine the force exerted on the bullet to bring it to a rest, we can use the equation:

Work = Force x Distance

First, we need to find the work done on the bullet. The work done is equal to the change in kinetic energy.

Initial kinetic energy = (1/2)mv^2
Final kinetic energy = 0 (as the bullet comes to rest)

Therefore, the work done on the bullet is given by:

Work = Final kinetic energy - Initial kinetic energy
= 0 - (1/2)(3.0 g)(350 m/s)^2

Next, we need to convert the mass of the bullet to kilograms, and the centimeters to meters:

Mass of the bullet = 3.0 g = 3.0 * 10^-3 kg
Distance penetrated by the bullet = 12 cm = 12 * 10^-2 m

Plugging in the values, we have:

Work = - (1/2)(3.0 * 10^-3 kg)(350 m/s)^2
= - (1/2)(3.0 * 10^-3 kg)(122500 m^2/s^2)
= - (1/2)(367.5 kg·m^2/s^2)
= -183.75 N·m

Since the work done on an object is equal to the force exerted on it multiplied by the distance it is displaced, we can rearrange the equation:

Force = - Work / Distance

Plugging in the values, we have:

Force = - (-183.75 N·m) / (12 * 10^-2 m)
= 183.75 N·m / (0.12 m)
= 1531.25 N

Therefore, the force exerted on the bullet to bring it to a rest is approximately 1531.25 Newtons.

To find the force exerted on the bullet, we can use the concept of work done and apply the work-energy theorem.

The work done on an object is given by the formula:

Work = Force × Distance

In this case, the work done on the bullet will bring it to a stop, so the work done is negative since the force opposes the motion. Therefore, the equation becomes:

Work = -Force × Distance

The work done on an object is also equal to the change in its kinetic energy:

Work = ΔKinetic Energy

The initial kinetic energy of the bullet is given by:

Kinetic Energy = (1/2) × mass × velocity^2

Given the mass of the bullet is 3.0 g (0.003 kg) and the velocity is 350 m/s, we can calculate the initial kinetic energy.

Initial Kinetic Energy = (1/2) × 0.003 × (350)^2

Finally, we can equate the work done to the initial kinetic energy, and solve for the force:

-Force × Distance = (1/2) × 0.003 × (350)^2

Simplifying the equation, we can find the force:

Force = -[ (1/2) × 0.003 × (350)^2 ] / Distance

Given the distance the bullet penetrated into the tree trunk is 12 cm (0.12 m), we can substitute this value into the equation to calculate the force exerted on the bullet.

183.75J