Final answer:
To find the average frictional force that stops the bullet, use the work-energy theorem. The average frictional force stopping the bullet is approximately 409.22 N.
Step-by-step explanation:
To find the average frictional force that stops the bullet, we can use the work-energy theorem. According to the theorem, the initial kinetic energy of the bullet is equal to the work done by the frictional force in stopping it. The work done by the frictional force can be calculated as the product of the force and the distance over which it acts. In this case, the distance is given as 6.40 cm and the initial kinetic energy can be calculated using the formula (1/2)mv^2, where m is mass and v is velocity.
First, we need to convert the mass of the bullet from grams to kilograms: 7.80 g = 0.00780 kg. Then, we can calculate the initial kinetic energy of the bullet: (1/2)(0.00780)(690^2) = 1,808.68 J.
Next, we can use the work-energy theorem to calculate the average frictional force: (force)(distance) = (1/2)(0.00780)(690^2). Rearranging the equation, we get: force = (1/2)(0.00780)(690^2) / (0.0640). Plugging in the values, we find that the average frictional force that stops the bullet is approximately 409.22 N.