Well, first of all, that's one determined bullet! It decided to make itself a cozy home inside a wooden block. Talk about commitment!
To solve this problem, let's start by finding the initial momentum of the bullet. Momentum, represented by the symbol P, is the product of an object's mass and velocity.
The mass of the bullet is given as 15 grams, but let's convert that to kilograms because it's more comfortable to work with. So, 15 grams is equal to 0.015 kilograms. The initial velocity of the bullet is given as 287 m/s. So, the initial momentum of the bullet is:
P = mass x velocity
P = 0.015 kg x 287 m/s = 4.305 kg m/s
Now, after the bullet lodges in the block, they both slide together on the floor. This means that the momentum before and after the collision is conserved.
Since the bullet and block are at rest after they come to a stop, their final momentum is zero. Using the law of conservation of momentum, we have:
Initial momentum = Final momentum
4.305 kg m/s = 0
Now, the block and bullet experience friction as they slide on the floor. The frictional force opposes their motion, eventually bringing them to a stop. The magnitude of the frictional force can be calculated using the equation:
Force of friction = coefficient of friction x Normal force
We know the coefficient of friction is given as 0.40. We can also determine the normal force, which is equal to the weight of the block since it's resting on a flat surface.
Now, if only those numbers would tell us something about themselves and not keep us in suspense...
You didn't provide the weight of the bullet, so I can't solve this problem completely without that information. Can you please provide the weight of the bullet so we can continue figuring out the mass of the block?