A lead bullet with a mass of 8.50 g traveling at 4.80 x 102 m/s strikes a 2.00 kg block of wood and is embedded in it. Both the bullet and the block are initially at 25.0°C. Assume that no heat is lost to the surroundings and that all the kinetic energy of the bullet is converted into heat in the block. The specific heat capacity of wood is 2.1 J/g • K and the specific heat capacity of water is 4.18 J/g • K.

What is the kinetic energy of the bullet?



How much energy does the block absorb?

What is the final temperature of the block?

To answer these questions, we need to use the concept of conservation of energy and apply the principle of the conservation of linear momentum.

1. To calculate the kinetic energy of the bullet:
The kinetic energy (KE) of an object is given by the formula KE = 0.5 * mass * velocity^2. In this case, the mass of the bullet is 8.50 g, which is equivalent to 0.00850 kg, and the velocity is given as 4.80 x 10^2 m/s. Plugging these values into the formula, we can calculate the kinetic energy of the bullet.

KE = 0.5 * 0.00850 kg * (4.80 x 10^2 m/s)^2

2. To determine the energy absorbed by the block:
Since the bullet gets embedded in the block, all of its kinetic energy is converted into heat energy absorbed by the block. Therefore, the energy absorbed by the block is equal to the initial kinetic energy of the bullet.

3. To find the final temperature of the block:
We can use the specific heat formula, Q = mcΔT, where Q is the heat absorbed or released, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we calculate the heat energy absorbed by the block, which we determined to be equal to the kinetic energy of the bullet (from step 2).
Then, we can rearrange the specific heat formula to solve for the change in temperature (ΔT) and substitute the known values:
Q = mcΔT => ΔT = Q / mc
We know the mass of the block is given as 2.00 kg, and the specific heat capacity of wood is 2.1 J/g • K. We need to convert the specific heat capacity to J/kg • K by multiplying by 1000 since 1 kg = 1000 g. Using the specific heat formula, we can calculate the final temperature of the block.