A 34-g bullet traveling at 120m/s embeds itself in a wooden block on a smooth surface. The block then slides toward a spring and collides with it. The block compresses the spring (k=100 N/m) a maximum of 1.25 cm. Calculate the mass of the block of wood.

To calculate the mass of the block of wood, we will use the principles of conservation of momentum and energy.

Step 1: Calculate the initial momentum of the bullet before it embeds itself in the wooden block.
Momentum (p) = mass (m) * velocity (v)
The mass of the bullet is given as 34 grams, which is equal to 0.034 kg.
The velocity of the bullet is given as 120 m/s.
p1 = 0.034 kg * 120 m/s

Step 2: Calculate the final velocity of the combined bullet and block after the collision.
Since the bullet embeds itself in the block, their masses combine.
Let the mass of the block be represented as (M).
The initial momentum of the block and bullet combined is equal to the final momentum after the collision.
p1 = (0.034 kg + M kg) * vf
vf = p1 / (0.034 kg + M kg)

Step 3: Calculate the potential energy stored in the spring when compressed a maximum of 1.25 cm.
Potential Energy (PE) = 0.5 * k * (x^2)
Where k is the spring constant (100 N/m) and x is the compression (0.0125 m).
PE = 0.5 * 100 N/m * (0.0125 m^2)

Step 4: Convert the potential energy to kinetic energy at maximum compression.
Assuming all the potential energy is converted to kinetic energy,
Kinetic Energy (KE) = 0.5 * M * vf^2
KE = 0.5 * M * vf^2

Step 5: Equate the potential energy and the kinetic energy at maximum compression.
Setting the equations in Steps 3 and 4 equal to each other, we can solve for M.
0.5 * M * vf^2 = 0.5 * 100 N/m * (0.0125 m^2)

Step 6: Solve for M.
Substitute the value of vf from Step 2 into the equation from Step 5 and solve for M.

M = (0.5 * 100 N/m * (0.0125 m^2)) / vf^2

Using the previous calculations, we can determine the mass of the block of wood by substituting the values obtained into the equation.