A 10 g bullet is fired horizontally into a 1 kg block of wood hanging from a 1 m long string attached to the ceiling, getting stuck in the block. Due to the impact, the block then swings on the string to a maximum angle of 60 degrees with respect to the vertical. How fast was the bullet traveling in m/s?

281m/s

45 To find the speed of the bullet, we can use the principle of conservation of energy. Here's how you can approach the problem step by step:

Step 1: Determine the initial potential energy of the block before the bullet hits it.
The initial potential energy can be calculated using the equation: PE = mgh, where m is the mass of the block (1 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the initial height of the block (1 m). Therefore, the initial potential energy is:
PE_initial = 1 kg * 9.8 m/s^2 * 1 m = 9.8 Joules.

Step 2: Calculate the maximum potential energy of the block at its highest point.
At the highest point of the block's swing, all the initial potential energy will be converted into potential energy. The potential energy at the highest point can be calculated as:
PE_max = mgh_max, where h_max is the maximum height from the equilibrium position. In this case, the maximum angle is given as 60 degrees. The maximum height can be found using the equation h_max = h * sin(angle). Therefore:
PE_max = 1 kg * 9.8 m/s^2 * (1 m * sin(60 degrees)).

Step 3: Find the difference in potential energy due to the bullet's impact.
The difference in potential energy can be calculated as:
ΔPE = PE_max - PE_initial.

Step 4: Use the kinetic energy equation to find the bullet's speed.
The kinetic energy equation is: KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass of the bullet (10 g = 0.01 kg), and v is the velocity of the bullet.
Since the bullet gets stuck in the block, the kinetic energy transferred to the block is equal to the difference in potential energy: ΔPE = KE. Therefore:
0.5 * 0.01 kg * v^2 = ΔPE.

Finally, substituting the values and solving for v, you can find the speed of the bullet in m/s.