A 10.0g bullet is fired with a speed of 500m/s into a pendulum block of mass 5.00kg, suspended from a cord 0.600m long. Calculate: (a)the vertical height through which the pendulum rises.

(b) the initial kinetic energy of the bullet. (c) the kinetic energy of the bullet and the pendulum immediately after the bullet becomes embedded in the pendulum.

height is 0.05m

a=0.05m

b=500J

c=600J

To calculate the answers to these questions, we'll need to use the principles of conservation of energy. Here's how you can find each value:

(a) To calculate the vertical height through which the pendulum rises, we can use the conservation of mechanical energy. The initial kinetic energy of the bullet will be converted into potential energy when the pendulum rises. The formula for potential energy is given by:

Potential energy = m * g * h

Where:
m is the mass of the pendulum block (5.00 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height through which the pendulum rises (which we need to find)

Since the bullet is embedded in the pendulum, the mass of the pendulum block will change. To account for this change, we can sum the masses of the bullet and the pendulum block:

Total mass = mass of the bullet (10.0 g) + mass of the pendulum block (5.00 kg)

Now, to find the height h, we can equate the initial kinetic energy of the bullet to the potential energy when the pendulum rises:

(1/2) * mass of the bullet * velocity^2 = total mass * g * h

Substituting the given values into the equation, we have:

(1/2) * 0.01 kg * (500 m/s)^2 = (10.01 kg) * (9.8 m/s^2) * h

Solving for h:

h = (0.01 kg * 500^2 m^2/s^2) / (10.01 kg * 9.8 m/s^2)

(b) To calculate the initial kinetic energy of the bullet, we can use the formula:

Kinetic energy = (1/2) * mass * velocity^2

Substituting the given values, we have:

Kinetic energy = (1/2) * 0.01 kg * (500 m/s)^2

(c) Lastly, we need to find the kinetic energy of the bullet and the pendulum immediately after the bullet becomes embedded in the pendulum. At this point, they both move with a common velocity. Since kinetic energy is proportional to the square of velocity, the kinetic energy after the bullet becomes embedded will be the same as the initial kinetic energy of the bullet:

Kinetic energy = (1/2) * 0.01 kg * (500 m/s)^2

Now let's calculate each value using the given equations and substitutions.