Final answer:
The kinetic energy of the wrecking ball when it swings through the lowest point of the arc is equal to its potential energy, which can be calculated using the equation K = m * g * h. Substituting the given values, the kinetic energy is calculated to be 58800 J.
Step-by-step explanation:
When the wrecking ball is released from an angle of 35 degrees, it will swing through the lowest point of the arc. At this point, it will have both kinetic and potential energy. The kinetic energy of the wrecking ball can be calculated using the equation:
K = 1/2 * m * v^2
Where:
- K is the kinetic energy
- m is the mass of the wrecking ball (600 kg)
- v is the velocity of the wrecking ball at the lowest point of the arc
To calculate the velocity, we can use the conservation of energy. At the highest point of the swing, all of the potential energy is converted into kinetic energy. Therefore, the potential energy at the highest point is equal to the kinetic energy at the lowest point. The potential energy can be calculated using the equation:
PE = m * g * h
Where:
- PE is the potential energy
- m is the mass of the wrecking ball (600 kg)
- g is the acceleration due to gravity (9.8 m/s^2)
- h is the height of the pendulum (10 m)
Solving for v, we get:
v = sqrt(2 * g * h)
Now we can substitute the values into the kinetic energy equation:
K = 1/2 * m * (sqrt(2 * g * h))^2
= m * g * h
Therefore, the kinetic energy of the wrecking ball when it swings through the lowest point of the arc is equal to its potential energy, which is:
K = m * g * h
Substituting the given values:
K = 600 kg * 9.8 m/s^2 * 10 m
= 58800 J