Understanding Gravitational Potential Energy and Mechanical Energy
How can we calculate the gravitational potential energy of a system initially?
a) What is the gravitational potential energy of the system initially?
What is the total mechanical energy of the system before the collision?
b) What is the total mechanical energy of the system before the collision?
What is the speed of the two blocks immediately after the collision?
c) What is the speed of the two blocks immediately after the collision?
How does the system's total energy change after the collision?
d) How does the system's total energy change after the collision?
Answers:
a) The potential energy of the system initially is 14,986.3 J.
b) The total mechanical energy of the system before the collision is also 14,986.3 J.
c) The speed of the two blocks immediately after the collision is 0 m/s.
d) The system's total energy remains the same after the collision.
Explanation:
a) The potential energy of the system initially can be calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, the mass is 485 kg, the acceleration due to gravity is 9.8 m/s^2, and the height is 3.1 m. Therefore, the potential energy is PE = (485 kg)(9.8 m/s^2)(3.1 m) = 14,986.3 J.
b) The total mechanical energy of the system before the collision is the sum of the potential energy and the kinetic energy. Since the masses are initially at rest, the kinetic energy is zero. Therefore, the total mechanical energy is equal to the potential energy, which is 14,986.3 J.
c) The speed of the two blocks immediately after the collision can be calculated using the principle of conservation of momentum. Since the masses stick together and move as one, the total momentum before the collision is equal to the total momentum after the collision. The momentum before the collision is calculated as the product of the mass and the initial velocity of the 485 kg mass, which is zero since it is at rest. Therefore, the total momentum before the collision is zero. Since the masses stick together and move as one, the total momentum after the collision is equal to the product of the combined mass and the final velocity. The combined mass is 485 kg + 82 kg = 567 kg. Therefore, the final velocity can be calculated as (567 kg)(v) = 0, where v is the final velocity. Solving for v, we get v = 0 m/s.
d) The system's total energy remains the same after the collision since there are no external forces acting on the system to change its energy. Therefore, the total energy of the system remains at 14,986.3 J.