Respuesta :
Answer:
Part 1; The total energy = Constant = 200 J
Part 2; Midway, the potential energy = The kinetic energy = 100 J
Explanation:
Part 1
According to the first law of thermodynamics, energy is neither created nor destroyed but changed from one form to another
The total (mechanical) energy = Potential energy + Kinetic energy = Constant
The kinetic energy given to the ball changed vertically up = 200 J
Potential energy = Mass, m × Gravity, g × Height, h
Given that the mass m of the ball and the acceleration due to gravity, g, remain the same, we have;
Potential energy ∝ The height of the ball
The potential energy at ground level = 0 J (Height , h = 0)
∴ The total (mechanical) energy = 0 J + 200 J = 200 J
At the maximum height, the ball momentarily stops, and the kinetic energy = 0 J
Therefore;
The potential energy of the ball at the maximum height, [tex]h_{max}[/tex], [tex]P.E._{max}[/tex] = 200 J
∴ [tex]P.E._{max}[/tex] = m·g·[tex]h_{max}[/tex] = 200 J
Part 2
At midway we have, the height, h = ([tex]h_{max}[/tex])/2
Therefore, [tex]P.E._{Midway}[/tex] = (m·g·([tex]h_{max}[/tex]))/2 = ([tex]P.E._{max}[/tex])/2 = (200 J)/2 = 100 J
The potential energy midway = 100 J
The remaining 200 J - 100 J = 100 J is the kinetic energy remaining in the ball
The kinetic energy midway = 100 J
Therefore, the total energy midway = 100 J + 100 J = 200 J
