A stone of mass 0.5kg is thrown to a height 200m.
(A). What is its kinetic energy and potential energy in its maximum height.
(B). Calculate its kinetic energy and hence its velocity after falling 50m.
To answer these questions, we need to understand the concepts of kinetic energy, potential energy, and the relationship between them.
(A). To find the kinetic energy and potential energy at the maximum height, we can use the following formulas:
1. Kinetic Energy (KE) = (1/2) * mass * velocity^2
2. Potential Energy (PE) = mass * gravity * height
Given:
Mass of the stone (m) = 0.5 kg
Height (h) = 200 m
1. Calculate the potential energy at the maximum height (PE):
PE = mass * gravity * height
= 0.5 kg * 9.8 m/s^2 * 200 m
= 980 J
2. Calculate the kinetic energy at the maximum height (KE):
At the maximum height, the stone would come to a stop, so its velocity is 0 m/s.
KE = (1/2) * mass * velocity^2
= (1/2) * 0.5 kg * (0 m/s)^2
= 0 J
Therefore, the kinetic energy at the maximum height is 0 J, and the potential energy is 980 J.
(B). To calculate the kinetic energy and velocity after falling 50 m, we can use the conservation of energy principle, which states that the total energy of a system is conserved.
Given:
Height (h) = 50 m
1. Calculate the final potential energy (PE_final) at the height of 50 m:
PE_final = mass * gravity * height
= 0.5 kg * 9.8 m/s^2 * 50 m
= 245 J
2. As the stone falls, the potential energy is converted into kinetic energy. Therefore, the initial kinetic energy (KE_initial) at the maximum height is equal to the final kinetic energy (KE_final) at a height of 50 m.
KE_initial = PE_final
3. Using the kinetic energy formula, we can solve for the final velocity (v_final):
KE_final = (1/2) * mass * v_final^2
245 J = (1/2) * 0.5 kg * v_final^2
v_final^2 = (245 J * 2) / (0.5 kg)
v_final^2 = 980 J/kg
v_final = sqrt(980 J/kg)
v_final ≈ 31.33 m/s
Therefore, the kinetic energy after falling 50 m is 245 J, and the velocity is approximately 31.33 m/s.