A) When the conversion between kinetic energy and potential energy is 100% efficient, the total mechanical energy (the sum of kinetic and potential energy) is conserved.
At the lowest point of its swing, the pendulum has only kinetic energy. The kinetic energy (K) can be calculated using the formula: K = 0.5 * m * v^2, where m is the mass of the pendulum (0.02 kg) and v is its velocity (0.87 m/s).
K = 0.5 * 0.02 kg * (0.87 m/s)^2 = 0.007 kg m^2/s^2 = 0.007 J
This kinetic energy at the lowest point is equal to the potential energy (PE) at the initial height (h) from which the pendulum was dropped. So, we can set K = PE and solve for h:
0.007 J = m * g * h
0.007 J = 0.02 kg * 9.81 m/s^2 * h
h = 0.007 J / (0.02 kg * 9.81 m/s^2) ≈ 0.036 m
Therefore, the pendulum was dropped from a height of approximately 0.036 meters.
B) When the conversion between kinetic energy and potential energy is 63% efficient, it means that only 63% of the initial potential energy is converted to kinetic energy at the lowest point.
Let PE be the initial potential energy at the height from which the pendulum was dropped. The total initial mechanical energy (ME) can be calculated as ME = PE = m * g * h.
At the lowest point, the kinetic energy (K) is 63% of the initial potential energy: K = 0.63 * PE.
Equating K to the actual kinetic energy at the lowest point (0.007 J), we get:
0.63 * m * g * h = 0.007 J
Solving for h:
h = 0.007 J / (0.63 * 0.02 kg * 9.81 m/s^2) ≈ 0.113 m
Therefore, when the conversion between kinetic energy and potential energy is 63% efficient, the pendulum was dropped from a height of approximately 0.113 meters.
A pendulum (m=20g) is puller and then dropped. It is measured to have a speed of 0.87m/s at the lowest point of its swing. From what vertical height was it dropped if the conversion between kinetic energy and potential energy is
A) 100% efficient?
B) 63% efficient?
1 answer
1 answer