Final answer:
Using the conservation of energy principle, the maximum height of the pendulum is calculated to be approximately 0.86 meters when the pendulum is moving at 4.1 m/s at its lowest point.
Step-by-step explanation:
To find the maximum height to which the pendulum rises, we can use the principle of conservation of energy. At the lowest point, all the pendulum's energy is kinetic, and when it reaches the maximum height, all energy is converted to potential energy.
First, calculate the kinetic energy (KE) at the lowest point:
KE = ½ · m · v^2
Where:
- m is the mass of the pendulum (2 kg).
- v is the velocity at the lowest point (4.1 m/s).
Next, since there is no kinetic energy at the maximum height, all the kinetic energy is converted to gravitational potential energy (PE):
PE = m · g · h
Where:
- g is the acceleration due to gravity (9.81 m/s^2 on Earth).
- h is the maximum height.
Because KE initially equals PE at maximum height:
½ · m · v^2 = m · g · h
h = ½ · v^2 / g
Plugging in the values:
h = ½ · (4.1 m/s)^2 / (9.81 m/s^2)
h = ½ · 16.81 / 9.81 ≈ 0.86 m
The maximum height of the pendulum is approximately 0.86 meters, which corresponds to choice B.