3. A 250-g is attached to a string 1.00 m long to make a pendulum. If the pendulum bob is pulled to the right, such that the string makes an angle of 150 with the vertical, what is the maximum potential energy

To find the maximum potential energy of the pendulum, we need to calculate the height at the maximum point of the swing and then use the formula for potential energy.

The maximum height of the pendulum is reached when the string makes an angle of 150° with the vertical. To calculate the height, we can use trigonometry.

1. Split the angle of 150° into two components: the vertical component and the horizontal component.
- The vertical component is given by:
vertical_component = length_of_string * sin(angle)
vertical_component = 1.00 m * sin(150°) ≈ 0.5 m

2. Now, calculate the maximum height reached by the pendulum by subtracting the vertical component from the string length.
- maximum_height = length_of_string - vertical_component
- maximum_height = 1.00 m - 0.5 m = 0.5 m

The potential energy of an object is given by the formula:
Potential Energy (PE) = mass * gravity * height

In this case, the mass of the pendulum bob is given as 250 g, which is equivalent to 0.250 kg. The acceleration due to gravity (g) is approximately 9.8 m/s².

3. Finally, we can calculate the maximum potential energy using the obtained values:
- PE = mass * gravity * height
- PE = 0.250 kg * 9.8 m/s² * 0.5 m
- PE ≈ 1.225 J

Therefore, the maximum potential energy of the pendulum is approximately 1.225 Joules.

Why are you posting the same question twice?