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
Use trigonometry to calculate the vertical rise of the bob, H.
The maximum potential energy is M g H
I love physics
To find the maximum potential energy of the pendulum bob, we need to consider its height above the lowest point in its swing.
The potential energy of an object is given by the formula:
Potential Energy = mass * gravity * height
In this case, the mass of the pendulum bob is 250 grams, but we need it in kilograms to use the formula. So, we convert the mass to kilograms:
Mass in kilograms = mass in grams / 1000
= 250 g / 1000
= 0.25 kg
The acceleration due to gravity is approximately 9.8 m/s².
To determine the height, we need to use the trigonometric relationship between the angle and the length of the string. In this case, the length of the string is 1.00 m and the angle is 150°.
Using trigonometry, we can find the vertical height of the pendulum bob:
Height = length * sin(angle)
= 1.00 m * sin(150°)
Since the sine function is negative in the second quadrant, the negative sign will indicate that the pendulum bob is to the left, opposite to the direction it was pulled.
Height = 1.00 m * sin(150°)
≈ 1.00 m * (-0.5)
= -0.50 m
Now, we can calculate the maximum potential energy:
Potential Energy = mass * gravity * height
= 0.25 kg * 9.8 m/s² * (-0.50 m)
= -1.225 J
The maximum potential energy of the pendulum bob is approximately -1.225 Joules. Note that the negative sign indicates a decrease in potential energy compared to the lowest point in the swing.