A 0.60 kg mass is attached to a 0.6 m string and displaced at an angle of 15 degrees before it is released. 1)What is the potential energy of the pendulum? 2) What is the angular frequency of the pendulum? What is the height of its displacement? 4) What is the velocity of the pendulum at the lowest point in its swing?
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To answer these questions, we'll need to use the formulas for potential energy, angular frequency, height, and velocity of a pendulum.
1) Potential Energy (PE) of the pendulum:
The potential energy of a pendulum at its highest point is given by the formula:
PE = m * g * h
Where:
m = mass of the pendulum (0.60 kg)
g = acceleration due to gravity (approximately 9.81 m/s^2)
h = height (displacement) above the lowest point of the pendulum
Since the height is not provided directly, we need to calculate it. The height can be determined using trigonometry.
Height (h):
The height of the displacement can be found using the formula:
h = L * (1 - cosθ)
Where:
L = length of the string (0.6 m)
θ = angle of displacement (15 degrees)
Substituting the given values:
h = 0.6 m * (1 - cos(15 degrees))
2) Angular Frequency (ω) of the pendulum:
The angular frequency of a simple pendulum is given by the formula:
ω = √(g / L)
Where:
g = acceleration due to gravity (approximately 9.81 m/s^2)
L = length of the string (0.6 m)
Substituting the given values:
ω = √(9.81 m/s^2 / 0.6 m)
3) The height of the displacement is calculated in step 1.
4) Velocity (v) of the pendulum at the lowest point:
The velocity of the pendulum is maximum at the lowest point of its swing. It can be calculated using the formula:
v = √(2 * g * h)
Where:
g = acceleration due to gravity (approximately 9.81 m/s^2)
h = height (displacement) above the lowest point of the pendulum (calculated in step 1)
Substituting the calculated value for h:
v = √(2 * 9.81 m/s^2 * h)
Now, you have the step-by-step explanation and the formulas to calculate the potential energy, angular frequency, height, and velocity of the pendulum.