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?

Question

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?

Answer 1

I figured it out!

Answer 2

To answer these questions, we need to apply some principles of physics related to pendulums. Let's go through each question step by step:

1) What is the potential energy of the pendulum?
The potential energy of the pendulum is given by the formula:
Potential Energy = m * g * h
where m is the mass of the object (0.60 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above a reference point.

In this case, the height h is equal to the length of the string multiplied by the sine of the angle the pendulum is displaced. Therefore, we have:
h = l * sin(theta)
where l is the length of the string (0.6 m) and theta is the angle of displacement (15 degrees).

Let's substitute the values into the formula:
Potential Energy = 0.6 kg * 9.8 m/s^2 * (0.6 m * sin(15 degrees))

2) What is the angular frequency of the pendulum?
The angular frequency, denoted by the symbol ω (omega), is given by the formula:
Angular frequency = sqrt(g / l)
where g is the acceleration due to gravity and l is the length of the string.

Let's substitute the values into the formula:
Angular frequency = sqrt(9.8 m/s^2 / 0.6 m)

3) What is the height of its displacement?
We already calculated the height of displacement as h = l * sin(theta):
Height = 0.6 m * sin(15 degrees)

4) What is the velocity of the pendulum at the lowest point in its swing?
At the lowest point in its swing, all of the potential energy has been converted to kinetic energy.
The kinetic energy is given by the formula:
Kinetic Energy = (1/2) * m * v^2
where m is the mass of the object (0.60 kg) and v is the velocity at the lowest point.

To find the velocity at the lowest point, we need the conservation of energy:
Potential Energy = Kinetic Energy
m * g * h = (1/2) * m * v^2
Simplifying the equation:
v = sqrt(2 * g * h)

Now we can substitute the value of h we found in question 3 into the equation to calculate the velocity.