Aaron went to Palatine Hill in Rome, Italy , by bus on a summer morning. At the very top of the hill Aaron was able to see the entirely of Rome. However Aaron got completely lost and had no way to find his way back to where his bus would meet him. Luckily one of the tourists from his group passed by and was able to help him find the bus again. Which detail about this trip should also be included in this summary
One detail about this trip that should also be included in the summary is which specific tourist from Aaron's group helped him find the bus again.
A pendulum has a string with the length 1.2 m. You hold it at an angle of 22 degrees to the vertical and release it. The pendulum bob has a mass of 2.0 kg.
What is the potential energy before it is released?___J. What will be the velocity of the pendulum through the bottom of its swing? ___m/s.
Note:- Use g = 10 m/s^2. Use geometry to determine the height when released.
The potential energy before the pendulum is released can be calculated using the formula:
Potential Energy (PE) = Mass (m) * Gravity (g) * Height (h)
Given:
Mass of pendulum bob (m) = 2.0 kg
Gravity (g) = 10 m/s^2
To determine the height (h), we can utilize the geometry of the situation. The initial angle (θ) is given as 22 degrees to the vertical. The height (h) can be calculated using the equation:
h = length of string * sin(θ)
Given:
Length of string = 1.2 m
Angle (θ) = 22 degrees
Calculating height (h):
h = 1.2 m * sin(22 degrees) ≈ 0.430 m
Now we can calculate the potential energy (PE) before the pendulum is released:
PE = 2.0 kg * 10 m/s^2 * 0.430 m = 8.6 J
The velocity of the pendulum through the bottom of its swing can be determined using the law of conservation of energy. At the bottom of the swing, all the potential energy (PE) is converted to kinetic energy (KE). So,
Potential Energy (PE) = Kinetic Energy (KE)
KE = 8.6 J
The formula for kinetic energy is:
Kinetic Energy (KE) = (1/2) * Mass (m) * Velocity^2
We can rearrange this equation to calculate velocity (v):
v = √(2 * KE / m)
Substituting the known values:
v = √(2 * 8.6 J / 2.0 kg) ≈ 4.17 m/s
Therefore, the velocity of the pendulum through the bottom of its swing is approximately 4.17 m/s.