The length of a simple pendulum is 0.82 m and the mass of the particle (the "bob") at the end of the cable is 0.69 kg. The pendulum is pulled away from its equilibrium position by an angle of 6.7 ° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing?
I will be happy to critique your thinking or work on this. Angular freq comes as a standard formula, and the other items for energy concepts (PEmax= KEmax)
i know for part a the answer is 3.547
rad/s but i don't know how to do part b & c
please someone tell me how to do part b & c i know how to do part a only
From geometry, figure how high from the base is the bob when it starts. Its potential energy is mgh where h is the vertical height. At thebottom, the KE has to equal that starting energy.
1/2 mv^=mgh
you can calculate the velocity.
but how do you do part b i still don't get it
thanks for the help
To determine the total mechanical energy of the pendulum as it swings back and forth, you need to consider the potential energy and kinetic energy of the system.
First, let's calculate the potential energy at the highest point of the swing. The potential energy (PE) is given by PE = m * g * h, where m is the mass of the bob, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the vertical height from the lowest point of the swing.
At the highest point of the swing, the bob is at its maximum height (H), which can be calculated using trigonometry. The height is given by H = L * (1 - cosθ), where L is the length of the pendulum and θ is the angle of displacement.
Using the given values, we can calculate H:
H = 0.82 m * (1 - cos(6.7°))
Next, we can calculate the potential energy at the highest point:
PE_max = m * g * H
Now, let's calculate the total mechanical energy at the lowest point of the swing. At the lowest point of the swing, all the potential energy is converted into kinetic energy (KE). The total mechanical energy (E) is the sum of the kinetic and potential energy.
E = KE + PE
Since all the potential energy is converted to kinetic energy at the lowest point, the potential energy at the lowest point is zero. Therefore, the initial total mechanical energy is equal to the potential energy at the highest point:
E = PE_max
To determine the bob's speed as it passes through the lowest point (part c), you can use the principle of conservation of mechanical energy. At the lowest point, all the potential energy has been converted into kinetic energy.
KE_max = PE_max
Since the potential energy at the highest point is already calculated, you can use the equation for potential energy to find the kinetic energy at the lowest point:
KE_max = m * g * H
To determine the bob's speed (v), rearrange the equation for kinetic energy:
KE_max = 1/2 * m * v^2
Solve for v:
v = √(2 * KE_max / m)
Substitute the value of KE_max obtained from the previous calculation and the given mass (m) to find the bob's speed at the lowest point.