Conservation of energy of a pendulum

In summary: Just plug in the new speed (1.4m/s) and solve for the new angle Theta. Remember to convert the length back to 80cm for the calculation. In summary, the pendulum has an initial length of 80cm and a bob mass of .60kg. At the bottom of the swing, the speed of the bob is 2.8m/s. Using the relevant equation, we can solve for Theta and determine that the angle with the vertical is approximately 60 degrees. To solve for part b, we can use the same method but with a new speed of 1.4m/s, resulting in an angle of approximately 29 degrees.
  • #1
maniacp08
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An 80cm long pendulum with a .60kg bob is released from rest at an initial angle of Theta with the vertical. At the bottom of the swing, the speed of the bob is 2.8m/s.

a)what is Theta?
b)What angle does the pendulum makes with the vertical when the speed of the bob is 1.4m/s?Revelant equation:
Ui + Ki = Uf + Kf

I converted 80cm to .8m.
mgh + 0 = 0 + 1/2 m v^2
.60kg * 9.81 m/s * h = 1/2 .60kg * (2.8m/s)^2
I need to solve for h which is .3995922528 approx .4m

Length is .8m
h = L - Lcos Theta
.4m = .8m - Lcos Theta
.5 = Cos Theta
Cos^-1 = 60Is this correct?
and Part b is the same procedure correct?
 
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  • #2
maniacp08 said:
An 80cm long pendulum with a .60kg bob is released from rest at an initial angle of Theta with the vertical. At the bottom of the swing, the speed of the bob is 2.8m/s.

a)what is Theta?
b)What angle does the pendulum makes with the vertical when the speed of the bob is 1.4m/s?Revelant equation:
Ui + Ki = Uf + Kf

I converted 80cm to .8m.
mgh + 0 = 0 + 1/2 m v^2
.60kg * 9.81 m/s * h = 1/2 .60kg * (2.8m/s)^2
I need to solve for h which is .3995922528 approx .4m

Length is .8m
h = L - Lcos Theta
.4m = .8m - Lcos Theta
.5 = Cos Theta
Cos^-1 = 60Is this correct?
and Part b is the same procedure correct?

Looks OK so far.
And you can solve part b in a similar way.
 
  • #3


a) Theta is the initial angle at which the pendulum is released from rest.
b) To find the angle when the speed of the bob is 1.4m/s, we can use the same equation but with the new velocity value:
mgh + 0 = 0 + 1/2 m v^2
.60kg * 9.81 m/s * h = 1/2 .60kg * (1.4m/s)^2
Solving for h, we get h = 0.0998m.
Now, using the same formula for h, we can solve for Theta:
h = L - Lcos Theta
0.0998m = 0.8m - 0.8mcos Theta
0.7002m = 0.8mcos Theta
Cos Theta = 0.8753
Theta = Cos^-1(0.8753) = 29.55 degrees
Therefore, when the speed of the bob is 1.4m/s, the angle with the vertical is approximately 29.55 degrees.
 

1. How does a pendulum conserve energy?

A pendulum conserves energy through the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. The potential energy of the pendulum at its highest point is converted to kinetic energy as it swings downward, and then back to potential energy as it swings back up. This process continues, with the total energy of the pendulum remaining constant.

2. What factors affect the conservation of energy in a pendulum?

The conservation of energy in a pendulum is affected by several factors, including the length of the pendulum, the mass of the pendulum bob, and the amplitude of the swing. A longer pendulum will have a slower frequency and therefore conserve energy for a longer period of time. A heavier pendulum bob will also conserve energy for longer, while a larger amplitude will result in more energy being transferred between potential and kinetic energy.

3. Is the conservation of energy in a pendulum affected by friction?

Yes, friction can affect the conservation of energy in a pendulum. Friction between the pendulum's string and the air can slow down its movement and cause energy to be lost. This is why pendulums in real life eventually come to a stop, unlike in idealized models where there is no friction.

4. Can the conservation of energy in a pendulum be seen in real life?

Yes, the conservation of energy in a pendulum can be observed in real life. A simple pendulum, such as a swing, will continue to swing back and forth with minimal loss of energy due to the conservation of energy principle. However, in real life, there will be some energy loss due to factors such as friction and air resistance.

5. What is the relationship between the length of a pendulum and its conservation of energy?

The length of a pendulum affects its conservation of energy in that a longer pendulum will have a slower frequency and therefore conserve energy for a longer period of time. This is because the potential energy of the pendulum increases with its height, and a longer pendulum will have a greater height and therefore a greater potential energy. This relationship can be observed in a simple pendulum by varying the length and measuring the time it takes to complete one swing.

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