Pendulum
Conservation of energy on a swinging pendulum
Name the energy changes in a windmill.
Try This at Home!
Insta-freeze
Dissolved gases in a liquid lower the freezing point temperature. When the gases leave, the liquid is able to freeze.
Ex 3) Pendulum
Where is PE max? KE max? PE = 0? KE = 0? KE = PE?
[ Flash ] — Show Me The Physics
If PE at A = 10 J, KE = 0
| PE | KE | |
|---|---|---|
| A | 10 J | 0 J |
| B | 0 J | 10 J |
| D | 10 J | 0 J |
If PE at C = 3 J, KE = ?
If the Wf as the pendulum moves from A to B is 1.5 J, what are the KE and PE of the pendulum at the bottom of the swing?
Wind turbines convert one form of energy into another. What is that conversion?
All Pendulums
Ex 4
A 1.0 kg pendulum swings to a height of 0.20 m above its lowest point.
What is the KE of the pendulum at the lowest point?
A pendulum is pulled to the side and released. Which plot of d vs PE is correct?
Answer
Review
Ex 5
A 5.00-kg cart is at the foot of a hill 10.0 m high. For the cart to reach the top of the hill, what is the minimum KE of the cart in the position shown?
[neglect friction]
m = 5.00 kg
h = 10.0 m
KE = ?
Finding the height of a pendulum from a pendulum angle
Enrichment
Pendulum Top View
Foucault's Pendulum — Proved the Earth rotates
School blocks YouTube? Foucault_PendulumReal.wmv
Pendulum mounted on a rotating base
School blocks YouTube? Foucault_Pendulum.mpg | Foucault_Pendulum.wmv
NYSSLS Reading Passage · Energy
The Pendulum Through History: How a Simple Swing Changed Science
Open Reading Passage → Regents Practice Version →Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. Where is a swinging pendulum's kinetic energy greatest?
2. A frictionless pendulum has 10 J of PE and 0 J of KE at its highest point. At a point where PE = 3 J, what is its KE?
3. A pendulum starts with 10 J of PE at the top. If 1.5 J of work is done against friction on the way down, its KE at the bottom is
4. A 1.0 kg pendulum swings to a height of 0.20 m above its lowest point. What is its KE at the lowest point? (g = 9.8 m/s²)
5. What energy conversion takes place in a wind turbine?
Pendulum Simulation With Friction
Students modified a pendulum computer simulation to include friction. As shown below, the pendulum is released from rest at a height of 40 cm and swings to a maximum height of 30 cm on the opposite side.
Diagram 1: Pendulum Swing With Friction
Diagram 2: Energy at Release Point (40 cm)
Which row in the table represents the fractional amounts of energy of the Earth–pendulum system at the highest point (30 cm) on the opposite side of the swing?
Opposite Highest Point (30 cm)
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. The pendulum bob in the simulation has a mass of 0.50 kg and is released 0.40 m above its lowest point. Substitute numerical values into a mathematical representation that can be used to determine the gravitational potential energy of the Earth–bob system at the release point (lowest point = zero level). Then calculate it.
C2. In the frictionless simulation, the bob is released from 0.40 m above its lowest point. Which mathematical representation gives its speed at the lowest point?
C3. In the frictionless simulation, the bob is released from 40 cm. Consider the Earth–bob system, with the lowest point as the zero level. Construct an energy bar graph for the system when the bob is 20 cm above its lowest point.
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.
C4. A student makes the following claim about the simulation with friction.
Place a check mark in either the Support or Refute box. Justify your response.
C5. Suppose friction removes ¼ of the bob’s remaining mechanical energy on every half-swing. After swinging over to 30 cm, how high will it rise when it swings back to the release side?
C6. A real pendulum clock also loses energy to friction and air resistance, yet it keeps swinging for days. Explain why the swing would die out on its own, and describe one way the clock’s design keeps the pendulum swinging.
