1 Energy Conservation
The Law of Conservation of Energy states that energy is neither created nor destroyed. Instead, energy can be converted, or changed, into another form of energy. In this activity, the mechanical energy of a pendulum will be investigated. Mechanical energy is the summation of an object's potential energy (stored energy) and kinetic energy (energy of moving objects). A pendulum is a weight, called a bob, hung from a fixed point so that it can freely move backward and forward. Each swing of the bob, from one side to the other forms an arc, as shown in Figure 1. Work is done on the pendulum when it is raised to position A. This means that energy is being transferred to the pendulum. When raised, the pendulum gains gravitational potential energy, which is stored energy due to an object's height. When released, gravity pulls the pendulum down and its gravitational potential energy is converted into kinetic energy.
Gravity is the force of attraction between any two objects with mass in the Universe. The greater the mass, the greater is an object's gravitational force. Earth is very massive; thus, it attracts objects near or on its surface in a direction toward its center. At position A, the pendulum has maximum gravitational potential energy, which is changed to kinetic energy as the pendulum swings down to position B. From position B to C, the pendulum is moving against the downward force of gravity; thus, it slows. During this upward part of the swing, the pendulum's kinetic energy changes into gravitational potential energy again.
The mechanical energy of a pendulum involves the transfer of kinetic energy into potential energy and back to kinetic energy, and so on. It is important to note that the amount of potential energy at position C is less than it was when the pendulum was first lifted to position A (Figure 1). This means the pendulum loses mechanical energy with each swing and each swing is lower and lower until it finally stops. This lost energy was changed into another form of energy, such as heat or sound (air vibration).
See for Yourself
Materials
string, 8 inch (20 cm)
tape
washer with a hole or any comparable weight
What to Do
1 Tie one end of the string to the washer.
2 Tape the free end of the string to the edge of a table (Figure 2).FIG 2
3 Pull the pendulum to the side a short distance and release. It should swing back and forth. Observe the movement of the pendulum. Make note of the pendulum's height during each swing.
What Happened?
In Figure 1 the pendulum is first held stationary at position A, which is higher than position C. This means work has been done on the pendulum by lifting it, giving the pendulum gravitational potential energy. When the pendulum is released, the force of gravity acts on the pendulum pulling it downward. When moving, the pendulum has kinetic energy. Halfway between A and B, half of the mechanical energy is divided between potential energy and kinetic energy. At position B, the potential energy of the pendulum is zero and the kinetic energy is at its maximum. This kinetic energy decreases as the pendulum moves toward position C. Halfway between B and C, mechanical energy is again divided between potential energy and kinetic energy. Finally, the pendulum rises slightly below position C. In this position, its potential energy is less than at the start of the swing. This reduction of mechanical energy decreases incrementally until the pendulum stops moving and hangs vertically at a standstill at position B.
2 Frequency
Frequency is how many times an event occurs in a specific amount of time, such as the back and forth swing of a pendulum. A pendulum is an apparatus with a hanging weight from a fixed point that can move freely back and forth. A string with a washer attached to the end is one example of a pendulum. The weight on a pendulum is called the bob. Each forward and back swing of the bob on a pendulum is counted as one cycle.
The frequency of a pendulum is determined by counting the number of cycles, the back and forth movements, the pendulum bob makes in a one-second interval. The length of the cable or string attached to the bob determines the pendulum's frequency. The longer the string, the lower the pendulum's frequency.
See for Yourself
Materials
string, 18 inches (45 cm)
washer with a hole, or any comparable weight
tape
What to Do
1 Tie one end of the string to the washer.
2 Tape the free end of the string to the edge of a table. Leave part of the end of the string free. This end of the string will be pulled to shorten the string.
3 Pull the washer to one side and release it. The washer should freely swing without touching anything (Figure 1).FIG 1
4 As the washer swings, slowly pull the end of the string to shorten it. As you shorten the string, observe the change in the frequency of the pendulum.
What Happened?
As the length of the string is shortened, the distance the bob swings gets shorter. Thus, it takes less time for the bob to swing back and forth. This means that, given the same interval of time, a shorter pendulum will swing back and forth more times than a longer pendulum. So, there is a relationship. The frequency of a shorter pendulum is higher than the frequency of a longer pendulum.
3 Coupled Pendulums
Coupled pendulums can be formed by two pendulums suspended from a common support. In this setup, energy from one swinging pendulum can be transferred through the medium connecting the two pendulums. As a result, one swinging