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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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Period of a Pendulum

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Analyze the design of the three experiments associated with the factors affecting the period of a pendulum.

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Make evidence-based claims regarding the factors affecting the period.

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Use provided graphs to retrieve values, interpolate, extrapolate, and identify relationships.

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The Period of a Pendulum A simple pendulum consists of a light string tied at one end to a pivot point and attached to a mass at the other end. The period of a pendulum is the time it takes the pendulum to make one full back-and-forth swing. A group of students are investigating factors that might affect the period of a pendulum. They conduct three experiments. Experiment 1 In the first experiment, the students make a pendulum by hanging a 200.0-gram mass on the end of a string. They pull the mass back such that it makes an angle of 30° with its usual vertical orientation. They then release the mass, allowing it to swing back and forth. They use a stopwatch to measure the time it takes the pendulum to complete five full swings. They use this time to determine the period. They vary the length of the string while keeping the mass and angle constant. A plot of their data is shown in Figure 1. Experiment 2 The students make a pendulum with a length of 65 cm. They release the mass from rest after pulling it back 30° from its vertical orientation. They conduct several trials using varying amounts of mass hanging on the end of the string. A plot of their data is shown in Figure 2. Experiment 3 The students hang a 200.0-gram mass on the end of a string to create a pendulum with a length of 67 cm. They conduct several trials while varying the angle that the string makes with the vertical orientation. A plot of their data is shown in Figure 3.

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Stopping Distance One aspect of safe driving involves the ability to stop a car readily. This ability depends upon the driver's alertness and readiness to stop, the conditions of the road, the speed of the car, and the braking characteristics of the car. The actual distance it takes to stop a car consists of two parts - the reaction distance and braking distance. When a driver sees an event in his/her field of view that might warrant braking (for example, a dog running into the street), a collection of actions must be taken before the braking actually begins. First the driver must identify the event and decide if braking is necessary. Then the driver must lift his/her foot off the gas pedal and move it to the brake pedal. And finally, the driver must press the brake down its full distance in order to obtain maximum braking acceleration. The time to do all this is known as the reaction time. The distance traveled during this time is known as the reaction distance. Once the brakes are applied, the car begins to slow to a stop. The distance traveled by the car during this time is known as the braking distance. The braking distance is dependent upon the original speed of the car, the road conditions, and characteristics of the car such as its profile area, mass and tire conditions. Figure 1 shows the stopping distance for a Toyota Prius on dry pavement resulting from a 0.75-second reaction time. The reaction time of the driver is highly dependent upon the alertness of the driver. Small changes in reaction time can have a large effect upon the total stopping distance. Table 1 shows the reaction distance, braking distance, and total stopping distance for a Toyota Prius with an original speed of 50.0 mi/hr and varying reaction times.