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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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Trajectory of a Juggling Club

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Trajectory of a Juggling Club Figure 1 shows a picture of a wooden juggling club. The mass of a juggling club is not evenly distributed between about the length of the club. There is more wood present near the club head, thus shifting the center of mass towards the head of the club. When a club is juggled, it rotates about its center of mass as it travels through the air. The three boxes on the club indicate three positions on the club. The center box (labeled COM) is the center of mass of the club. A video of a juggled club was taken and then analyzed to produce the graph shown in Figure 2. The motion of the club through the air began approximately 1.8 seconds into the video. As shown on the graph, the club was released from a height of 100-cm above the ground. The horizontal and the vertical position of the three marked points are shown as a function of time. The horizontal position is the X-position and the vertical position is the Y position. The zero position for the vertical motion is the ground.

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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.

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