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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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Vibrating Mass on a Spring

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Use the graphs to determine information about the position or the velocity of the mass at specific moments in time.

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Analyze the graphs to answer questions related to amplitude and period.

Inspect position-time and velocity-time data for a vibrating mass on a spring.

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Relate the location in the up-and-down trajectory of the mass to points on the position-time or velocity-time graph.

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Mass on a Spring A mass is suspended on a spring and hangs at its rest position. The mass is pulled below its rest position and released. It vibrates up and down between two extreme positions – A and E. See Figure 1. The motion repeats itself over and over again. The vertical position and velocity of the vibrating mass change over time. Velocity describes how fast an the mass moves and in what direction it moves. A + and - sign is used to indicate the direction of velocity. A + sign indicates an upward direction of motion and a - sign indicates a downward direction of motion. A motion detector is placed below the vibrating mass to detect the vertical position (height above the detector) and velocity as a function of time. The results are shown in Figure 2.

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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.