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# How Much Energy Can an Object Conserve After Traveling Different Paths?

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Source:
Author: Jerry Silver

### The Idea

This experiment compares how much energy an object has after following several different paths. We can determine how much energy a ball has after rolling down an incline by measuring how far it rolls off a table.

### What You Need

• 2 inclines supported by a ring stand or a stack of books (one incline that works well with golf balls is a vinyl bullnose section of molding available at home supply stores)
• 2 golf balls or other matched objects to roll down the incline, such as marbles, coffee cans, toy cars, or a air track glider
• meterstick or tape measure
• optional: motion sensor

### Method

1. Set up the inclines at two different slopes, as shown in Figure 49-1. Allow enough space at the bottom of the incline so that the golf balls roll off the table horizontally.
2. Avoid an angle that is so severe as to cause the golf balls to bounce on the edge of the table.
3. Align the inclines so they are pointing in the same direction.
4. Hold the two golf balls at equal height above the table. This may be easier with two people.
5. Predict what you think will happen with each of the balls. Which will come down with the greatest velocity? The velocity can be determined either by using a motion sensor or by comparing the point that it hits the floor after rolling off the table.
6. Release both golf balls and compare the results with your prediction.

### Expected Results

Both balls should move with the same velocity, as they roll horizontally across the table. The balls then hit the floor at the same distance from the edge of the table.

### Why It Works

In this, as in all other projects, energy is conserved. The energy each of the two golf balls starts off with is the same because they are released from the same height. This is equal to the object's weight times gravitational acceleration. All of this energy is converted to kinetic energy (neglecting frictional losses) when the balls get to the bottom of the incline. With equal kinetic energy, the objects will move at the same velocity.

### Other Things to Try

Pick one of the slopes and hold a golf ball on the incline at each of three different places (for example at 6-inch intervals starting from the top of the incline). Predict the outcome. Release the ball from each of the three positions and compare the results with your predictions. Here, the ball starts with three different amounts of potential energy. It comes off the incline with three different velocities, as shown in Figure 49-2. According to the law of conservation of energy (neglecting friction), the potential energy (mgh) is converted to kinetic energy (½ mv2). The distance that a horizontal projectile travels is proportional to its horizontal velocity. As a result, the range or distance along the floor will go as the square root of the height above the table.

### The Point

Total mechanical energy (consisting of kinetic and potential energy) is conserved unless some energy is consumed in overcoming friction. Objects released from the same height have equal potential energy. When this energy is converted to kinetic energy, the path the objects move toward the bottom is not important.