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Merrily We Roll Along

Purpose: To investigate the relationship between distance and time for a ball rolling down an incline.

Materials: wooden ramp, toy cart, stopwatch, meter stick, protractor, tape

Discussion: Measurement of the motion of a freely falling object is difficult to calculate because the speed increases rapidly. In fact, it increases by nearly 10 m/s every second (something we will talk about later in the year). The distance that the object falls becomes very large, very quickly. Galileo slowed down the motion by using inclined planes. The component of gravity acting along the direction of the inclined plane is less that the full force of gravity that acts straight down-so the change of speed happens more slowly and thus it is easier to measure. The less steep the incline, the smaller the acceleration. The physics of freefall can be understood by first considering the motion of a ball on an inclined plane.

Procedure:

Step 1: Set up a ramp with the angle of incline at about 10º to the horizontal (2 textbooks)

Step 2: Divide the ramp’s length into 6 equal parts and mark the six positions on the board with the pieces of tape. For example, if your board is 200 cm long, divide 200 by 6 to get 33.33 cm per section. Mark your release points every 33.33 cm from the bottom.

Step 3: Use a stopwatch to measure the time it takes the ball to roll down the ramp from each of the six points. You will be making three timings from each position. Record your data in data table A.

Data Table A

Distance

(m)

|Time

Trial 1 |Time

Trial 2 |Time

Trial 3 |Average of Time Trials |Acceleration

d=vit + 1/2at2 |Final Velocity

vf = vi + at | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Step 4: Graph your data, plotting distance (y-axis) vs. average time (x-axis) on a piece of graph paper. Draw a line of best fit and calculate the slope.

Step 5: Repeat steps 2 – 4 with the incline set an angle of 20º (4 textbooks) to the horizontal. Record your data in data table B. Make sure to make a graph of these data values as well.

MAKE A HYPOTHESIS: Do you think the times will be faster when you increase the angle by 10 degrees? Why? (Use at least 2 sentences)

Data Table B

Distance

(m)

|Time

Trial 1 |Time

Trial 2 |Time

Trial 3 |Average of Time Trials |Acceleration

d=vit + 1/2at2 |Final Velocity

vf = vi + at | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Questions:

1. What happens to the speed of the ball as it rolls down the ramp?

2. Does the ball accelerate down the ramp? What evidence do you have to defend your answer?

3. What is acceleration?

4. What happens to the acceleration if the angle of the ramp is increased? Why? Was your hypothesis correct?

5. What at least two possible sources of error that could have occurred during the lab?

Distance vs. Time (Chart A)

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Distance vs. Time (Chart B)

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6. Which graph has the steeper slope?

7. What does the slope of the graph represent? (Write out slope formula using units)

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