merrily we roll around
Purpose:
The purpose of this lab is to investigate the relationship between acceleration and velocity
Step 1:Set up a ramp with the angle of the incline at about 10° to the horizontal,
Step 2: Divide the ramp’s length into six equal parts and mark the six positions on the board with pieces of tape. These positions will be your release points. Suppose your ramp is 200 cm long. Divide 200 cm by 6 to get 33.33 cm per section. Mark your release points every 33.33 cm from the bottom. Place a stopping block at the bottom of the ramp to allow you to hear when the ball reaches the bottom
Step 3:Use either a stopwatch or a computer to measure the time it takes the ball to roll down the ramp from each of the six points. (If you use the computer, position one light probe at the release point and the other at the bottom of the ramp.) Use a ruler or a pencil to hold the ball at its starting position, then pull it away quickly parallel to incline to release the ball uniformly. Do several practice runs with the help of your partners to minimize error. Make at least three timings from each position, and record each time and the average of the three times in Data Table A
Step 4:Graph your data, plotting distance (vertical axis) vs. average time (horizontal axis) on an overhead transparency. Use the same scales
on the coordinate axes as the other groups in your class so that you can compare results.
Step 5:Repeat Steps 2–4 with the incline set at an angle 5° steeper.Record your data in Data Table B. Graph your data as in Step 4.
Step 6:Remove the tape marks and place them at 10 cm, 40 cm, 90 cm,and 160 cm from the stopping block, as in Figure B. Set the incline oft he ramp to be about 10°.
Step 7:Measure the time it takes for the ball to roll down the ramp from each of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.Step 7:Measure the time it takes for the ball to roll down the ramp from each of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.Step 7:Measure the time it takes for the ball to roll down the ramp fromeach of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.
Step 8:Graph your data, plotting distance (vertical axis) vs. time (horizontal axis) on an overhead transparency. Use the same coordinate axes as the other groups in your class so that you can compare results.
Step 9:Look at the data in Column 2 a little more closely. Notice that the difference between t2andt1is approximately the same as t1itself. The difference between t3and t2is also nearly the same as t1. What about the difference between t4and t3? Record these three time intervals in Column 3 of Data Table C.
Step 10:If your values in Column 3 are slightly different from one another, find their average by adding the four values and dividing by 4.Do as Galileo did in his famous experiments with inclined planes and call this average time interval one “natural” unit of time. Note that t1isalready listed as one “natural” unit in Column 4 of Table C. Do you see that t2will equal—more or less—two units in Column 4? Record this, and also t3and t4in “natural” units, rounded off to the nearest integer.Column 4 now contains the rolling times as multiples of the “natural”unit of time
Step 12:Investigate more carefully the distances traveled by the rolling ball in Table D. Fill in the blanks of Columns 2 and 3 to see the pattern
Step 13:You are now about to make a very big discovery—so big, in fact,that Galileo is still famous for making it first! Compare the distances withthe times in the fourth column of Data Table C. For example, t2is two“natural” time units and the distance rolled in time t2is 22, or 4, times asgreat as the distance rolled in time t1
Step 14:Repeat Steps 6–10 with the incline set at an angle 5° steeper.Record your data in Data Table E_
Data at 10 degrees
The purpose of this lab is to investigate the relationship between acceleration and velocity
Step 1:Set up a ramp with the angle of the incline at about 10° to the horizontal,
Step 2: Divide the ramp’s length into six equal parts and mark the six positions on the board with pieces of tape. These positions will be your release points. Suppose your ramp is 200 cm long. Divide 200 cm by 6 to get 33.33 cm per section. Mark your release points every 33.33 cm from the bottom. Place a stopping block at the bottom of the ramp to allow you to hear when the ball reaches the bottom
Step 3:Use either a stopwatch or a computer to measure the time it takes the ball to roll down the ramp from each of the six points. (If you use the computer, position one light probe at the release point and the other at the bottom of the ramp.) Use a ruler or a pencil to hold the ball at its starting position, then pull it away quickly parallel to incline to release the ball uniformly. Do several practice runs with the help of your partners to minimize error. Make at least three timings from each position, and record each time and the average of the three times in Data Table A
Step 4:Graph your data, plotting distance (vertical axis) vs. average time (horizontal axis) on an overhead transparency. Use the same scales
on the coordinate axes as the other groups in your class so that you can compare results.
Step 5:Repeat Steps 2–4 with the incline set at an angle 5° steeper.Record your data in Data Table B. Graph your data as in Step 4.
Step 6:Remove the tape marks and place them at 10 cm, 40 cm, 90 cm,and 160 cm from the stopping block, as in Figure B. Set the incline oft he ramp to be about 10°.
Step 7:Measure the time it takes for the ball to roll down the ramp from each of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.Step 7:Measure the time it takes for the ball to roll down the ramp from each of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.Step 7:Measure the time it takes for the ball to roll down the ramp fromeach of the four release positions. Make at least three timings from each of the four positions and record each average of the three times in Column 2 of Data Table C.
Step 8:Graph your data, plotting distance (vertical axis) vs. time (horizontal axis) on an overhead transparency. Use the same coordinate axes as the other groups in your class so that you can compare results.
Step 9:Look at the data in Column 2 a little more closely. Notice that the difference between t2andt1is approximately the same as t1itself. The difference between t3and t2is also nearly the same as t1. What about the difference between t4and t3? Record these three time intervals in Column 3 of Data Table C.
Step 10:If your values in Column 3 are slightly different from one another, find their average by adding the four values and dividing by 4.Do as Galileo did in his famous experiments with inclined planes and call this average time interval one “natural” unit of time. Note that t1isalready listed as one “natural” unit in Column 4 of Table C. Do you see that t2will equal—more or less—two units in Column 4? Record this, and also t3and t4in “natural” units, rounded off to the nearest integer.Column 4 now contains the rolling times as multiples of the “natural”unit of time
Step 12:Investigate more carefully the distances traveled by the rolling ball in Table D. Fill in the blanks of Columns 2 and 3 to see the pattern
Step 13:You are now about to make a very big discovery—so big, in fact,that Galileo is still famous for making it first! Compare the distances withthe times in the fourth column of Data Table C. For example, t2is two“natural” time units and the distance rolled in time t2is 22, or 4, times asgreat as the distance rolled in time t1
Step 14:Repeat Steps 6–10 with the incline set at an angle 5° steeper.Record your data in Data Table E_
Data at 10 degrees
Data at 15 degrees:
- What is acceleration?
- Acceleration is the rate at which velocity changes over a certain distance that an object travels.
- Does the ball accelerate down the ramp? Cite evidence to defend your answer.
- The ball travels faster down the ramp as the distance of travel is decreased and slower down the ramp as the distance of travel is increased.
- What happens to the acceleration if the angle of the ramp is increased?
- The ball travels faster if the angle of the ramp is increased because the factor of gravitational force along the ramp is greater and travels slower as the angle of the ramp is decreased because the factor of gravitational force along the ramp is lessened.
Data with two tracks:
- What is the relation between the distances traveled and the squares of the first four integers?
- The squares of the first four integers are proportional to the distances.
- Is the distance the ball rolls proportional to the square of the “natural” unit of time?
- The distance is proportional to the square of the “natural” unit of time.
- Is the distance the ball rolls proportional to the square of the “natural” unit of time?
- Yes, the distance the ball rolls is about proportional to the square of the natural unit of time.
- What happens to the acceleration of the ball as the angle of the ramp is increased?
- The acceleration increases with increasing angle.
- What happens to the speed of the ball as it rolls down the ramp? Does it increase, decrease, or remain constant? What evidence can you cite to support your answer?
- As the ball rolls down the ramp, the speed increases. This can be inferred because it is known that the ball takes the same amount of time to roll down each section of the ramp.
Conclusion:
For this lab an iron ball was rolled down a track three times, each one increasing evenly in distance. The first experiment had the track at a 10 degrees inclination, the second at 15 and the for the the third experiment was two tracks made even. the results, as predicted, showed that the larger the inclination the larger the increase in acceleration as it traveled down the track and the longer it traveled the faster it traveled.