# Merrily We Roll Along

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Merrily We Roll Along

Purpose: To determine how the acceleration of a car rolling down a ramp varies with the angle of the ramp and with the mass of the car.

Required Equipment/ Supplies: ramp, photogate system, car & cardboard, ruler, masses

Background Info: It can be very challenging to measure the acceleration of objects in free fall. In a famous experiment, Galileo extrapolated the acceleration due to gravity by measuring the acceleration of balls rolling down a series of ramps that were inclined at different angles. When you roll an object down a ramp, the component of the gravitational force that acts along the direction of the inclined plane is less than the full force of gravity that acts straight down – so, the change of speed happens more slowly and is easier to measure. The steeper the incline, the larger the acceleration.

We will replicate Galileo’s experiment to see how acceleration changes when the angle of incline increases and to see if we can extrapolate the value of acceleration due to gravity. We will place a car with a long cardboard paper on it, on the ramp just in front of the photogate. We will release the car from rest (vi = 0) and it will pass under the photogate, blocking the light source for a short time period. The photogate will tell us the time it takes for the cardboard (of known length, x) to pass through the photogate. From this, we can calculate acceleration using our kinematic equations.

We will replicate this experiment 5 times at six different angles to determine how acceleration changes with angle of incline. We will also replicate the experiment 5 times with 3 different masses to determine how mass influences acceleration down a ramp.

Pre-Lab Questions

1. What are our independent and dependent variables?
1. What variables should be controlled?
1. How will we calculate acceleration for each trial? What are our known variables? What variable will we get from the labquest? What equation do we use?
1. If all we have is a ruler and our knowledge of trig, how can we find the angle of the ramp?
1. What is the difference between instrument uncertainty and measurement uncertainty, and how do you find each?

Procedure:

1) Prop up your ramp at a low angle. Measure the base of the ramp and the height of the ramp, calculate your angle, and record your data.

2) Put a cardboard standing up along the length of the car. This is what will trigger the photogate. The photogate will measure the time that the cardboard is under the photogate; thus, the length of the cardboard is your distance.

3) Plug the photogate into the labquest. Turn on the lab quest. Select “lab application”, “Photogate timing” and pulse mode. Leave the distance as set. Make sure the gate is unblocked. If its not, then either some object is blocking the laser or a switch on the photogate is in the wrong position. Hit play to collect data.

4) Hold the photogate close to the bottom of the ramp. The exact position doesn’t matter. Hold the cart so that the cardboard is just before the photogate … this will make your initial velocity be very close to zero.

5) Carefully release the car so that it moves straight down the ramp, under the photogate. Record the time shown on the lab quest.

What data do you need to collect?

You need to measure the time it takes for the car to travel a certain distance on the ramp when it is inclined at 6 different angles. From this data, you will calculate the average acceleration at each angle. You must conduct at least 5 replicate trials at each angle.

You also need to pick one angle and measure the time it takes for cars of 3 different masses to travel a certain distance down the ramp. From this data, you will calculate the average acceleration of cars of each mass. You must conduct at least 5 replicate trials at each mass.

HINT: Don’t try plan your exact angles. You will waste too much time struggling to prop the ramp up exactly right. Instead, just start with a very low angle, and increase it slightly each time.

Lab Report

You will write the lab report individually. The lab report must be typed, but the graph should be done on graph paper, by hand.

If the report is not typed or if the graph is not done on graph paper, the report will NOT be graded and it WILL be counted as late.

The basic components of the lab report are listed below.

1. Pre-lab questions (you can turn in the worksheet)
2. Data tables and calculations
3. Graph of average acceleration vs sin include measurement uncertainties as error bars and hand-drawn best fit line)
4. Graph of average acceleration vs mass include measurement uncertainties as error bars and hand-drawn best fit line)
5. Discussion (should be written in the form of one or more paragraphs, and should including the following information)
6. Did the car accelerate down the ramp? What did you observe? Make sure that your answer shows me you know the meaning of acceleration!
7. How does the acceleration depend upon the angle of the ramp? Support your answer by referencing the data and use your physics knowledge to comment on why acceleration depends on the angle of the ramp.
8. Use your data to extrapolate the value of acceleration for a 90o ramp (i.e. extend your best fit line to sin 90 and determine what the line suggests the acceleration of the car will be). What is the theoretical value of acceleration for a 90o ramp (i.e. free fall!)? How close are you? What factors may account for differences between the theoretical value and your extrapolated value?
9. How does the acceleration depend upon the mass of the car? Support your answer by referencing the data and use your physics knowledge to comment on why acceleration does or does not vary with mass.
10. Discuss the uncertainty in your data. Is it large? Is it larger for some trials than others? Is it small enough that you can still be confident in your conclusions, or is it so large that its hard to see trends? Can you think of reasons for your uncertainties and ways you might minimize them in the future? DO NOT mention ‘human error’ – that’s the lazy way out!
11. How might you improve or expand upon this experiment in the future? These ideas should be specific and realistic.

Pre-lab questions – Pre lab questions are neatly and accurately answered / 10
Data Tables –
- Instrument uncertainties and controlled variables should be included in headings where indicated.
- The data should be recorded with consistent precision
- Calculations should be done correctly, and all work should be shown.
- Uncertainties should only have one sig fig, and averages should be rounded to the same place value as the uncertainty. / 20
Graphs – Each should be neatly drawn on graph paper, and should include
• a legend that includes a descriptive title, an explanation of your error bars, and the number of replicates
• axis labels with units
• error bars showing measurement uncertainty
• a best fit curve or line
Graphs must be appropriately scaled so that the data can be clearly visualized and accurately plotted.
There should be two graphs, one of acceleration vs sin  and oneof acceleration vs mass. / 40
Discussion – Your discussion should be written in paragraph form and should address all the questions on the other side of this paper. / 30

Merrily we roll along lab reportName:______Class______