The Efficiency of a Ramp
By: Tony Akiki
Partner: Nikolas Dobson
Teacher: Mr. Devine
Class: SPH3U1
School: Saint Johns Collage
Date Concluded: June 10, 2016
Due Date: June 17, 2016

Question:
How does the angle of inclination on a ramp affect the efficiency of the ramp?

Hypothesis:
I believe that the steeper the ramp is the more work you have to put in to push it up making to less efficient. If the angle of the ramp is very low, then you will have to put less force into it. This makes sense because if the angle of the ramp is close to 90 degrees the closer it is to free fall. This means that there is nothing under the cart to support it and the only thing preventing the cart from falling is the force of you holding it up in the air, which means that it will take the most force. To conclude the closer, the angle of the ramp is to 90 degrees the more force you will have to put into it to push it up which means that you are getting more work done and thus making it more efficient.

Experimental Design:
A chair and a piece of wood served as the ramp. A cart flipped on its back with weights attached to it and a newton scale served as the object that had to be pulled up the ramp. The data collected in this experiment will show us how efficient the ramp is at different angles.

Table #1: Variables Controlled | Dependent | Independent | * Time of day * Person pulling * Length of ramp * The speed the object is getting pulled up by | * How efficient the ramp is | * The angle of the ramp |

Equipment and Materials: * Chairs * Wood * Cart | * Weights * Newton scale | | ChairsWood | Newton ScaleCartWeights | Figure #1: Setup of experiment Figure #2: Setup of experiment Photo Credits: Tony Akiki Photo Credits: Tony Akiki

Procedure:
Please refer to page 143 in Nelsons Physics 11 and the hand out giving by Mr. Devine called “The efficiency of a ramp” given on June 10, 2016. No changes were made.

Observations:
Qualitative observations and possible errors: * Sometimes the weights would fall out * Sometimes the wood would slide out of place * Sometimes the cart would fall off the wood * The wood was a little bit wobbly Quantitative: * The length of the ramp was 0.945m * The mass of the cart with the weights attached was 0.3301kg

Table #2: Data collected Trails | #1 | #2 | #3 | #4 | Height(m) | 0.06 | 0.29 | 0.41 | 0.50 | Amount of force(N) | 0.10 | 2.2 | 3.0 | 4.5 |
Patterns or trends from table #2: * It appears that the higher the ramp is the more newton’s it takes to pull the cart up
Analysis:
Calculation #1: Finding the angle of inclination for trial #1 Data from table #2 sinθ=OppHyp sinθ=.410.945 sin-1θ=0.433862 Figure #3: Diagram of calculation #1Photo Credits: Google images | θ=27.71° Therefore, the angle of inclination for trials #1 is 27.71° The data for the rest of the trials can be found in Table #3

Calculation #2: Finding the energy input for trail #1 Data from analysis section Ein=Length of ramp×Force Figure #4: Diagram of calculation #2Photo Credits: Google images | Ein=0.945×3 Ein=2.835 Therefore, the total amount of energy that went into the system was 2.835J The data for the rest of the trials can be found in table #3

Calculation #3: Finding the energy output for trial #1 Data from analysis section Eout=Mass×Gravity×Height Eout=0.3301×9.81×0.41 Eout=1.328 Therefore, the energy output is 1.328J The data for the rest of the trials can be found in table #3

Calculation #4: Finding Efficiency for trial #1 Data from calculations #2 and #3 Efficiency=EoutEin×100 Efficiency=1.3282.835×100 Efficiency=0.458×100 Efficiency=46.80% Therefore, trial #1 is 46.80% efficient The data for the rest of the trials can be found in table #3

Table #3: Data for calculations #1, #2, #3, #4 Trials | #1 | #2 | #3 | #4 | Angle of Inclination(Degrees) | 3.54 | 17.87 | 27.71 | 31.94 | Energy Input(J) | 0.0945 | 2.079 | 2.835 | 4.253 | Energy output(J) | 0.1943 | 0.0939 | 1.328 | 1.619 | Efficiency (%) | 1.83 | 29.35 | 46.80 | 38.07 |

Patterns or trends from table #4: * The bigger the difference is between energy input and energy output the higher the efficiency is

Graph #1: Efficiency Vs Angle of Inclination

Patterns or trends from graph #1: * Efficiency increases when the angle of inclination increases * There are no outliers * Direct Relationship * Graph is consistent

Conclusion:
In conclusion, the angle of inclination plays a big part in how efficient a ramp is. As you can see in graph #1 the lower the angle of inclination is the less efficient it is while the higher the angle is the more efficient. This is true because when the angle of the ramp is lower you are covering less distance. When the angle of inclination is high the object will be able to cover more distance in less time therefore making it more efficient.

Sources of Experimental Error/Evaluation
The data is somewhat reliable because when there was a mistake we would redo the trial to make sure the everything was accurate. In the graph there was no outliers which shows that there were no big mistakes in the lab, but when the person pulling the cart can not be completely consistent at all times and the person pulling may pull the cart faster at certain points of time.

Table #4: Error analysis Obser or Proc | Possible Error | Possible Affect | Possible Improvement | Proc | The person pulling may go to fast | It could make the data unreliable | Take your time and try to pull the cart with the minimal amount of force at a constant speed | Obser | The wood would slide out from the chair | Could destroy equipment | Put an object at the end of the ramp to keep it from sliding | Obser | The wood was a little bit wobbly | Could make data unreliable | Get a straight piece of wood to keep it from wobbling |
It appears that the hypothesis is correct because like it hypothesis said the more work you can get done the more efficient the ramp is. This is true because more work means a higher energy output and that directly effects the efficiency equation because the energy output is on top of the fraction and the higher the number on top is the higher the number is.

Discussion/Synthesis: 1. If you change the mass of the object on the ramp you would increase the efficiency. That means that it would directly effect energy out. Energy out=m×g×H and if you increase the mass you would increase the total amount of energy out and energy out is over top of energy in in the efficiency equation which would give you a bigger number.

2. One advantage of using a ramp is that you would have to use less force then lifting the object straight up to get to your destination. The disadvantage would be you would have to cover a greater distance then lifting it straight up.

3. In the data it seems that the lower the angle of the ramp is the less efficient the ramp is and the only thing making it less efficient would be friction. This also means that the higher the angle of the ramp is, the less friction there is because it is getting closer to the free fall stage which has no friction.

4. The most efficient way to put an object on the back of a truck would be to lift it straight up because it would cover the least amount of distance and thus making the energy input as little as possible. In the efficiency equation energy input is on the bottom and if you reduce it as little as possible you would increase the efficiency percentage.