Where F is force equaled to mass times acceleration.

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His second law defines a **force** to be equal to the differential change in **momentum** per unit time as described by the calculus of mathematics, which Newton also developed. The momentum is defined to be the mass of an object **m** times its velocity **v**. So the differential equation for force **F** is:

F = d(m * v) / dt

If the mass is a constant and using the definition of acceleration **a** as the change in velocity with time, the second law reduces to the more familiar product of a mass and an acceleration:

F = m * a

Since **acceleration** is a change in velocity with a change in time **t**, we can also write this equation in the third form shown on the slide:

F = m * (v1 - v0) / (t1 - t0)

The important fact is that a force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways. The velocity, force, acceleration, and momentum have both a **magnitude** and a direction associated with them. Scientists and mathematicians call this a vector quantity. The equations shown here are actually vector equations and can be applied in each of the component directions.

The motion of an aircraft resulting from aerodynamic forces and the aircraft weight and thrust can be computed by using the second law of motion.

**Question:**

How does the force effect the acceleration of a car?

We chose this question because we could make a clear relationship between force and acceleration of the car. We also chose it because Jimmy was really interested in doing this project. The relationship is important because we can apply our findings to real life situations like towing.

**Background Information:**

Prediction - the greater the force on the car, the more acceleration the car will have. This because the greater the force pulling the car, the faster the car will be pulled along the track. If there is less force, then the car won't be pulled as fast.

The amount of inertia, or mass, determines how difficult it is to change the way it is moving. The car has a weight of 658 g, so we need a weight on the string to change the resting position the car is in. The car weight was measured in grams, while the force was measured in grams and Newtons. The acceleration was measured in meters per second squared. Newton's First Law: Every object continues in a state of rest or of motion in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon it. The outside force acting on the car is the weight on the end of the string.

**Procedure:**

Materials:

*Paper/Pencil

*Weights (50-500 g)

*String

*Pulley

*Car (658 g)

*Motion Detector (To The 1,000th m/s^2)

*Track

*Weight Holder (50 g)

*Force Detector (To The 1000th N)

Steps:

1.) Gather Necessary Materials

2.) Set Up Experiment As Shown In Diagram A-1

3.) Tie A 50g (.03N) Weight To The Car (W=Independent Variable)

4.) With Someone Holding The Car On The Track, Put The Weight In the Position Shown In Diagram A-2 (Logger Pro Should Be Up And Running At This Point)

5.) On The Count Of Three, Let Go of The Car And Press "Collect" On Logger Pro Exactly At The Same Time

6.) Stop The Car Before The Weight Hits The Ground To Prevent Damage On The Car Or Weight

7.) Have Logger Pro Analyze The Force (In Newtons) And Acceleration (A=Dependent Variable)

8.) Record Results On Paper

9.) Repeat Steps Four Through Eight Two More Times

9.) Untie 50g (.03N) Weight And Replace With 100g (.162N) Weight.

10.) Repeat Steps Four Through Nine

11.) After Recording The Results For the 100g (.162N) Weight, Increase The Weight By 50g Each Trial. (Be Sure To Perform Three Trials For Each Weight)

12.) Repeat Steps Four Through Nine Until You Get Up Through 550g (2.127N)

13.) After Completing Experiment, Put All Necessary Materials Away.

Comments:

The weight of the car is kept constant by keeping it from getting damaged and not adding or subtracting weight from it. We did the procedure the way we did because it was the most time efficient way to do it and easiest to get clear results. There were no changes made during our procedure. Helpful hints are repeating your tests several times to ensure accuracy because sometimes there might be a problem with detecting the motion or force. Don't use a hand to stop the cart from getting damaged. Try to use something else to stop the cart. Trials were rejected if the data did not follow the trend before it.

**Data Table:**

Uncertainty = + or - .075N & + or - .001 for acceleration

Car Weight (g) | Force (N) | Acceleration Trial #1 | Acceleration Trial #2 | Acceleration Trial #3 | Average |

658 | 50g - .03 N | .536 m/s^2 | .537 m/s^2 | .536 m/s^2 | .576 m/s^2 |

658 | 100g - .162 N | .791 m/s^2 | .791 m/s^2 | .791 m/s^2 | .791 m/s^2 |

658 | 150g - .415 N | 1.182 m/s^2 | 1.182 m/s^2 | 1.182 m/s^2 | 1.182 m/s^2 |

658 | 200g - .638 N | 1.496 m/s^2 | 1.495 m/s^2 | 1.495 m/s^2 | 1.495 m/s^2 |

658 | 250g - .856 N | 1.759 m/s^2 | 1.759 m/s^2 | 1.759 m/s^2 | 1.759 m/s^2 |

658 | 300g - 1.161 N | 2.105 m/s^2 | 2.104 m/s^2 | 2.105 m/s^2 | 2.105 m/s^2 |

658 | 350g - 1.389 N | 2.341 m/s^2 | 2.342 m/s^2 | 2.341 m/s^2 | 2.341 m/s^2 |

658 | 400g - 1.537 N | 2.679 m/s^2 | 2.679 m/s^2 | 2.679 m/s^2 | 2.679 m/s^2 |

658 | 450g - 1.631 N | 2.884 m/s^2 | 2.884 m/s^2 | 2.884 m/s^2 | 2.884 m/s^2 |

658 | 500g - 1.986 N | 3.246 m/s^2 | 3.246 m/s^2 | 3.247 m/s^2 | 3.246 m/s^2 |

658 | 550g - 2,217 N | 3.412 m/s^2 | 3.412 m/s^2 | 3.412 m/s^2 | 3.412 m/s^2 |

**Analysis:**

Sample Calculations:

Averages-.537 + .537 +.536=.536666=.537 + or - .001

.791 +.791 +.791=.791 + or - .001

We analyzed our data by using a motion and force detector. Then we set up the logger pro to make force and acceleration graphs. Then we selected portions of the slope of the graphs to find the acceleration and force by analyzing the slope. We rejected data based on that if it did not follow the pattern of the previous test. For instance, if the car had less acceleration and more force then the test before, then we rejected the data because something went wrong to cause our data to be abnormal. To get the accurate results, we did the test again.

**Conclusion:**

We have observed through our experiment that as the mass increased, the force and acceleration of the car increased as well. This is because there is a greater portion of the mass of the weight pulling on the car to make it accelerate more. Not all the force of the falling weight is pulling the car, but a greater portion of it is pulling and increasing the acceleration. If one was to look at our table, they would clearly notice that the average acceleration of the car increased as the force increased. Our results turned out exactly the way we predicted it would. Our findings relate to our research question because it shows that the greater the force of the falling weight, the greater the acceleration of the car.

**Evaluation of Results:**

We thought our results were very reasonable because they are what one would expect and it follows Newton's 2nd Law (F= Mx A or A=F/M)). There isn't much room to disagree with our results because of what Newton's 2nd law states. Each data point on our graph were closely consistent with other data points. We had the force and motion detector which we will assume gave us accurate information. We should therefor expect consistent data because of the tools we used. The acceleration increased every time we increased the weight. The two most important points of uncertainty were force and acceleration because the depend on each other. The uncertainty was + or - .075 for the force. The uncertainty for the acceleration was + or - .001. We had the uncertainty because it was it was extremely difficult to select the same exact section of the data to analyze from our graph. We can however get pretty close because one would expect to trust the motion detector. Overall these uncertainties would not have changed our results greatly enough to alter our conclusion.

**Generalizations:**

The findings are very universal because it would be safe to say that if anyone in the world were to conduct the same experiment, they would get the same results. Newton's 2nd law applies to everything and makes our test very universal. Limitations to our findings where our results would not hold true are in space or in a bad weather condition. If the motion or force detector were not set right, our results could have been wrong. To improve the experiment, people should not use a hand to stop the car. Instead they should use something that stops the car and shows a clear distinction of the car stopped on the graph. Another way to have it more thoroughly tested would be notice our human errors in advance and take advantage of it. By this we mean, we could conduct more trials and two people agree on our results to get second opinions. Other related experiments include how does the mass of the car effect the acceleration or how the acceleration changes with the slope of the ramp.

Walter

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