## LAB #1 (LAB #2 #3 below)

**Equipment:**

- Kinematics Cart
- 2 500g bar masses
- Kinematics Track
- 50g hanger
- Several 100g masses
- String
- Pulley
- iBook Computer
- USB Cable
- Motion sensor

**Purpose: **

How will the acceleration of an object’s mass (*m) *change when the net force acting on it changes?

**Prediction: **

We predict that the acceleration of an object mass will increase constantly when the net force acting on the object itself changes. This is because, if we keep the mass of the object constant and we increase the net force we will get a change in acceleration as stated and proved by Newton’s Second Law (Fnet = m * a – in where m = mass, a = acceleration, and Fnet =Fa)

**Observations: **

Hanging Mass (Kg) | Acceleration (m/s/s) | Force of Gravity (N) |

.5 | .21 | 5 |

1.0 | .42 | 10 |

1.5 | .63 | 15 |

2.0 | .85 | 20 |

2.5 | 1.06 | 25 |

3.0 | 1.27 | 30 |

**Calculations:**

Force of gravity = mass x gravity (10 N)

- Fg1 = .50 kg x 10 N = 5 N
- Fg2 = 1.0 kg x 10 N = 10 N
- Fg3 = 1.5 kg x 10 N = 15 N
- Fg4 = 2.0 kg x 10 N = 20 N
- Fg5 = 2.5 kg x 10 N = 25 N
- Fg6 = 3.0 kg x 10 N = 30 N

**Proportional Statement:** a ~ Fg

**General Equation:** a = k * Fg

**N****ote:** k is equal to slope of **Acceleration vs Net Force**

k = rise/run = 1.27-0.21/30-5 = 1.06/25 = .0424

Specific Equation: a = .0424 * Fg

**Proof:**

- Fg1 = 5: a = .0424 * 5 = .212
- Fg2 = 10: a = .0424 * 10 = .424
- Fg3 = 15: a = .0424 * 15 = .636
- Fg4 = 20: a = .0424 * 20 = .848
- Fg5 = 25: a = .0424 * 25 = 1.06
- Fg6 = 30: a = .0424 * 25 = 1.272

**Analysis:**

From the data that was taken during this investigation, we can see that this graph shows accelerations that change constantly at the same rate. Throughout this experiment the hanging mass (force) is increased which reduces the amount of air resistance it faces, thus making the acceleration faster, but still constant with the other accelerations.

**Conclusion / Source of Errors: **

We learned that our prediction at the start of this experiment was proven to be correct. We hypothesized that as the mass on the hanger increases, the air resistance, will decrease, thus the acceleration of the object towards the center of the earth would be increased.

The relationship between acceleration and mass is proportional. It shows that the acceleration is directly proportional to the mass. This experiment proved our point, but many possible errors were overlooked.

Throughout the experiment, we have not considered the force of friction. Even though this experiment has not included friction, it was present in between the cart’s wheels and along the surface of the track. Even though it is treated as frictionless, friction is always present everywhere, even if it is regarded as not present.

Another force that we excluded was air resistance. During the experiment the window in the classroom was open and the wind was blowing, changing the air resistance in the room. Even though the change in air resistance might be minor, it is still another source of error that can lead to miscalculation.

The last source of error we overlooked is that the car was not always placed in the exact same place on the track. Since it was not placed on the same spot every time, the friction and air resistance was not always exactly the same but still close enough to prove Newton’s Second Law.

Throughout the experiment, we proved our hypothesis right, and we scouted, and avoided all the avoidable sources of error to the best of our abilities.

**LAB #2**

**Equipment: **

- Kinematics cart
- 2 500g bar masses
- Kinematics Track
- 50g hanger
- Several 100g masses
- String
- Pulley
*iBook*Computer- USB Cable
- Motion sensor

**Purpose: **

To show how the acceleration of an object changes when the mass changes and the net force is kept constant

**Prediction: **

We predict that by changing the mass of the object in question we will produce a change in acceleration. When plotting a mass-acceleration graph, we will notice that the graph is curved downwards, thus a negative slope, hence loss of acceleration. When the mass of the object in question is increased, while keeping the net force the same, will result in the object losing acceleration but it will not be proportional until the mass is inverted.

**Observations and Calculations: **

Total Mass(kg) | Acceleration (m/s/s) |

1.55 | 0.3266 |

1.75 | 0.2882 |

1.95 | 0.2578 |

2.15 | 0.2334 |

2.35 | 0.2140 |

2.55 | 0.1960 |

**Analysis:**

The relationship we can see through this experiment showed that as the mass of the object became greater, while the net force stayed the same, the acceleration became less.

When the mass and acceleration are graphed (on the graph titled **Mass and Acceleration**) it doesn’t form a straight line, thus not proving Newton’s Second Law. To straighten this line the mass must be inverted (on graph titled **Invert Mass and Acceleration**) so the variation statement would be acceleration is proportioned to 1/m.

To straighten this curve we must invert X (mass). A table is presented below with our new values.

Total Mass(kg) | Acceleration (m/s/s) | Mass – 1/m |

1.55 | 0.3266 | 0.65 |

1.75 | 0.2882 | 0.57 |

1.95 | 0.2578 | 0.51 |

2.15 | 0.2334 | 0.47 |

2.35 | 0.2140 | 0.43 |

2.55 | 0.1960 | 0.39 |

**Calculations:**

- Variation Statement: a ~ 1/m
- General Equation: a = k * 1/m
- Note: K is equal to slope of
**Inverted Mass vs Acceleration** - k = rise/run = 0.3266-0.19/0.65-.39 = 0.1306/.026 = 0.5
- Specific Equation: a = 0.5 * 1/m

**Applied to all inverted masses:**

- mass 1.55 Kg: a=0.5* 1/1.55 = 0.325 (Answer: 0.3266, possible error, rounding)
- mass 1.75 Kg: a=0.5* 1/1.75 = 0.285 (Answer: 0.2882)
- mass 1.95 Kg: a=0.5* 1/1.95 = 0.255 (Answer: 0.2578)
- mass 2.15 Kg: a=0.5* 1/2.15 = 0.235 (Answer: 0. 2334)
- mass 2.35 Kg: a=0.5* 1/2.35 = 0.215 (Answer: 0. 214)
- mass 2.55 Kg: a=0.5* 1/2.55 = 0.195 (Answer: 0.196)
- Note: Although errors due to rounding, the equation is still correct due to the relative closeness of all answers.

**Conclusion:**

In this lab, we learned the relationship that occurs when the mass of an object is increased while the net force is left constant. Every time more mass is added onto the object and it is pulled with the net force (which remains constant) the acceleration decreases because of the increased mass.

When graphed it is not a straight linear line and this means that the acceleration is not proportional. To make these two values proportional the mass had to be inverted to create 1/m thus proving our hypothesis correct. When this is done the two values are proportional and when graphed create a straight line.

Throughout this experiment the sources of error are minimal. One of the forces that were overlooked was friction. Although friction was disregarded for this experiment, it was still present in between the car’s wheels and the track. The air resistance is also a force that was overlooked.

When the window in the classroom was opened, the amount of air resistance was constantly changing because of the sudden bursts of wind. The gusts of wind that occurred weren’t very strong, thus not affecting our calculations a great deal. Another source of error is the masses of the weights are not always accurate.

One of the 100g weights was measured after the experiment and it showed 98g, but these measurements did not affect the calculations. None of these sources of error affected our calculations and the outcome of the lab was still achieved

- Note: Although errors due to rounding, the equation is still correct due to the relative closeness of all answers.

**LAB #3**

**Introduction**

Sir Isaac Newton was a celebrated physicist who lived and conducted his scientific research in the late 17th century. Newton made vast leaps in physical sciences, created three laws of motion, discovered gravity, developed more powerful ways of solving calculus problems, explored white light, and discovered the color spectrum of light.

Newton grew up in a humble manor farm in rural Lincolnshire County in England and was the first scientist to be knighted. Today, his childhood home is a famous historical location that has served as a site of pilgrimage to many great scientists since Newton’s time.

This experiment will be exploring, in depth, Newton’s second law. Newton’s second law says: Force equals mass times acceleration (F= m x a). Simply put, his law describes the relationship between the mass of an object, the acceleration of an object, and the force needed to move it.

For example, if a person wanted to move a 10 kg object at an acceleration of 10 m/s/s, they would need to use a force equal to 100 Newtons. This equation can also be re-arranged in terms of mass and acceleration. In terms of mass, the equation becomes: m= F/a. In terms of acceleration, the equation becomes a= F/m. It is important to note the units that this equation uses: the unit for Force in the equation is Newton’s, the unit for Mass is Kilograms, and the unit of acceleration is m/s/s (meters per second squared).

**Hypotheses**

- If force and acceleration are directly proportional, then when we increase force, we would expect acceleration to increase.
- If Mass and acceleration are indirectly proportional, then when we increase mass, we would expect acceleration to decrease.

**Materials**

- Vernier data collection sensor (in cart mode)
- LabQuest Stream
- Data cable
- USB cable
- Charging cable for LabQuest (opt)
- Chromebook
- 1.2 meter long Pascal low-friction track
- Low friction Pascal Dynamics cart
- Low friction pulley
- 1.3 meter long string
- Bucket of weights
- Digital balance

**Procedure**

## Part A: Equipment Setup

- Gather materials
- Place low friction track on counter and place low friction cart on track
- Position motion sensor at the stopper end of the track. It should be arranged so the cart will be moving away from the stopper and motion sensor during the experiment.
- Connect the LabQuest and motion sensor with the data cable and connect the LabQuest and chromebook with the USB cable. Plug the charging cable into the LabQuest and a plug socket if necessary.
- Attach pulley to the far end of the track and run a string across it, fastening it to the cart.

## Part B1: Conducting Part One of the Experiment

- Open Vernier Graphical Analysis on chromebook and select the three graph option to display acceleration data.
- Ensure that motion sensor is in cart mode
- Weigh the cart and record in data table.
- Replace cart onto the track and line up at the starting end near the motion sensor.
- Attach relevant weight(s) (50g) to the far end of the string and place the weighted string on the counter so that it is not applying force to the cart.
- Start the motion detector on the chromebook through the Graphical Analysis software
- Drop the weight off the end of the counter and allow it to drag the cart along the track. Stop the cart before it falls off the track
- Press the zoom button on the Graphical Analysis software to see the data.
- Highlight the flattest part on the graph, then select the statistics function and identify the mean of the highlighted data points. Add this number to the table.
- Repeat steps 4-9 two more times to complete a total of three trials and record data.
- Repeat steps 4-10 twice with new weights (50, 100, 200g) on the end of the string

## Part B2: Conducting Part Two of the Experiment

- Open Vernier Graphical Analysis on chromebook and select the three graph option to display acceleration data.
- Ensure that the motion sensor is in cart mode
- Weigh the cart with weights on the digital balance. Record in data table.
- Place cart onto the track and line up at the starting end near the motion sensor.
- Add 100 g weight to the string. The string weight will not change in this part of the experiment. Place weighted string on the counter so that it is not applying force to the cart.
- Add 200 gram weight to cart.
- Start the motion detector on the chromebook through the Graphical Analysis software
- Drop the weight off the end of the counter with the string hooked into the pulley, and allow it to drag the cart along the track. Stop the cart before it falls off the track
- Press the zoom button on the Graphical Analysis software to see the data in depth.
- Highlight the flattest part on the graph, then select the statistics function and identify the mean of the highlighted data points. Add this number to the table.
- Repeat steps 1-10 two more times with different weights (200,250,300) and record data.

## Part C: Calculations

- Convert hanging mass to Force (Newtons) using the formula: F= m x a
- Convert mass in grams to mass in kilograms by dividing by 10. T0 use above formula, mass must be in kilograms
- Acceleration of gravity equals 10.

- Calculate True Acceleration using the formula: a= F/ m. Use the force on the string as found in step one and the mass of the cart to calculate the true acceleration.
- The answer will be in m/s^2

- Calculate Percent Error using the formula: % Error = (Experimental- True)/ True

Percent Error shows the experimenter how precise they were compared to the known values. In this equation, the values for “true” are the calculated values for the acceleration. The closer the experimental values of acceleration are, the more precise the experiment was.

**Conclusion:**

As previously stated, if force and acceleration are directly proportional, then when we increase force, we would expect acceleration to increase. The hypothesis that force and acceleration are proportional was supported by the data. The data shows corresponding increases and decreases in acceleration when force is increased or decreased.

Our second hypothesis was: if mass and acceleration are indirectly proportional, then when we increase mass, we would expect acceleration to decrease. The hypothesis that force and acceleration are proportional was supported by the data. The data showed a pattern of indirect proportionality between the mass of the Dynamics cart and its acceleration.

The data in Table 1 and Figure 1 show a trend of direct proportionality between force and acceleration of the Dynamics cart. When the force on the cart was .49 Newtons, the average acceleration was .89 m/s/s. Then, when the force on the cart was .98 Newtons, the average acceleration was 1.63 m/s/s. This is a marked increase in acceleration and force which starts a pattern that is continued for the next set of trials in which the force was 1.96 Newtons.

When the force exerted on the cart was 1.96 Newtons, the average acceleration was 2.87 m/s/s. This supports the hypothesis because it is clearly seen in the data that when the force increases, so does the acceleration. A trend of increasing acceleration when force is increased is seen consistently throughout all the trials. To sum it up, when the force was increased by .49 Newtons, the acceleration increased by .74 m/s/s. Likewise, the data shown in Table 2 and Figure 2 display the trend of indirect proportionality between mass and acceleration of the Dynamics cart. When the mass of the cart was .69 Kilograms, the average acceleration was 1.22 m/s/s.

Then, when the mass of the cart was.99 Kilograms, the average acceleration was .92 m/s/s. This is a very obvious decrease in acceleration when the mass of the cart increased. To be exact, when the mass of the cart increased by .3 Kg, the acceleration of the cart decreased by .3 m/s/s. Finally, in the third set of trials, when the mass of the cart was 1.49 Kg, the average acceleration was .63 m/s/s.

The pattern of decreased acceleration with increased mass continued in these trials. For these trials, when the mass increased by .5 kilograms, the acceleration decreased by .29 m/s/s. This clearly supports the hypothesis because a consistent pattern formed in the data showed that when the mass of the cart increased, its acceleration decreases.

The first part of the experiment tested Newton’s second law which states that. This law indicated that force and acceleration are directly proportional. The acceleration of the carts with more force on them increased because force causes motion; therefore, an increase in force equals an increase in motion, or, in our case, acceleration.

The second part of the experiment tested Newton’s second law which states that. This law indicates that force and mass are indirectly proportional. The acceleration of the carts with higher masses decreased because higher masses require more force to move them.

This experiment, for the most part, had a very low percent error. The percent errors for the first part of the experiment ranged from .92% to 4.8%. The percent errors in the second part of the experiment ran slightly higher, ranging from 4.8% to 14.8%. It is possible, however, to decrease the percent error even more.

A) The way that this could be done would be to use a lubricant like WD-40 to make sure the wheels of the cart move smoothly. One could also apply lubricant to the pulley to make sure it isn’t causing any additional tension on the string. Lubricating the moving parts of the equipment would increase precision by making the transfer of energy more direct and fluid.

B)Further investigation into the topic of this experiment be completed by testing a more realistic scenario. This experiment utilized specialized low-friction equipment that, while very accurate for calculating force and acceleration, does not simulate the real world very effectively. If the goal of a student was to observe the effects of Newton’s second law in a realistic setting, this experiment would not achieve that goal.

In daily life, friction is almost always a consideration of force and acceleration, and this experiment does not reflect that. To test how force and acceleration interact in the real world, I would recommend using equipment that is not specially made to be low friction. One example of a new experiment set up would be to use a wagon attached to a string line on concrete or tarmac instead of a low friction cart on a track. This is more realistic because friction would be taken into account and collected data would more closely represent real life.

**References:**

“Discover Isaac Newton at Woolsthorpe Manor.” *National Trust*, National Trust, 19 May 2016, www.nationaltrust.org.uk/woolsthorpe-manor/features/discover-isaac-newton-at-woolsthorpe-manor.

“Isaac Newton.” *Biography.com*, A&E Networks Television, 28 Aug. 2019, www.biography.com/scientist/isaac-newton.

*NASA*, NASA, www.grc.nasa.gov/www/k-12/airplane/newton.html.

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@maria , u could use equation vf2=vi2+2a delta D . You just subsitute the values and find for a

how did you figure out the acceleration?