**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 the 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 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.

**PART 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 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 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 titles **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 effecting 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 effect the calculations. None of these sources of error effected our calculations and the outcome of the lab was still achieved

how did you figure out the acceleration?

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