### Purpose

To identify the relationship between force, mass, and also acceleration using a cart attached come a sheave with varying weights.

You are watching: Slope of force vs acceleration graph

### Hypothesis

If the fixed of the weights attached to the sheave is increased, the pressure exerted on the cart and also the acceleration the the dare will also increase.

### Labeled Diagrams

See attached sheet.

### Data

Weight of Cart and Sensor (N) | 6.624 | |||||

Weight that Cart mechanism (kg) | 0.6759 | |||||

Weight of pulley-block (g) | 60 | 50 | 40 | 30 | 20 | 10 |

Force Exerted on cart (N) | 0.5472 | 0.4921 | 0.4059 | 0.3227 | 0.2321 | 0.1404 |

Average Acceleration of dare (m/s^2) | 0.8252 | 0.736 | 0.7222 | 0.4469 | 0.3395 | 0.2148 |

Weight that Cart and also Sensor and 300 g (N) | 9.718 | |||||

Weight the Cart system (kg) | 0.9916 | |||||

Weight of pulley (g) | 60 | 50 | 40 | 30 | 20 | 10 |

Force Exerted on dare (N) | 0.588 | 0.5049 | 0.418 | 0.3323 | 0.2385 | 0.1442 |

Average Acceleration (m/s^2) | 0.6655 | 0.5182 | 0.4263 | 0.3478 | 0.2633 | 0.1476 |

### Graphs

See attached sheets.

### Questions

**1. Is the graph of pressure vs. Acceleration for the cart a directly line? If so, what is the value of the slope?**

Yes, the graph produces nearly a straight line; the correlation because that a linear fit is 0.9787. The value of the slope is 0.6129 N/(m/s^2).

**2. What space the units of the steep of pressure vs. Acceleration graph? simplify the devices of the steep to an essential units (m, kg, s). What does the slope represent?**

The units of the steep of force vs. Acceleration room N/(m/s^2). This simplifies to kg. The slope to represent the mass of the pulley.

**3. What is the complete mass that the mechanism (both with and also without extra weight) that you measured?**

The total mass the the device without the extra weight was 0.6759 kg and the fixed of the mechanism with the extra load (300 g) was 0.9916 kg, which seems to make sense. 0.9916 kg is almost exactly 300 g much more than 0.6759 kg.

**4. Just how does the slope of her graph to compare (percent difference) through the complete mass of the mechanism that girlfriend measured?**

The slope of the graph there is no any included weights was 0.6129 kg, i m sorry is a 9.78% difference. The slope of the graph with the added weights to be 0.8939 kg, which is a 10.36% difference.

**5. Are the net pressure on an object and the acceleration the the object directly proportional?**

Yes, together the net force is increased, the acceleration is likewise increased.

**6. Compose a basic equation that relates all 3 variables: force, mass, and acceleration.**

F = ma

### Conclusion

**Lab Summarized**

The as whole goal of the lab to be to determine and also show the relationship between force, mass, and also acceleration. The score was completed using a cart and also pulley device with varying weights to measure up force and also acceleration. The forces and accelerations collected were then graphed versus each other the construct a direct fit line, whose slope verified the mass of the mechanism (the cart, sensor, and any added weights). This value could then be contrasted to the massive calculated from the pressure of the free hanging system. The force and acceleration from each trial operation could also be analyzed to show any relationship between the 2 values.

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The data built up seemed to present a direct correlation between force and also acceleration. Thus, the declared hypothesis was evidenced that if the pressure was increased, the acceleration would likewise increase. The compared values because that the masses the the cart equipment were about 10% various in every case. Because that the trial there is no any included weight, the calculated worth of 0.6759 kg is 9.78% various from the extrapolated worth of 0.6129 kg. In regards to the trial with the included weight, the calculated value of 0.9916 kg is 10.36% various than the extrapolated value of 0.8939 kg. This error could have been led to by a variety of factors. Because that instance, the wait resistance native the load on the pulley dropping could have brought about error, and any possible friction from the track can have attributed to this, too. That could additionally be thought that if the sheave did not drop directly downward, i.e. It was swaying in ~ all, this would have additional error. Lastly, if the rope to be not totally taught when the mechanism was placed in motion, that can have resulted in error together well.