Force and Acceleration PDF

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Alicia Wong June 25, 2018 PHY 133 L69 TA: Alfonso Lanuza Force and Acceleration

Introduction/Theory

In physics, earth’s gravitational acceleration constant g is 9.81

m /s 2 , meaning every

second, the speed increases by 9.8 m/s 2 if you neglect air resistance. When there is force, this can have an impact on acceleration. Newton’s second, law states that the acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. In this lab, we will look at the relationship between force and acceleration and find the mass of an object (iOlab device). The equation F=ma will be useful since we can use it to calculate for the mass and we can also find the mass of the object by looking at the slope of the graph. Methods/Procedure Part 1: 1. Connect the iOlab device to a computer. 2. Connect the plate to the force sensor. 3. Placing the device with its wheels up, push the device a few times while recording this data. 4. Place the device on its y direction and calculate for its force and acceleration. 5. Place the device downwards and take off the plate and replace it with a screw. 6. Record data of the device on the table and then pick it up and place it down. 7. Find the mass of the device using the formula: F=ma. 8. Attach the plate to the force probe. 9. Place the device with its wheels facing up and give it 5 consecutive pushes, with more strength each consecutive push. 10. Record the data. 11. Find the slope of the data. 12. Obtain the mass of thee device. Part 2: 1. Screw the screw onto the force probe and use a long spring. 2. Connect the other end of the spring to a book. 3. Place the device vertically and oscillate it. 4. Make a parametric plot of the acceleration and find its slope.

Data/Graphs Figure 1: Force vs. Time

Figure 2: Acceleration vs Time

Figure 3: Gravitational Force of the iOlab Device.

Figure 4: Acceleration vs. Time m s2

X: -0.009

m 2 s

Y: -9.823 Z: 0.236

m s2

Table 1: Acceleration and Force Calculations

Acceleration (

m s2

Force (N) )

4.585

0.397

6.888

0.741

10.957

1.335

12.068

1.726

16.314

2.616

Slope= 0.18826 Intercept= -0.55023

Error = 0.078 kg

Graph 1: Acceleration vs. Force Correlates with Table 1

Analysis/Calculations In figures 1 and 2, the peaks correspond with when we pushed the iOlab device. As we can see the peaks are noticeable. In figure 1, the peaks are all positive whereas in figure 2, the peaks are both positive and negative. From this we can see that when we push the device, when the device is pushed with a force it gains a positive acceleration and then before it comes to a stop, a negative acceleration or deceleration give us a negative peak value. The Acceleration vs time largest peaks are in accordance with Force vs time peaks since they occur at the same time.

After obtaining the average force and and acceleration due to gravity, we can calculate for the mass of the device by using Fg=mg. F=mg, F= -1.979 N, g= -9.823 (-1.979 N)=m (-9.823

m 2 s

m ) s2

m= 0.202 kg

Since there are 5 peaks in the Force and Acceleration vs. Time graph since we pushed the device 5 times, we have 5 values for the peak force and peak acceleration. From this we can calculate for the mass of the device and then take those 5 values and calculate for the average of the 5 values. y=mx+b

⇒ m= y/x

y= force, x= acceleration m1= 0.347/4.585 = 0.0865 kg m2= 0.741/6.888 = 0.1075 kg m3= 1.335/10.957 = 0.1218 kg m4= 1.726/12.068 = 0.143 kg m5= 2.616//16.314 = 0.160 kg avg= 0.6188/5 = 0.124 kg

y2-y1/x2-x1 = -3+4.1/-6+12 = 0.183 kg

The mass we have found from the previous steps, 0.202 kg is much closer to the expected than the average mass we calculated for at 0.124 kg and 0.183 kg. Although those two calculated values are similar to one another, there is a clear difference between those values and 0.202 kg. This could be due to errors that might’ve occurred while completing the experiment and while doing the calculations. Discussion/ Conclusion

After completing this lab, I’ve gained a better understanding of force and acceleration. The value of the mass at 0.202 kg is what we expected as was the y value for our acceleration at 9.823

m . Overall, my data supported my hypothesis. Although the calculated masses were 2 s

slightly off, some sources of error that might’ve contributed to this are human error in calculations as well as while completing the lab. It is possible that I didn’t push the device enough with increasing strength giving us peak values that were not along the expected. The results were along the expected even though there were some uncertainties. We can also see that the slope of the line for our graph is not constant. One way to obtain more better results would be to do the lab several more times to obtain more accurate data. More data will allow for us to discard the uncertainties. As we can see, finding the acceleration and force allowed for us to calculate for the mass. The values do still follow Newton’s Second Law which was expected and this allowed for me to better understand how force and acceleration work together which was what we were ultimately trying to understand....