Question

2. Choose the data from one of the objects from Table 1. The previous class measured the time t it takes to roll the entire distance d down the ramp multiple times to decrease the random error. DATA:

Object # =3			ramp angle =5
radius = 12.5
mass = 70.8
run times
trial 1	2	3	4	5	6	7	8	9	10
2.21	2.37	2.14	2.23	2.11	2.3	2.13	2.31	2.03	2.11

4. Calculate the acceleration of object’s center of mass using the equation below: a_cm = 2d/t²3. Calculate average, standard deviation, and standard error for the time. What source of systematic error is expected in this measurement?

5. How is the equation you just used in step 5 derived?

Answer 1

Okay, I will find average, standard deviation, and standard error for the time.  

average of given times

T = 2.21 + 2.37 + 2.14 + 2.23 + 2.11 + 2.3 + 2.13 + 2.31 + 2.03 + 2.11 / 10

T = 2.194 seconds

Now,

To find standard deviation, we subtract each reading from the mean, then square it, then add them up and divide by 10 and then take the square root.

so,

sum of squares = 0.10524

divide it by 10, we get = 0.010524

then

standard deviation = 0.10813572

and

standard error = standard deviation /

where n = sample size = 10

so,

standard error = 0.034195

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These systematic errors are usually caused by measuring instruments that are incorrectly calibrated or are used incorrectly.