Question 1

In the free fall experiment using the spark timer apparatus, what is the primary purpose of the thermal paper?

Accepted Answer

To record the position of the falling mass at regular time intervals.

Question 2

Given the kinematic equation $$y(t) = y_i + v_{y,i} t - \frac{1}{2} g t^2$, if Excel provides a curve-fit equation y = A + Bx$$ + $$Cx^2$$, how do you determine the experimental value of $$g$$ from the coefficient $$C$$?

Accepted Answer

$$g = -2C$$

Question 3

If the spark timer operates at 60 Hz, what is the time interval $$\Delta t$$ between each dot on the thermal paper?

Accepted Answer

$$\Delta t = 0.0167 s$$

Question 4

A student fits their position vs. time data and obtains $$y = -4.90x^2$ + 0.20x + 0.01. $$What is their experimental value for the acceleration due to gravity $$g$$?

Accepted Answer

$$g = 9.80 m/s$^2$$

Question 5

When calculating the average velocity between two points with positions $$x_1$$ and $$x_2 at $$times $$t_1$$ and $$t_2$$, which formula should you use?

Accepted Answer

$$v = \frac{x_2$ - x_1$}{t_2$ - t_1$}$$

Question 6

If the velocity vs. time graph for a falling mass is linear and has a best-fit equation $$y = -9.5x + 0.2$$, what is the experimental value for $$g$$?

Accepted Answer

$$g = 9.5 m/s$^2$$

Question 7

Which of the following is a correct method for propagating uncertainty when adding two measured values $$J \pm \delta J$$ and $$K \pm \delta K$$?

Accepted Answer

$$J + K \pm (\delta J + \delta K)$$

Question 8

Suppose you measure the displacement $$\Delta y = -0.0160 m $$with uncertainty $$\delta y = 0.0010 m$$, and the time interval $$\Delta t = 0.0167 s $$with uncertainty $$\delta t = 0.0002 s. $$What is the fractional uncertainty in the average velocity $$v = \frac{\Delta y}{\Delta t}$$?

Accepted Answer

$$\frac{\delta v}{v} = \frac{\delta y}{\Delta y} + \frac{\delta t}{\Delta t}$$

Question 9

In the experiment, why is it important to include error bars on your position vs. time and velocity vs. time graphs?

Accepted Answer

To visually represent the uncertainty in each measurement.

Question 10

If your experimental value for $$g is$$ $$9.6 \pm 0.2 m/s$^2$$ and the accepted value is $$9.80 m/s$^2$$, does your result agree with the accepted value within uncertainty?

Accepted Answer

No, because $$9.80 is $$outside the range $$9.4 to$$ $$9.8 m/s$^2.$$

Question 11

Which of the following is a specific source of error in the spark timer free fall experiment?

Accepted Answer

Parallax error when reading the ruler to measure dot positions.

Question 12

Why is it necessary to start labeling dots from the first clearly distinguishable dot rather than the very first dot on the thermal paper?

Accepted Answer

The mass may not have been moving when the first dot was made.

Question 13

If you want to improve the accuracy of your measurement of $$g in $$this experiment, which of the following would be the most effective upgrade?

Accepted Answer

Use a more precise ruler to measure dot positions.

Question 14

When fitting a velocity vs. time graph, the slope of the best-fit line is $$-g. If $$the best-fit line is $$y = -9.7x + 0.1$$, what is the initial velocity $$v_{y,i}$$?

Accepted Answer

$$v_{y,i} = 0.1 m/s$$

Question 15

If you are propagating uncertainty for the product $$JK$$ where $$J \pm \delta J$$ and $$K \pm \delta K$$, which formula should you use?

Accepted Answer

$$JK \pm JK \left( \frac{\delta J}{J} + \frac{\delta K}{K} \right)$$

Question 16

A student finds that their velocity vs. time graph has several points that do not fit the best-fit line and lie outside the error bars. What is the most appropriate action?

Accepted Answer

Investigate possible sources of error or outliers and consider repeating the measurement.

Question 17

Why is it important to include units and uncertainties with every numerical value in your data tables?

Accepted Answer

To ensure clarity and allow for proper error analysis.

Free Fall and Measurement of Gravitational Acceleration Using Spark Timer

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