Down the track In this part of the lab, we'll examine the motion of a cart when it accelerates down an inclined plane.

Discussion

The following discussion questions are related to the graphs you generated for the cart moving down the track.

1. Based on the shape of your velocity vs. time graph, does the cart accelerate down the track (i.e. is the acceleration nonzero)? Is the acceleration constant? How can you tell? Can you identify which part of the graph is you holding the cart and which part is after the cart was released?

2. Describe the shape of the position vs. time graph. Is the slope increasing or decreasing? Does this agree with the motion you observed?

3. Go to the velocity vs. time graph. Use the select button to highlight a range of data that indicates the cart is accelerating. Use the linear fit button to get a line of best fit for this data (this is similar to a linear regression that you may have learned in statistics). Once you have your line of best fit, use that to find the acceleration of the cart. HINT: what is the relationship between velocity and acceleration?

4. In general, for an object moving on a frictionless inclined plane, the acceleration is given by ? = ? sin ? where ? = 9.8 m s ? 2 and ? is the angle of inclination of the plane. Using whatever method you wish, calculate the angle of the inclined track. Use this value of ? to calculate the theoretical value of the acceleration using the equation above. Compare the two values of acceleration (theoretical and experimental) and explain what causes the difference.

5. In the velocity vs. time graph, what physics quantity is obtained from the area under the curve? (4 pts) 4

6. On the velocity vs. time graph, pick two points (call them ?1 and ?2).

?1 = _______

?2 = ________

On your graph, highlight the region between ?1 and ?2. Use the area button to determine the area under the curve bounded by ?1 and ?2 (remember to include units!).

Area under ?(?) between ?1 and ?2 = __________

Now return to your position vs. time graph and find the position at ?1 and ?2

?(?1 ) = _______

?(?2 ) = _______

What is the relationship between the area under the ?(?) curve between ?1 and ?2 and the position of the cart at ?1 and ?2? HINT: Be careful of units.

_cap.cap"-PASCO Capstone Edit Workbook Display Journal Help EG Page #1 x Page #2 Page #3 Page #4 dware Data Summary tup 140 Sensor Data Son minary 120 Motion Bet libration Position (m) 2Run =1 100 elculator Velocity (m/s) Run # 1 Run #1 sition (cm 80 Curve Fit Acceleration (m Editor Run #1 60 Clock 40 Time (s) Run #1 20 1.500 s, 58.58 cm 0.0 0.5 1.0 1.5 2.C 2.5 3.0 3.5 4.0 Time (s) (t) - down the track 00:04.15 Motion Sensor v 20.00 Hz Recording Delete Last Run Conditions Record Continuous Mode Ready 5:01 PM 6/22/2008 C DELL