Investigation 2 (Section 1.5) – Motion Down a Ramp
Conducted: March 1st, 2013
By: Danish Shakil

Purpose
The purpose of this experiment was to determine the kind of motion that a cart undergoes while rolling down a ramp and to find the shape of the velocity-time graph.

Question
What does the velocity-time graph look like for a cart rolling down ramp? How can you determine displacement and acceleration from a velocity-time graph?

Hypothesis/Prediction
The velocity-time graph should be a straight line with positive slope because the velocity of the cart will increase as it moves down the ramp. Also, the displacement-time graph can be determined by calculating the area under the line of the velocity-time graph and the acceleration-time graph can be determined by calculating the slope of the velocity-time graph.

Design
A recording timer and a recording tape were used to measure the time and distance for the cart rolling down a ramp. The independent variable was the time while the displacement, velocity and acceleration of the cart were the various dependent variables. Some controlled variables included the timer, length of the recording tape and the angle and height of the ramp.

Materials
C-clamp
Ramp
Masking tape
Recording tape
Ruler
Graph paper
Loaded cart
Power supply
Recording timer

Procedure
1. A safe area to set up the apparatus was selected.
2. An observation table similar to Table 1 was prepared.
3. The ramp was set up near the edge of a lab counter and the recording timer was clamped to the ramp.
4. A length of recording tape slightly longer than the distance the cart would cover was obtained.
5. The recording tape was threaded through the timer and attached to the cart from the other end with a small piece of masking tape.
6. The cart was kept steady, just beside the timer by holding its upper end.
7. The recording timer was started and the cart was immediately released down the ramp and the recording tape was pulled smoothly through the timer.
8. The recording timer was turned off right away as the cart reached the end of the ramp.
9. The recording tape was checked to make sure that the dots were clear and that no dots were missing because it is necessary to obtain a tape that accurately interprets the cart's motion.
10. The tape was analyzed as the numbers of dots were counted and the distance between every six dots was measured. The observations were recorded in table 1.
11. The average velocity for each interval was calculated and recorded in the observation table.
12. A velocity-time graph was plotted for the cart’s motion by plotting the average velocities at half-time intervals.
13. A line of best fit was drawn from the origin through the points on the velocity-time graph.
14. The average acceleration of the cart was calculated in cm/s² by finding the slope of the velocity-time graph.
15. All equipment was put away and all waste was recycled or disposed of.

Observations

Table 1: Time, Displacement and Average Velocity
Time (s)
Displacement (cm[down])
Average Velocity (cm/s[down])
0.1
Δd1= 4.5
45
0.2
Δd2= 7.5
75
0.3
Δd3 =11
110
0.4
Δd4=13.5
135
0.5
Δd5=17.5
175
0.6
Δd6=20.5
205
0.7
Δd7=23
230
0.8
Δd8=25
250
0.9
Δd9=28.5
285
1
Δd10=30
300

Average velocities at half-time intervals
Time (s)
Average Velocity (cm/s[down])
0.05
22.5
0.15
60
0.25
92.5
0.35
122.5
0.45
155
0.55
190
0.65
217.5
0.75
240
0.85
267.5
0.95
292.5

Average acceleration = slope of the velocity time-graph rise/run or y2 - y1/x2 – x1 217.5-155/0.65-0.45 312.5 cm/s2

Displacement of the cart by finding the area of the triangle beneath the velocity-time graph
Area = ½ bh ½(0.95s) (292.5cm/s) 138.93750 cm 139.0 cm

Displacement of the cart by measuring the length of the recording tape = 181 cm

Analysis

1. To calculate average velocity for an interval, this