Acceleration of Gravity on an Inclined Plane

Procedure: 1) To find the acceleration of gravity by studying the motion of a cart on an incline. 2) To gain further experience using the computer for data collection and analysis.


Ramp 1 1.65 degree

This is the first ramp (not drawn to scale). The length of the long leg is 228.2 cm. To find the height (short leg), we took the height from the ramp on either side and then subtracted them. From there we went to find the angle of elevation. We took arc tan(6.2/228.2) and this came out to theta = 1.56 degrees.

Ramp 2 3.6 degree

This is the second ramp (not drawn to scale). This one had larger angle of elevation. We did the same thing to both sides of the ramp to find the height and it came out to be 14.3 cm. Then we took arc tan(14.3/228.2). Theta = 3.6 degrees.

Graph 1

This is the position verses time graph. It is a parabola because the car went up the ramp and then back down. The car went up the ramp where the velocity was decreasing, and then the car went back down the ramp where the velocity increased.

Graph 2

This is the velocity verses time graph. For this line, there are two different accelerations. This is because there are two different events happening, the car increasing in velocity and the car decreasing in velocity. It is linear because it shows the slope of the parabola from the position verses time graph.

Table 1.56 degree

Trial for 1.56 degree incline	a1 (motion up) m/s2	a2 (motion down) m/s2	Gexp m/s2	% difference
1	0.33	0.18	9.4	4.10%
2	0.36	0.18	9.9	1.00%
3	0.34	0.19	9.7	1.00%

This table shows the acceleration for the incline of 1.56 degrees. Both the acceleration for the car moving up and down are on there. By using the equation Gexp=arc sin((a1+a2)/2) we get experimental gravity. Also, we got the percent difference between them and gravity (9.8). For example, Gexp=arc sin((.33+.18)/2)=9.4 for trial one.

Table 3.6 degree

Trial for 3.6 degree incline	a1 (motion up) m/s2	a2 (motion down) m/s2	Gexp m/s2	% difference
1	0.69	0.5	9.5	3.30%
2	0.69	0.54	9.8	0.00%
3	0.72	0.52	9.9	1.00%

Conclusion: This table shows the acceleration for the incline of 3.6 degrees. Both the acceleration for the car moving up and down are on there. By using the equation Gexp=arc sin((a1+a2)/2) we get experimental gravity. Also, we got the percent difference between them and gravity (9.8). For trial two, we get a zero percent difference. A source of error would be that we didn't calculate the angle, height, or length of the ramp correctly. We could have done more trials to get even better results.