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Rectilinear Motion
Purpose: Students will analyze the relationship between the angle of an incline and the normal force and with the parallel forces of an object on the incline. The student will also calculate ฮผ and determine g while using acceleration at different inclines. Equipment: 1.2m Pascar Dynamic track with PasCar, Computer interface (Science Workshop), Motion sensor, (2) 500 mg weights, caliper, and level. Experimental setup
d = at + v t + d
2 0 0 , for a car on the incline plane.
d
t
Figure 1 Fit to: y = ๏ก x^2 + ๏ข x + x 0 ๏ก =
a
ma FT FD FF
๏ฒ ๏ฒ^ ๏ฒ^ ๏ฒ
= = โ from Figure 2.
FD = mg sin ๏ฑ FF = ๏ญ FN F (^) N = mg cos ๏ฑ๏ป mg ( for small ๏ฑ)
Figure 2 ma = mg sin ๏ฑ โ๏ญ mg [sin ๏ฑ =
h
L
]
a = g (sin ๏ฑ โ๏ญ) ๐ 1 = ๐(๐ ๐๐๐ 1 โ ๐ 1 )
= g โ
h
L
1 ๏ญ 1 ๏ญ 1 1 1
h
L
a
g
๐ 2 ๐ 1 = (โ^2 ๐ฟ โ ๐ 2 ) ( โ 1 ๐ฟ โ^ ๐^1 )^ = ๐
21 , ๐ 3 ๐ 1 = (โ^3 ๐ฟ โ ๐ 3 ) ( โ 1 ๐ฟ โ^ ๐^1 )^ = ๐
31 , ๐ 3 ๐ 2 = (โ^3 ๐ฟ โ ๐ 3 ) ( โ 2 ๐ฟ โ^ ๐^2 )^ = ๐
32 assuming ๐ 2 ๏ป ๐ 1 ๏ป ๐, let ฮผ = ๐ 21 then, ๐ 21 = (๐
21 โ 1 ๐ฟ โ^ โ 2 ๐ฟ ) (๐
21 โ 1 ) , ๐ 31 = (๐
31 โ 1 ๐ฟ โ^ โ 3 ๐ฟ ) (๐
31 โ 1 ) , ๐ 32 = (๐
32 โ 2 ๐ฟ โ^ โ 3 ๐ฟ ) (๐
32 โ 1 )
get ๐ฬ
from
๐ 21 +๐ 31 +๐ 32 3 ๐ = ๐ 1 โ 1 ๐ฟ โ ๐ 1 Procedure:
- Adjust the incline of the ramp.
- Observe the position vs. time graph. Find the acceleration:
- Start by making sure the track is level, then raise the height of one end of the track at least 1.5 cm but no more than 1. 8 cm. Take the calipers and measure the height at 10 cm (on the track) from the table and also at 110 cm (on the track) from the table. Take the difference and find h ( 1 .5 cm โค hmin โค 1. 8 cm, and the difference between each of the hโs should be at least 1 cm, ie. If h 1 is 1. 5 cm then h 2 must be at least 2. 5 cm but less than 2. 8 cm and similar for h 3 which should be 1 cm above h 2 ), place the PAScar about 10 cm from the Motion Sensor. Simultaneously press the Start Button in DataStudio and release
