Name:W # :Section: Time: Date: Lab partner:
Name:
W # :
Section: Time: Date:
Lab partner:
Lab # 4
Experiment 1
Newton’s second law – Atwood’s Machine
with a Massless Pulley
Purpose:
Introduction:
Procedure:
Data
Mass of system msys = (m + M) = 200 g
| m (g) | M (g) | Fext = (M – m)*g (dyne) | aexp (cm/s2 ) Trial 1 Trial 2 Trial 3 Average | |||
| 50 | 150 | 458.3 | 446.6 | 451.6 | ||
| 60 | 140 | 15.1 | 19.7 | 18.6 | ||
| 70 | 130 | 50.7 | 53.0 | 86.4 | ||
| 80 | 120 | 34.9 | 29.8 | 86.4 | ||
| 90 | 110 | 44.4 | 79.2 | 65.9 | ||
| a (m/s2) | F (N) |
Plot a vs. F (F on y-axis and a on x-axis), evaluate the slope of the curve (best line fit), then compare the slope to the mass of the system (m + M) through your error analysis
F = msysa
Analysis:
Conclusions
Experiment 2
Newton’s second law
Acceleration along a frictionless horizontal surface
Purpose:
Introduction:
Procedure:
Data
M = Mcart = 510 g
| m (g) | aexp (cm/s2 ) Trial 1 Trial 2 Trial 3 Average | 1 / m ( 1 / kg) | 1 / aexp (s2 / m) | |||
| 55 | 88.6 | 88.2 | 88.9 | |||
| 65 | 104.5 | 103.8 | 104.6 | |||
| 75 | 120.8 | 119.1 | 116.9 | |||
| 85 | 130.6 | 134.9 | 138.5 | |||
| 95 | 145.6 | 145.5 | 146.9 | |||
Analysis:
Starting with Eq. 1:
Eq. 1
With little algebra (left as an exercise), we can re-write this equation as:
Eq. 2
If we denote
and 
;
then Eq. 2 can be expressed as a straight line given by:
Plot (1/aexp) vs. (1/m), where 1/aexp along y and 1/m along x.
Find the best line fit to your data points.
Evaluate the slope and the intersection of the best line fit.
The slope of your curve should be compared to its theoretical value M/g and the intersection should be compared to its theoretical value of 1/g
Questions:
Verify Eq. 2 starting from Eq. 1
Conclusions
Experiment 3
Frictionless motion on an
Inclined Plane
Purpose:
Introduction:
In the figure below:
The driving force of the system (msys = m+M) is
F
= mg – Mg sinθ
(the assumption here is that mg > Mg sinθ thus system is accelerating clockwise)
Using Newton’s 2nd law we can write the acceleration of the system as:
We can re-write this as:
Eq. 1
If we denote x = sinθ and y = a, then this relation of Eq. 2 can be represented by a straight line of the form:
y = (slope). x + (intersection)
where slope = 
and intersection = 
Procedure:
Data
m = 150 g ; M = Mcart = 510 g
| θ ( o ) | Trial # | a (cm/s2 s) | sinθ | a (m/s2) |
| 3 | 1 2 | 61.7 82.8 | ||
| 6
| 1 2 | 38.4 67.1 | ||
| 9 | 1 2 | 61.2 56.8 | ||
| 12 | 1 2 | 77.3 61.1 | ||
| 15 | 1 2 | 54.7 55.3 |
Find experimentally the critical angle θC where a = 0 (system about to move when mg = Mg sinθ)
θC =
Plot sinθ on the horizontal axis and a on the vertical axis, fit your data points to a straight line. Compare the slope and intersection of your straight line to their theoretical values.
Compare the experimental value of θC to its theoretical prediction of Eq. 1.
Analysis
Conclusions
