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Experiment

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Experiment 6
Newton’s Second and Third Laws

PHY 2091- 01
Experiment Performed : 03/2/15
Report Submitted : 03/20/15

Lab Partner:
Nicholas Bautista
Instructor:

Introduction
The experiment determines newton’s second and third laws using real life experiments such as the mass pulley system using the Atwood’s machine and using springs (2) in series and parallel to determine their spring constants and extensions when a mass is hanged from them. Newron’s second law states that the force on an object is directly proportional to the rate of change of momentum, which later gives the formula F =ma , m= mass and a is acceleration. Newton;s third law suggests that every action occurring on an object has an equal and opposite reaction when they occur in pairs, are acting in opposite directions and has same magnitude. In part one, we measure the acceleration of the mass pulley system using the photo gate.
Data
M1 = 151.25 g M2 =171.25 g
Mean acceleration = 0.5992 m/s^2
Standard deviation 0.05463

Data Analysis
Part 1 (Atwood’s Machine) –
Formula and calculation of theoretical acceleration (ath) –
A =(m1-m2)/(m1+m2) * g , ath= (0.17125-0.15125)/( 0.17125+0.15125)* 9.79 = 0.6083 m/s^2
% error = 0.05463/0.5592 *100 =9.76 %
Formula and calculation of percent difference between ae and ath – % difference = (difference / A_th) *100 = (0.55992-0.6083) /0.6083 *100 =8.01%

Part 2 (Springs in Series) –
Hooke’s law equation – F = -Kx
Calculation of spring constants, k1 and k2 using Hooke’s law equation – k1 = mg/ x = (2.75)/0.052 =52.9 k2 = mg/ x = (7.73)/ 0.058 = 90.9
Calculation of experimental keff for series combinations of springs –
K eff = Fs / del(xs )
K = F/x =10.31 /0.052 =198.32 N/m
Derivation of equation of theoretical keff –
F = kx , F =mg
X = extension of spring 1 + extension I spring 2
K = m g /X = 1/47.4 + 1/141.75
K eff = 35.53 Part 3 (Springs in Parallel) – 1) Calculation of experimental keff for parallel combination of springs –
Keff = F /x = 9.81 / 0.06 = 163.5 2) Derivation of theoretical keff for parallel combination of springs –
Keff = K1 + K2
Keef (parallal) = F / X = mg / X ( where X is extension for both series and parallel springs) 3) Calculation of theoretical keff for parallel combination of springs –
= 9.81 / 0.06 = 163.5
% difference = (198.32-189.13 )/198.31 *100 =4.6 %
Discussion – Physical quantity | Answer | Unit | Part 1 | | | Experimental acceleration, ae | 0.5952 m/s^2 | | Standard deviation in experimental acceleration, σae | 005463 | | % error in ae | 9.76 % | | Theoretical acceleration, ath | 0.6083 m/s^2 | | % difference between ath and ae | 8.01 % | | Part 2 (Springs in series) | | | Spring constant for spring k1 | 52.88 | | Spring constant for spring k2 | 133.3 | | Experimental keff 24.525 | | | Theoretical keff 32.7 | | | % difference 15.25 % | | | Part 3 (Springs in parallel) | | | Experimental keff 198.32 | N/m | | Theoretical keff 198.3 N/m | | | % difference 4.6% | | |

Discussion
The experiment shows that the mass pulley system moves in the direction the net force is acting and that force is equal to the product of its mass and acceleration. AS one side of the pulley moves down, the other side with the small mass moves up by Newton’s third law. The acceleration calculated has 9.76 % difference from theoretical and some errors possible are discussed below.
Error Analysis
Random error in measurement – error while reading mass from spring balance, parallax error
Systematic error in measurement – Friction and air resistance are not taken in account when commpared to theoretical acceleration.
Systematic intrinsic error – Air movement I room may derive the masses to move apart from only gravity.
Part 2 & 3) –
The springs connected in series and parallel gives different characteristics and they all follow the hooks law of spring which is the proportional relationship of extension of springs with mass( weight) added to it. The spring lengths are measured using meter rule and the masses are measured by spring balance.
Error Analysis –
Random error in measurement – Parallax error while measuring lengths using meter rule, occurs if eye not perpendicular to meter rule scale.
Random intrinsic error – The springs in parallel bents when connected together, thus their lengths may be inaccurate.
Systematic error in measurement – Meter stick may not be perpendicular to the ground level where experiment is conducted.
Systematic intrinsic error – The springs keeps on oscillating and are very hard to get them still or stationery, which might cause readings to alter

Conclusion
The experiment has % differences and errors above 5% in all the parts. So, the errors that occurred in the experiment comes into play to describe why the results varied by this much.

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