Theory

The goal of the Newton’s second law experiment is to understand and demonstrate the validity of Newton’s 2nd law of motion. The goal is achieved by tactically using a cart moving on a track, a hanging mass providing the motion through gravitation pull and a string connecting the two masses through a single pulley. Once the hanging mass is released, the cart starts moving over the track smoothly whose motion movement are taken by the rotary motion sensor and plotted in the Logger Pro. The acceleration obtained from the velocity plot which is then compared with the calculated value. The force time plot is also used to obtain the measured force which is compared with the calculated force to further verify the Newton’s 2nd Law. The Newton’s 2nd law is described by F=Ma. Mass remains constant throughout this experiment with force and acceleration being used as the variables which rearranges the equation to a=M/F.

The tension exerted on the string by the hanging mass is given by;

T=mg-ma

The mass rolling over the track exerts a tension of;

T=Ma

Equating the two set of equation gives;

Ma+ma=mg

a=m/(M+m) g

With the force acting on moving cart being;

F=Ma=M m/(M+m) g

Error Analysis

The calculated acceleration was 0.4589m/s2 whereas the gradient of the velocity-curve (measured value) was obtained as 0.3368m/s2. The ∆% error was therefore calculated as 26.61%. The force, which was a variable in this experiment was calculated using equation (ii) as 0.28023N and measured (average value of force vs. time) 0.2705N which gave a ∆% error of 3.473%. The irregular ∆% errors suggests the presence of systematic errors possibly due to friction between the wheels of the cart and the cart and in the movement of the pulley. Such errors may be highly reduced through lubrication

Expansion Questions

The tension of the string changes with small magnitudes once the system is released to move. The tension is at its maximum when the cart is held in place, preventing the system from moving. Once the system is allowed to move freely, the tension does not always remain at the maximum level which triggers the conclusion that the external forces might be involved in controlling the motion of the system. Such external forces include friction and inertia.

The tension of the string is not always equal to mg since there are friction and inertia whose interaction causes instability in the tension between the cart and the mass. To prove this, we compare the tensions as the string approaches each mass. The mass m=0.03kg and M=0.6106kg;

T=mg=0.03×9.8=0.294N

T=(M+m)a=(0.6106+0.03)×0.3368=0.2158N

The tension of the string is therefore not always equal to mg as some tension difference is always seen as the system begins to move.

When mass m is zero, the equation becomes;

a=0/(M+0) g

Ma=g

This equation does not make sense physically. In real life cases, making mass m zero would mean removing the overhanging mass causing the acceleration. In that case, the cart would not move and the acceleration is also expected to be zero, hence the acceleration equation does not make sense.

When mass M is zero, the equation becomes;

a=m/(0+m) g

ma=mg=F

a=g

This equation makes sense since, it represents a case where the hanging mass falls freely. In a free fall, the acceleration a is always equal to g even though the values may slightly differ due to air friction. In real life case, this would be imagined as cutting the string of the hanging mass and measuring the acceleration. The acceleration will be approximately 9.8m/s2.