Physics Lab Practices: Reaction Time, Density, Energy, Pendulums, Inertia, and Oscillation
Practice 1: Random Errors, Determination of Reaction Time
We know that the fall of a body is accelerated motion, with a relationship between the distance traveled and time. So, it is possible to determine the time it takes to react to stimuli, trying to catch a falling body by measuring the area it runs through before catching it.
- Medium-haul space: The sum of all measures / number of measures +/- error.
- Absolute error: Given by the measurement equipment.
- Relative error: |Δe| / |e|.
- Random error: (1 / (n (n-1)) Σ(x-media x)2)1/2.
- Reaction time: t = (2e / g)1/2
- Δt: [½ (Δe / g)] * 2t.
Practice 2: Density of a Material
We measure its mass and its volume (directly using a sample, or indirectly through measurements of length, radius, etc.). Determine Vhollow cylinder with its error and density (calculated in advance the radius (outdoor and indoor), the Vinternal (π D2int h / 4), Vpool, V = Vext cylinder – Vint, with its errors). Determine the density of the plastic body (measured Vbody = Vfinal – Vinitial, ΔVbody, ρ = m / V, Δρ).
Use of a micrometer to measure the thickness of road practice: We calculate the thickness of sheets from its mistake.
Practice 3: Instantaneous Velocity and Conservation of Mechanical Energy
Instantaneous velocity is the derivative of the position vector with respect to time, or even an average velocity for an increment of time that tends to zero. We measure the average velocity values of a slider that moves along an inclined plane for distinct time intervals and represent them in a graph (line y = ax + b inclined downward whose break with the y-axis is the value of v0). We can determine the average value of v when the increment tends to 0. To calculate the Ec final of the plane and Ep initial of the plane, we see that they coincide. However, to act only conservative force, gravity, the mechanical energy is kept at that: ΔEp = ΔEc. The slope does not influence the final velocity, although they are almost equal, due to a measurement error. In fact, the final velocity = (2ghm / m)1/2, which indicates it only depends on the height and gravity.
Practice 4: Simple Pendulum, Determination of Gravity
A direct measurement of the value of the acceleration of gravity is not easy due to the high value it presents. We employ indirect methods to measure gravity. The most used is to calculate the value of g from the measurement of the period of a simple pendulum since it is related to g: T = 2π√(l / g), where the maximum separation angle of the pendulum position is less than 23°. But the mass influences the period of the pendulum since the length of the pendulum does not vary with different masses (experimental data). It is possible to observe a slight variation due to errors in measuring time with a chronometer. In theory, the period is independent of the amplitude of a simple pendulum motion, but for large amplitude angles, there is no longer a simple harmonic motion, so many times. Representing T in front of the length of the wire (straight up), we can determine the value of k (for l = 1, T = k), and the exponent n (n = Δy / Δx, measured in the chart), which relate T as a function of l (T = k * ln).
Practice 5: Moments of Inertia
The restoring torque (M) of a spring is determined by measuring the force required to close it a certain angle, as M = kmedium * θ (M: moment of force, θ: angle in radians). When it is hard to put a torsion beam and it starts to oscillate, the period depends on the moment of inertia of the solid and the restoring torque of the spring: T = 2π√(l / k). Thus, we can measure moments of inertia experimentally. The moment of inertia of a requested disk depends on its mass and distribution in relation to the shaft. The moment in theory you can measure: I = Σ r2Δm. Calculate the moments of inertia of the hollow and solid cylinder. They are different because the moment of inertia depends on how the masses are distributed. This will be greater the larger the radius of separation from the center of mass with respect to the differential of mass. As in the hollow cylinder, the masses are distributed around the perimeter, and in the solid cylinder, they are distributed uniformly, the moment of inertia of the hollow cylinder is larger.
Practice 6: Damped Oscillations, Torsion Pendulum
In a simple harmonic motion, the oscillator gradually loses energy, and the amplitude of the motion decreases. It is said to be damped. Measuring the amplitude of an oscillatory motion several times can be studied if it is damped and its damping constant can be calculated: A = A0 * e-bt, ω = 2π / T. Graphically, ω = At: descending. If we make the curve A0 / e = A -> bt = 1 -> see the value of t graphically when A = A / e. To calculate the angular natural frequency, we have to turn off the damper.