An infrared light emitting diode (source) and a photodiode (sensor) are placed on each side of the U-shaped frame. The Photostat is considered unblocked as long as the sensor is picking up the infrared light. When something passes through the Photostat, the sensor is blocked from the source and a signal is sent to the computer. In this labs case, a picket fence is placed on top of the cart and is positioned to pass through the Photostat while the cart is in motion. A picket fence is a rectangular shaped plastic composed of an alternating order of transparent and black slits.
The Photostat is blocked while the black slits re in between the sensor and source but it is unblocked when the transparent component is in between the source and sensor. The Photostat is able to measure the relative times that the Photostat is blacked and unblocked. The slats on the picket fence are positioned at a set distance delta X apart. Each slat will block the Photostat momentarily as the picket fence passes through. The computer can then measure the relative times that the Photostat is blocked and unblocked. Figure 1. The picket Fence In the First experiment, acceleration of gravity will be determined using the one hotplate method. The acceleration of a cart will be measured traveling down an inclined plane. The computer will measure the timing of the slats traveling through the Photostat and produce an acceleration. The acceleration down an inclined plane is related to gravity by equation 1. 1. Sin is the angle of the incline plane. A = g sin (Ө) 1. 1 In the second experiment, a two Photostat system is used to determine the value of g by allowing the near frictionless cart to move down an inclined ramp.
The only difference is two Photostats will be used to find the change in velocity. Instead of a picket fence there will be a metal flag with a measured width. The flag will pass through each Photostat which will measure the lengths of time that each Photostat is blocked, the same way that it did in the single Photostat method but with a different series of calculations since, a picket fence is not being used. The time that the first Photostat is blocked will be called delta TTL . The second length of time will be the time in between when the first Photostat is blocked until when the second Photostat is unblocked (delta TTL 2).
The third time measured will be the time that the second Photostat is blocked (delta). The average velocity that it takes for the flag to pass through each Photostat will be calculated by the change in the known distance of the flag divided by the time it takes to pass through the Photostat in question. The acceleration of the cart can then be calculated by equation 1. 2. A = VI-VI / Delegate Equation 1. 2 The next experiment will be the measurement of acceleration due to a horizontal force, measured by a single Photostat.
The force will come from a weight hanging vertically from a string that runs through a pulley that is connected horizontally to the cart, measure by a single Photostat. Figure 1. 3:Horizontal Force cause by Hanging Weight The acceleration can be expressed by considering three free body diagrams. First the sum of the Y forces on the hanging weight. F(y) = MGM D TTL = ma Equation 1. 3 Notice that TTL is equal to MGM ma. Next, evaluate the sum of the horizontal forces acting on the cart. C) F(x) = mass(cart) * a Equation 1. 4 Additionally, the tension TTL and TO contribute to the torque on the pulley. – torque = l = ART 1 -ART 2 = R(MGM-ma-m(cart)a) Equation 1. 41 is the moment of inertia and can be calculated by considering the mass of the pulley and the radius. Equation 1. 5 The angular acceleration denoted as alpha () is simply = a/R, which makes equation 1. 4 m(cart)a) ( (1 = R(MGM-ma- Equation 1. 6 The acceleration of the cart moving in a horizontal direction as a result of a vertical force can now be solved by rearranging equation 1. 6 to solve for a. The theories of horizontal motion can also be applied to how fast a person is walking or fast a person is accelerating.
The measurement may be examined by measuring the position and velocity versus time as a person starts, walks at a constant velocity, and then stops. Figure 1. : Velocity versus Time Graph FIGURE 1. 5: Position versus Time Graph The velocity of an object with a particular acceleration can be calculated by equation 1. 7. V = Vow at Equation 1. 7 This is such that Vow is the initial velocity, a is the acceleration and t is the time. If looking closely, equation 1. 7 is the equation of a straight line where Vow is the y-into and a is the slope. This relationship can be seen in figures 1. . When starting from rest with a positive acceleration, the slope of the graph is positive. Ata constant speed, the slope of the graph will be O and at a negative acceleration the slope will be negative. The constant velocity is simply found by finding the point on the graph where the slope is equal to zero. The positive and negative accelerations are found wherever the slope is positive and negative in figure 1. 5. Also, figure 1. 4, the position versus time plot, can be used to determine the constant velocity and acceleration. X = Ox + Vote + h Equation 1. Ox is the initial starting position. Data Recognize that this is a quadratic equation with both t and text. If started from rest, the value of Ox and Vow are zero and equation 1. 8 can be simplified to the Arabic equation 1. 9. X = h Data Equation 1. 9 The equation is a simple parabola. The first segment of figure 1. 3 shows the parabola which is positioned upward showing a positive acceleration for when the walking is started. Once the normal walking speed is reach, there is no acceleration and the velocity stays at a constant, as shown in both figures 1. And 1. 5. The position can be calculated by using x = Ox + Vote Equation 1. 10 This is a straight line with Vow as the slope and Ox as the y-intercept. As the person slows down, the position can be determined by using equation 1. 8. In opposition too positive parabola, the parabola will be position downward in accordance with a negative acceleration. The walking experiment will measure the position and velocity as the person starts from rest, walks for a short distance, and then comes to a stop. The distance will be roughly 10 feet.
The constant velocity will be determined from the position versus time graph which will be compared to the constant velocity of the velocity versus time graph. The positive and negative accelerations will be calculated by fitting both ends of the velocity versus time graph (as illustrated in Geiger 1. 2) with a straight line. A motion detector will be used to measure position and velocity as the person walks. The motion detector emits ultrasonic pulses with frequencies outside the range of human hearing. The pulses will reflect off of the moving person and be detected by a microphone which is connected to the computer.
The computer measures the time between pulse emission and echo detection. The distance to the object from the detector is x=Vat/2, with Va being the velocity of sound in air. The equation is divided by two to account for the signal traveling to and from the moving object. The pulses will be a fixed rate so the velocity is just the change in distance divided by the time between two pulses. Experimental Setup The One dimensional motion lab requires various pieces of equipment used correctly in order to achieve accurate results. A brief description of each piece of equipment in provided.
A Photostat uses infrared light to detect the time of blockage. A motion detector uses pulse frequency to measure the distance of an object. A microphone is attached to the motion detector apparatus which detects the reflected frequencies. A computer with logger pro capabilities is seed to analyze the data sent from the Photostats and the motion detector. The logger pro software also contains modules to plot the incoming data and produce graphs. Standing lab equipment such as poles, air tracks, weights, and picket fences are also used.
Experiment 1: Determination of using the One Photostat Method The experiment was uses an air track, one Photostat, an aluminum cylinder used to create a slight angle, a single foot screw for the air track stability, a picket fence for delta measurements, a tape measure, a dial caliper, a calculator, and logger pro software for analysis of the incoming hotplate data. The experiment was set up much like Figure 1. 1. The air track was positioned on a flat table. A small block was then placed under one end of the track. Measurements were then taken on the width of the block with the dial caliper, the length of the track, and the delta value.
A single Photostat was mounted by rods and clamps so that the picket fence would travel undisturbed through the infrared signal. The picket fence was placed on the cart and the air track was turned on so that friction would be at a minimum. The cart was placed a few centimeters above the Photostat and released down the plane. The Photostat recorded to data and sent it to the computer loaded with the logger pro software. The logger pro software created a velocity vs… Time graph and enabled the calculations of acceleration (slope) and initial velocity (intercept).
The experiment was run five times, averages and standard deviations were calculated, and calculations were made. Experiment 2: Determination of G using the Two Photostat Method The experiment used the same components as the one Photostat method, except now there are two Photostats. In addition, the picket fence was replaced by a metal flag that passed through the Photostats hill in motion down the inclined plane. The width of the metal flag was recorded. In the same fashion as before, the cart was placed a few centimeters above the first Photostat and was released down the incline plane.
The information from the Photostat was sent to the logger pro software which measured the three changes in time that were mentioned in the theory section. From the changes in distance and time, the velocity was calculated. Logger pro will also calculate the acceleration with an algorithm similar to equation 1 . 2. The acceleration were recorded, averages and standard deviation were taken, and ululations were made. Experiment 3: Acceleration Due to a Horizontal Force, the One Photostat Method This experiment was set up as illustrated in figure 1. 3.
The experiment included an air track, a cart with a flag or picket fence, a pulley, a rope, a weight, a scale used for measuring the mass of the weight, measuring tape, one Photostat, and the logger pro software. The weight was measured and attached to a string which was then fed through the pulley and attached to the cart. The air track was turned on and the cart was released through the Photostat. The cart and Photostat were positioned so that once leased, the weight would pull the cart through the Photostat as a result of the horizontal force. The information was then sent to the logger pro software.
The logger pro software then created a velocity versus time graph which produced a line equation. The acceleration (slope) and initial velocity (intercept) were recorded. The experiment was run five times, averages and standard deviations were taken, and calculations were made. Experiment 4: Walking Motion This experiment required the use of measuring tape, a motion detector equipped with sensing microphone, a person, and the logger pro software. The starting stance was selected a few feet in front of the motion sensor. A person walked about ten feet and came to stop.