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# Velocity and Smart Timer

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Abstract – Kinematics of linear motion is defined as the studies of motion of objects without considering the effects that produce the motion. This experiment will show how to determine the linear motion with constant (uniform) velocity particularly the dynamic cart and linear motion with constant (uniform) acceleration, (e.g. free fall of motion). At the end of the experiment we found out that the velocity is a speed that involves direction of an object as well as the time. While for the acceleration, it is directly proportional to the distance or height but inversely proportional to the time.

By close observations, recording of data and right computations we were able to come up with accurate results. Hence, the objectives of this experiment were successfully achieved.

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I. INTRODUCTION – Kinematics is a branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it. Kinematics uses the following basic concepts: distance, displacement, speed, velocity and acceleration.

It describes the position and motion of an object as a function of time, but does not include the causes or factors that affect the motion. The two methods by which the motion of an object can be described are those using mathematical equations and graphical analysis.

We can say that motion is exhibited by a change in position. For us to clearly define motion, we must know where the body is located within the given area of reference. An area of reference is a physical entity such as the earth’s surface, the deck of a ship or a moving vehicle, to which the position and motion of an object is relative. Our laboratory experiment is conducted for us to understand more the concepts of Kinematics. We also focused on the relationships of the distance, speed, height and acceleration of moving objects with respect to an adjustable plane.

Although motion often occurs in more than one dimension, it can be simplified by considering one dimension at a time. Motion in one dimension is any motion that occurs along a straight line and is represented by a particle. Velocity is defined by displacement divided by the time it took for the object to cover the distance. The unit commonly used for velocity is meters per second (m/s). On the other hand, acceleration, which is the rate of change of speed, is defined by the change in velocity over a period of time. The unit commonly used for acceleration is meters per square seconds (m/s2).

Slope in the position-time plot

Slope in the velocity time plot

II. MATERIALS
Dynamics Cart, Dynamics Track with Angle Indicator and End Stop – It will be used to investigate one dimensional accelerated motion. The cart will be launched over the floor using the built-in spring plunger. The cart will “decelerate” over the floor under the combined action of rolling friction and floor slope. You will be able to establish whether or not the acceleration of the cart is constant. This will be done by initially assuming a constant acceleration and then by examining the results to see if they are consistent with this assumption.

Clamp and stand – An item of laboratory equipment which consists of a metal pole with a solid, firm base, used to hold, or clamp, laboratory glassware and other equipment in place, so that they do not fall down or come apart.

Photogate – The photogate is a timing device which is useful for measuring events which happen faster than you can time by hand. It is also useful in determining the speed of many objects.

Smart timer and picket fence – provides the most versatile, cost-effective,
portable way for making time, speed, acceleration, and count measurements.

III. PROCEDURE
Part A: Determination of the Average Velocity of a Dynamics Cart

We placed the track in the table. The track is levelled perpendicular to the ground and see if it moves in any way. Adjust the track if the cart moves until it became stationary. We then attached the picket fence to the cart. The first photo gate was set mounting at 25 cm mark and the second at 65 cm mark to the track. We adjust the photo gates height so the picket fence attached to the cart will not touch the photo gate. We securely placed the gates to the track perpendicular to minimize errors.

The phone plug of both photo gates are connected to the smart timer, photo gate 1 to channel 1 and photo gate 2 to channel 2. We then set the mode of the smart timer to measure TIME, TWO GATES. And press the third button on the smart timer to start/restart. The cart is placed at 0 cm mark on the track. The cart was launched be pressing the trigger, we take the reading on the smart timer and record this as the time interval for the first trial. The displacement is figured by subtracting the distance of the first photo gate to the second photo gate. The cart is launch 5 times more, with each launch adjusting the position of the photo gate 2 by 10 cm. Then we compute for the cart’s average speed. After the data gathering, we plot a graph with displacement against time.

Part B: Determination of Acceleration Due to Gravity Using Cart’s Acceleration.

We set up the track with the 0 cm end elevated using a stand, with the end stop at the lower end and record it as final position, Xf. The height, H of the track is adjusted to 10 cm as its initial height. We placed the photo gate 1 at 80 cm and set the mode of the timer to measure ACCEL, ONE GATE. And press the third button on the smart timer to start/restart. We compute for the track’s inclination, Ɵ using the total length of the track and its height, H. The cart is placed with the picket fence mounted on it at the higher end of the track and we record its initial position as X0. The cart is released at rest, we take the reading from the smart timer and record it as acceleration, a. We perform it 5 time for the 5 trials needed in the experiment, each trial increasing height of the track by 5 cm. The cart’s displacement is computed by Xf- X0. We compare the experimental value of g, to its accepted value (g = 980 cm/s2) and solve for the percent error.

Part C: Determination of Acceleration Due to Gravity Using Picket Fence and Smart Timer

We set the photo gate horizontally. We set the smart timer to measure ACCEL, ONE GATE. And press the third button on it to start/restart. We dropped the picket fence vertically to the photo gate. Make sure that that the picket fence will pass through the photo beam perpendicularly. Take the reading on the smart timer and record this as acceleration, a. Perform it 5 times and take note of the readings. We compute for the average acceleration, and compare it to g (g = 980 cm/s2) and solve for the percent error.

IV. RESULTS AND DISCUSSION

The first part of the experiment did not require a hard set up because our table is leveled and stable but there is discrepancy on the position of the photogates on the track. We set up the track on a flat table with the end positioned at the 118 cm mark. Two photogates were positioned at the 25 and 65, in cm unit. These photogates are the apparatus used to determine the time that the cart takes to pass through them. The cart has a picket fence that serves as the indicator for the photogates to start and end the measurement of the time the cart takes to pass the photogates. We made the experiment for five times. In every trial, we adjusted the position of the second photogate by 10 cm. Having the mass of the object and the force that was exerted were constant, the average speed on each trial is expected to be same or close to each other. The results were as follows.

Table 1: Determination of the Average Velocity of a Dynamics Cart

Analyzing the results for the five trials, we had seen external factors that may affect the results. It may be the impact time of our release of our finger that prolonged the cart released and slowed down its acceleration.

Trial
Position of Photogate
Cart’s Displacement
Time(t)
Average speed
1
65 cm
40 cm
0.6210 s
64.41 cm/s
2
75 cm
50 cm
0.7697 s
64.96 cm/s
3
85 cm
60 cm
0.9349 s
64.18 cm/s
4
95 cm
70 cm
1.0854 s
64.49 cm/s
5
105 cm
80 cm
1.2319 s
64.94 cm/s

By graphing the results, the y intercept is the distance travelled by the cart. It is equal to the initial position of photogate minus the final position of photogate. This graph says that as the distance travelled by the cart increases, the time elapsed by the cart also increases. The distance travelled is directly proportional to the time elapsed by the cart. Thus, the graph produced a slope from every two points on the curve which are the same. This slope manifests the constant acceleration of the cart. See Figure 6.0

Fig. 6.0

In the second part of the experiment, we had a hard time in setting up the elevation on one end of the track but it produced results close to the accepted constant value of acceleration of gravitational pull. Also, the smart timer did not function well that it produced different readings but still it produced a close results to the accepted constant value of acceleration of gravitational pull. We use the formula g = (a/sin ϴ) for solving the component of the gravity that makes the object slide down. Every trial should have the same results since the acceleration due to gravity is constant and is equal to 980 cm/s2 using the formula for the acceleration due to gravity. After getting the gravity in every trial, we computed for its average and we arrived with a value of 1004.27 cm/s2 and a small percent error of 2.48%. In this part, the experiment requires the plane to be inclined to different height and only one photogate is required. This photogate directly displays the acceleration of the cart. The results are as follows, Table 2: Determination of Acceleration due to Gravity Using Cart’s Acceleration Getting the average acceleration due to gravity for the experiment, we arrived at 979.7 cm/s2. The curve’s slope is inclined at an angle ϴ. It is equal to height of the track over the track’s total length.

This graph only says that as the sinϴ or curve’s slope increases, the acceleration produced by the cart also increases. The sinϴ is directly proportional to the cart’s acceleration Trial
Height of track
Acceleration
sinΘ
g
Time
1
5 cm
42.3
0.0417
1014.39
1.6843 s
2
7 cm
52.9
0.0583
907.38
1.5061 s
3
9 cm
75.6
0.0750
1008
1.2599 s
4
11
cm
100.1
0.0917
1091.60
1.0949 s
5
13
cm
108.3
0.1083
1000
1.0526 s

Graphing the data (In figure 7.0), this slope represents the constant acceleration due to gravity. This implies that acceleration during free fall is approximately 980 cm/s2.

Lastly, it required a simpler set up. The photogate is placed horizontally. The picket fence is dropped vertically and is allowed to pass through the photogate. The results were follows, Table 3: Determination of Acceleration due to Gravity Using Picket Fence and Smart Timer After getting the acceleration in every trial, we solved for its average and we arrived with a value of 981.41 and with 0.12% error. Trial

1
2
3
4
5
Ave
% Error
Acceleration
990.9
970.9
980.1
970.3
993.5
981.14
0.12%

V. EVALUATION
1.)
VI. CONCLUSION
In conducting this experiment, it has been easier for our group to set-up the materials except for the positioning of the two gates because sometimes it moves due to the members itself. This happened on table 2 where in the height of track on one end changes. Since the two gates need to be perpendicularly aligned to the track, it has been a hassle act to attain desired angle. So there is an angle indicator available where it helped the alignment of gates perpendicularly. Another rough thing happened is the positioning of the sensors. It is needed in order to determine the time travelled by the dynamics cart and by the smart timer. As a result, our group gathered high percentage of errors on Table 2 due to different factors. Apparently, kinematics is a part of mechanics that has been described in motion. One can get things to move either by pushing or pulling them. Here, by determining the velocity and acceleration, studying motion follows through. Since these quantities have simple definitions in Physics given by the physicists that may be different to the ones that human used in everyday living. Velocity and acceleration are both vectors. Talking about speed, it is the rate at which distance is covered at a given time. Likewise to velocity, instead that velocity is associated with direction.

Velocity is determined by the total distance travelled over by the total elapsed time while acceleration is determined by the change in velocity over the elapsed time. In this experiment, when the motion is along a straight line, its only nonzero component is along that line. In a straight line motion, acceleration may refer speeding up or speeding down. Since acceleration is a change in velocity, it also involves direction. Thus, acceleration is a vector. Base upon the results, it seems that the average speed of the cart in different displacement must be all equal. Hence, the speed is gradually decreasing when the displacement is increasing.

Gravity acts on falling objects, make them accelerate. At the latter experiment, acceleration due to gravity using cart’s acceleration has been determined. Based on the gathered data, we got a low percentage error. When the height of the track increases, the acceleration also increases. This may be due to the verticality of the track slowly. And also, as the height increases, the angle of inclination also increases giving the cart a faster speed to the lower end and when it released from the initial point. Hence, the objectives of this experiment of kinematics were achieved.

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