Real-time experiments approach in kinematics using ComLab

equipment

Tine Golež, St. Stanisalv institution for education, Ljubljana, Slovenia

ComLab Conference 2007Computerised laboratory in science and technology education

30. November in 1. December, 2007 Radovljica, SLOVENIJA

Kinematics (using comLab software)

Physics

Graphs based approach; comprehension before computation

... and an additional outcome...

Mathematics

Calculus; precursor for calculus

(Prematurely) equations approach

v = v0 + at

x = x0 + v0t + at2/2

v2 = v02 + 2ax

... Followed by calculatin tasks

Fig. 1. A student has walked in front of sonic sensor. The x(t) graph is displayed.

(1.4 s, -0.40 m)

(5.2 s, 0.80 m)

Figure 2: The slope of the curve x(t) is defined as the slope of the tangent at that point. The calculated slope at t = 4,0 s equals the instantaneous velocity at that instant (x/t = 0.32 m/s). Graph v(t) confirms the result. The reverse process is shown on v(t) graph. The displacement during time interval is determined by calculating area (in our case x = 1,0 s·0,45 m/s = 0,45 m)

(1.4 s, -0.40 m)

(5.2 s, 0.80 m)

Figure 2: The slope of the curve x(t) is defined as the slope of the tangent at that point. The calculated slope at t = 4,0 s equals the instantaneous velocity at that instant (x/t = 0.32 m/s). Graph v(t) confirms the result. The reverse process is shown on v(t) graph. The displacement during time interval is determined by calculating area (in our case x = 1,0 s·0,45 m/s = 0,45 m)

Figure 3. An ordinary ball was held under the motion sensor and dropped from rest. It rebounded twice from the floor during the measurement. Graphs show that the instantaneous speed (which is equal to the magnitude of the instantaneous velocity) at points of equal elevation in the path is the same whether the ball is moving upward or downward during one rebound (e. g., compare t = 0.80 s and t = 1.40 s). In addition, during one rebound the ball slows from the initial upward velocity to zero velocity. At the highest point it changes its direction of motion. Certainly, it experiences the same acceleration on the way down. The acceleration, which is the rate of change of velocity, is constant. Therefore this part of v(t) graph is linear. The slope of the line equals the acceleration. As calculated for this case:

Figure 4: Motion sensor analyzed pendulum motion. The graphs x(t), v(t) and a(t) are not displayed in this order. Students must find out the legend of each graph by investigating their slope and iterrelationship between the graphs.

ScienceMath Project

• Comenius 3 years project, (Germany, Finland, Danmark and Slovenia – 4 Universities and 4 high schools)

• The project ScienceMath is an interdisciplinary European co-operation project for the promotion of mathematical and scientific literacy. Objective is the development of proven teaching sequences and –modules that lead to a comprehensive and multidimensional learning of mathematic contents and concepts. It is the basic idea to encourage mathematic learning in scientific contexts and activities of the pupils.

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Photo:T. Golež