PHYS 250 Velocity Lab PreLab Assignment

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1 PHYS 250 Velocity Lab PreLab Assignment Name Section For each of the two position versus time graphs shown below, sketch (before coming to lab) the corresponding velocity versus time graphs: x (A) x (B) t t v x v x t t Explain in words how you determined the velocity-versus time graph from the position versus time graph.

2 PHYS 250 Laboratory #1: 1D Kinematics Score: Section #: Name: Name: Name: Lab-Specific Goals: To investigate velocity as the time rate of change of position. To learn to use photogates to determine velocity of an object. To explore position, velocity, and acceleration graphs. To develop general graphing skills. Equipment List: Airtrack system with one glider Photogate timer with Accessory Photogate Introduction and Pre-Lab Questions: Position of an object is simply the object s coordinates within a reference frame. For example, in the coordinate system of latitude and longitude, Penn State is at 40 degrees 48 minutes 07 seconds North latitude and 77 degrees 51 minutes 23 seconds west longitude. Any coordinate system is arbitrary, but a common coordinate system is important to communicate information about positions. Velocity is the time rate of change of position. We learned in lecture that this means that velocity is the slope of the position versus time graph. If the slope of the position versus time graph is constant, the velocity of the object is constant; if the slope of the position versus time graph changes over time, then the velocity of the object changes over time. Velocity (for one-dimensional motion) can be described as positive or negative depending on whether the object is moving in the positive direction of the coordinate system (e.g., to the right for horizontal motion as we have generally made our coordinate

3 system in class). The sign (+/-) tells us in what direction an object is moving. Velocity conveys both speed (how fast) and directional information. Acceleration, which we will be looking at in Activity 2, is the time rate of change of velocity (just as velocity is the time rate of change of position). So just as velocity (v x ) is the slope of the position (x) versus time graph, acceleration (a x ) is the slope of the velocity versus time graph. And just as displacement is the area under the velocity versus time graph, so change in velocity is the area under the acceleration versus time graph. The velocity versus time graph is a valuable tool in analyzing motion since from it we can get the displacement (area under the velocity versus time graph) and the acceleration (slope of the velocity versus time graph). v x = slope of x a x = slope of v x x v x a x x = area under v x v x = area under a x

4 Activity 1: Measuring Glider Velocity Set up the air track as shown in the figure below (though we want it level, so we won t be elevating one end as shown in the figure). The photogates will let us find the speed of the glider at different places along the track. The photogates work in two modes: GATE and PULSE. You will need to know how to use each mode and when it s best to use which mode for several labs in this course. GATE Mode: Turn on the photogate timer and set it to GATE mode. In this mode, the timer measures the time interval t that the photogate is blocked by the glider as the glider passes through the gate. The glider has an effective length L. Make sure that the glider is gliding freely and smoothly (minimum wobble) as it passes through the photogates. The average speed of the glider as the gate passes through the gate is given by v gate = L/t, Where t is the time interval recorded by the photogate.

5 Using 1 photogate in GATE mode: 1. Measure the length L of the flag on the glider. 2. Turn the memory switch to Off. 3. Press RESET between readings to zero the timer. 4. Send the glider through the photogate 5. Read off t from the display Activity 1.1: Set up just one photogate along the track. Before giving the glider a light push to send it through the gate, carefully make sure that the glider will not collide with the photogate and that the glider flag is triggering the photogate (i.e., the red LED on the photogate lights up). Now send your glider through SLOWLY and make sure to catch it before it hits the opposite end of the track. L = t = Now calculate: speed = Don t forget to include units in all the values you report above! Now send the glider through the photogate faster than before (but be careful not to have it move too fast!). L = t = Now calculate: speed = What happened to t when you sent it through faster? What happened to v=l/t when you sent it through faster?

6 You can use a second photogate in GATE mode to get a second measurement of speed. Using 2 photogates in GATE mode: 1. Measure the length L of the flag on the glider. 2. Flip the memory switch to On. 3. Send the glider through both photogates. 4. The time displayed on the screen is the time that the first photogate triggered was blocked. (We ll call that t 1.) 5. Toggle the memory switch to Read and another time will be displayed. This time is the total time that the photogates were blocked, or t 1 + t 2, where t 2 is the time the second photogate triggered was blocked. Activity 1.2: Add the second photogate to the track. Once again, carefully make sure that the glider will not collide with the added photogate and that the glider flag is triggering the photogate (i.e., the red LED on the photogate lights up). Now send your glider through and make sure to catch it before it hits the opposite end of the track. L = t 1 = t 1 + t 2 = t 2 = Speed through first photogate = Speed through second photogate = Don t forget to include units in all the values you report above!

7 PULSE Mode: Turn on the photogate timer and set it to PULSE mode. You will need to have two photogates on the track, separated by a distance D. In PULSE mode, the timer measures the time interval t between when the first photogate is blocked by the glider and when the second photogate is blocked. The average speed of the glider as it moves between the two gates is given by v pulse = D/t, Where t is the time interval recorded by the photogates. Using PULSE mode (two photogates): 1. Measure and record D, the distance the glider moves on the air track from where it triggers the first photogate, to where it triggers the second photogate. (Move the glider and watch the LED on top of the photogate. When the LED lights up, the photogate has been triggered.) 2. Turn the memory switch to Off. 3. Press RESET between readings to zero the timer. 4. Send the glider through both of the photogates 5. Read off t from the display Activity 1.3: Set up two photogates on the track and carefully measure the distance D between them. Before giving the glider a light push to send it through the gates, carefully make sure that the glider will not collide with the photogates and that the glider flag is triggering the photogates (i.e., the red LED on each photogate lights up). Now send your glider through and make sure to catch it before it hits the opposite end of the track. D = t = Now calculate: speed = Don t forget to include units in all the values you report above!

8 Activity 2: Velocity Graph Exercise The table below shows the velocity at various times for a runner traveling in a straight line (which we will call the x-axis). Time (s) Velocity (v x ) (m/s) ) Make a velocity-time graph for the runner on the graph paper provided below. Be sure to follow rules for making good graphs: make the time and velocity axes linear, use the space (i.e., don t make it too small), label the axes, be neat. 2) Show on your velocity-time graph how to calculate the slope between t = 10 and t = 20 seconds. 3) Make an acceleration-time graph for the runner on the graph paper provided below. Once again, be sure to follow rules for making good graphs. 4) For the interval between 10 and 20 seconds, show on your graphs that the area under the acceleration-time graph corresponds to the change in velocity during that interval. 5) Make a position-time graph for the runner on the graph paper provided below, indicating her position at the times provided in the table above. Assume that she starts at x = 0. [Question to ponder: why can t you connect these points with straight lines?]

9 Velocity-Time Graph for Runner

10 Acceleration-Time Graph for Runner

11 Position-Time Graph for Runner

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