Teacher s notes 13 Motion up and down an inclined plane

Transcription

1 Sensors: Loggers: Motion Any EASYSENSE Physics Logging time: 5 seconds Teacher s notes 13 Motion up and down an inclined plane Read In this investigation, the Motion sensor is used to plot the position of a cart as it moves up and down a slope. The Motion sensor collects the time distance for the whole journey of the cart up and down the slope; this is a significant step up from recording spot times at 1 or 2 locations on the journey. The investigation starts to tie several strands together, the students will be working with a time distance graph and they will start to use the advanced features of the software to calculate the velocity and acceleration. Students should be using the notation for time, velocity and acceleration, v = initial velocity u = final velocity s = displacement (this can create confusion, s is normally given as the unit for time) Δ = difference t = time = seconds a = acceleration A the end of the investigation students should be able to Produce and identify a Distance vs. Time (s - t) curve for travel down a slope. Produce and verify a Velocity vs. Time (v - t) curve from Distance vs. Time data. Know that the area under the velocity- time curve = distance travelled. ( u + v) s = Δt 2 Know that Velocity = the gradient of the s - t curve. Know that Acceleration = the gradient of the v - t curve. Produce an acceleration curve from the distance time data using the tools in the software. Apparatus 1. An EASYSENSE logger. 2. A Smart Q Motion sensor - with the range set to distance. 3. Dynamics track or a rigid track at least 1.2 m long that can be sloped. 4. Dynamics cart with end reflector fitted. Set up of the software Use the setup file 13 Motion on a slope MS UD If you wish to set up the logger or software manually, the table shows the conditions used in the setup file. Recording method Length of recording Intersample time Graph 5 seconds 20 ms T13-1 (V2)

2 Note: No trigger is used. The whole of the up and down motion is displayed. The time of recording (5 s) should be ample for a student to collect the data. If students require a longer period to collect data it is very simple to extend the logging time using the New recording wizard. Make sure the intersample time remains at 20 ms. Notes Attaching the Motion sensor to the Dynamics system The instructions show the Motion sensor attached to the bracket using a wing bolt, the space on the platform made by the large bracket should be large enough that the Motion sensor will fit and stay in place without this bolt. T13-2 (V2)

3 The reflector should be mounted on the edge of the cart facing the Motion sensor. It is a good idea to lubricate the bearings of the cart before use and check their smooth running. The use of differentiation of the distance / time data to produce velocity and acceleration means that any erratic motion of the cart is amplified and can confuse the final results. Students will need some time to find out how much shove / push they need to get the cart to about ¾ of the distance up the ramp. This becomes increasingly harder to estimate as the ramp angle gets steeper. With larger ramp angles (15 degrees +) a catcher will be required to field the cart as it stops against the buffer. You may wish to consider placing some soft material on the bench top around the end of the ramp to catch the cart should it bounce off the track as it is brought to a stop. Sample data and analysis The following data was obtained using a cart moving first up then down a Data Harvest Dynamics track. The sensor could be used at either the top or bottom of the slope. This data was collected with the sensor at the bottom of the slope. The velocities are positive when moving up the slope and negative when the cart is descending the slope, which brings out the vector nature of velocity as an additional teaching point. It is worth pointing out to the students that the use of a ve does not quite have the same meaning here as it does in most mathematical operations they will have met, it is a simple device to show the direction of the movement. When adding vectors they do act as mathematical operations, e.g. a displacement of +5 m added to a displacement of -5 m gives a resultant displacement of 0 m. If the sensor is at the bottom of the ramp, it is essential that a stop is positioned to prevent the cart from hitting the sensor. A crash barrier is difficult to use with the Motion sensor as it can deflect the ultrasound pulses that are used to calculate the distances. Use the Gradient tool on the Velocity curve to find the acceleration. Data as recorded. T13-3 (V2)

4 Use Selection used to remove the data from the cart stopping Use Selection applied, Sensor settings adjusted to match data range recorded. Velocity shown. Calculated using the Post-log Function: Motion, Velocity derived from Distance data. Values line in position of the zero velocity point, note how it matches the maximum distance from the sensor. T13-4 (V2)

5 Acceleration shown. Calculated using the Post-log Function: Motion, Acceleration as a second derivative of Distance data. Note how acceleration reduces form ms -2 to 0.72 ms -2 from the sensor. The acceleration values either side of this point should be the same sign. The force acting on the cart slowing it down is the same as the force acting on the cart speeding it up i.e. gravity. An explanation of the change is friction; this force will be acting with gravity on the up journey to slow the cart down and against gravity on the down journey resisting any increase in speed. Table of typical values taken from graphs (for one half of the journey of the cart i.e. the up or down only) Time (s.) Gradient (ms -1 ) Velocity (ms -1 ) From the v - t curve t (s) v (mms -1 ) Gradient = Acceleration (mms -2 ) Average acceleration = ms -2 T13-5 (V2)

6 Initial time t Final time t Time interval Δt = (t 2 t 1 ) 1.34 Velocity at t 1 = u Velocity at t 2 = v Initial distance s Final distance s Average velocity = v+ u ( ) = / 2 = Average velocity x Δt x Area under v - t graph between t 1 and t Distance travelled Δs = s 2 s The values in the last three rows are in very close agreement. T13-6 (V2)