Supplemental Lab 6 Questions

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Part 1: The Remote on its own. The gravitational potential energy of an object is given by U g = mgh , where h is the object’s height above some chosen reference point. An object’s kinetic energy is K = 1 2 mv 2 Keeping in mind that total energy (U + K) remains constant (assuming no losses due to friction or air resistance), derive an expression that relates the position of the remote on the ramp (in terms of distance from the starting point) to its speed for a given ramp angle. v = √ 2 gh Now that you have that expression, open your first exported .csv file for the 10-degree system in a spreadsheet program. Make a plot with position on the x-axis and velocity squared (v 2 ) on the y- axis, covering only the portion of the plot where the remote was actually rolling down due to gravity. If Newton’s laws still work, the plot should be a straight line. Add a trendline to the data and display the equation.  What are the units of the slope? (You will have to figure this out based on your derivation.) y = 2.6702x – 0.0029 y = m x + b  What is the physical meaning of this slope? For the equation, m is the slope, 2.6702, and b is the y-intercept (0, - 0.0029). This means that for each unit increase in height, the velocity 2 increases by 2.6702.  Knowing this, use the value of the slope to determine a measurement of the acceleration due to gravity. It is 2.6702 m/s 2 .

Repeat this with your other 5 data files.  Were your measurements of gravity consistent between your data runs? Did it change when you changed the angle of the ramp? (y = 2.6118x - 0.0054): Slope ≈ 2.6118 (y = 5.8967x + 0.0034): Slope ≈ 5.8967 (y = 5.9647x + 0.0037): Slope ≈ 5.9647 (y = 8.7462x - 0.0347): Slope ≈ 8.7462 (y = 8.771x - 0.0134): Slope ≈ 8.771 The slopes varied across my data runs. This indicates that the steeper the ramp, the faster the acceleration.  If you found an apparent dependence of gravity on the ramp angle, what physical reason could there be for it? Frictional force acts on the ramp and the remote. The gravitational force is being exerted in many different spots. The ramp isn’t completely smooth and can alter each run slightly. The location of starting and stopping points aren’t exact either. Part 2: The remote and a hanging mass: Recall from the video that for two masses (m 1 is the remote and m 2 is the hanging mass). Repeat the same procedure that you used on your data from part 1, plotting position (height – h) vs. velocity squared (v 2 ), and answer the same questions. ∆ x = m 1 + m 2 2 g ¿¿

∆ x = 204.1 + 90.0 2 ( 9.8 ) ¿¿ Topics to address in your lab report: 1. When relating position to speed, is it easier to use energy or Newton’s laws of motion (and the kinematic equations)? I think with the precise measurements and detailed analysis that we are having to do, Newton’s laws and kinematic equations are more suitable for me to use. 2. Compare the measured initial energy to the final energy (Potential to Kinetic) for each of the five cases assuming g = 9.8 m/s 2 . (I recommend setting your initial energy to zero in all cases to make the calculation simpler). Did the energy appear to increase or decrease? Did some cases lose or gain more energy than others? Where could explain the energy gain/loss? The ramp set at 10° had minimal energy loss, 20° had minimal energy loss, 30° had more energy loss due to an increase in incline. The hanging mass of 50g contributed to a heavier energy conversion, which compensated for any losses and the 90g hanging mass was pretty equal and balanced and had minimal gain/loss. Energy gain/loss can be seen through friction, ramp angle, mass, and energy conservation. 3. Discuss any sources of errors in your measurements. Sources of error are the placement of the objects are not going to be exact and vary every single run, computing errors when calculating data, computer data error from software or remote, the ramp is not the same exact texture the whole distance down,

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