Question
2 Analysis You should collect several points of data (at least 5 unique data points, to make a trendline; more data is better)to construct at least one graph that relates work (W) to the changes in energy of your system (K, U, or the sum of the two depending on how you defined your system), or to examine whether when the work done on a system is zero, that the total energy of a system will remain constant (such as by graphing Delta K vs. Delta U) Analyze whether the relationships learned so far in class agree with or are challenged by your experiment. 3 Discussion 1. In a brief written paragraph, describe the experiment your group conducted Include: (a) an identification of all objects in the system of interest; (b) a sketch of the experimental setup, showing at least one force diagram; (c) an explicit statement about whether work will be done by any force(s) in the diagram on the system of interest.
Solution
4.2
(309 Votes)
Pablo
Master · Tutor for 5 years
Answer
## Example Experiment: Rolling a Ball Down a Ramp**2. Analysis:**This example experiment investigates the relationship between the work done on a ball rolling down a ramp and the change in its kinetic and potential energies.**Data Collection:**We will measure the following for at least 5 different starting heights (h) on the ramp:* **Height (h):** Vertical distance from the starting point to the tabletop.* **Distance Rolled (d):** Horizontal distance the ball rolls on the tabletop after leaving the ramp.* **Time to Roll (t):** Time taken for the ball to roll the distance (d).From this data, we can calculate:* **Final Velocity (v):** v = d/t (assuming constant velocity on the tabletop)* **Change in Kinetic Energy (ΔK):** ΔK = 1/2 * m * v² (where m is the mass of the ball, measured separately)* **Change in Potential Energy (ΔU):** ΔU = m * g * h (where g is the acceleration due to gravity)We will then plot two graphs:1. **ΔK vs. ΔU:** This graph will help us determine if the total mechanical energy is conserved (i.e., if ΔK = -ΔU). A linear relationship with a slope of -1 would indicate conservation of energy.2. **ΔK vs. h:** This graph will help us visualize the relationship between the change in kinetic energy and the initial potential energy (represented by the starting height).**3. Discussion:****(a) System of Interest:** Our system consists of the ball and the Earth.**(b) Experimental Setup and Force Diagram:**[Insert a simple sketch of a ball rolling down a ramp. The sketch should show the ball at the top of the ramp, and again on the tabletop. Include a force diagram for the ball at the top of the ramp, showing the force of gravity (mg) downwards, the normal force (N) perpendicular to the ramp, and the force of friction (f) parallel to the ramp, opposing motion.]**(c) Work Done by Forces:*** **Gravity:** Gravity does positive work on the ball as it rolls down the ramp, as the force of gravity has a component parallel to the displacement of the ball. This work contributes to the increase in the ball's kinetic energy.* **Normal Force:** The normal force does no work on the ball, as it is always perpendicular to the displacement of the ball.* **Friction:** Friction does negative work on the ball, as it acts opposite to the direction of motion. This work converts some of the ball's mechanical energy into thermal energy. If the friction is small, we may still observe an approximately linear relationship between ΔK and ΔU, but the slope might be slightly less than -1, indicating some energy loss due to friction.**Expected Results and Connection to Classroom Learning:**We expect to see a negative linear relationship between ΔK and ΔU. If the total mechanical energy is conserved (negligible friction), the slope of the ΔK vs. ΔU graph should be close to -1. This would confirm the work-energy theorem and the principle of conservation of energy, which state that the work done by the net force on an object is equal to the change in its kinetic energy, and that the total energy of an isolated system remains constant. The ΔK vs. h graph should show a positive linear relationship, indicating that a greater initial potential energy (higher starting height) leads to a greater increase in kinetic energy.**Note:** This is a sample experiment and analysis. You should adapt it to your specific experiment and include your actual data, calculations, and graphs. Be sure to discuss any discrepancies between your experimental results and the theoretical predictions, and suggest possible reasons for these discrepancies.