Download Lab 6 Work and Conservation of Energy | PHY250L | Spring Constant & Graphs and more Exams Physics in PDF only on Docsity!
Student Name: Giovana Costarelli
Access Code (located on the underside of the lid of your lab kit): AC-KW80U
Lab Report Format Expectations Utilize college level grammar and formatting when answering text based questions. Report all equations in a proper mathematical format, with the correct signs and symbols. Submissions with incomplete or improperly formatted responses may be rejected.
Pre-Lab Questions
- In this lab, you will conduct three experiments that will demonstrate the concepts of work, potential energy and kinetic energy. Briefly explain those three concepts and their mathematical definitions.
- Work is defined as the force applied to an object multiplied by the displacement in the direction of the force, and its equation is W=F⋅d⋅cos(θ). Where F is the force applied, d is the displacement, and θ is the angle between the force and displacement.
- Potential Energy (U): Energy stored due to the position of an object. In the gravitational case, its equation is U=mgh. Where m is the object’s mass, g is the acceleration due to the gravity, and h is the object’s height.
- Kinetic Energy (K) is the energy associated with an object's motion, and its equation is K=1/2mv^2. Where v is the object's velocity.
- Both kinetic and potential energy are part of the thrill of roller coasters. Refer to Figure 6, below.
a. Describe the kinetic and potential energy at each point of the roller coaster path. Point A: Maximum potential energy, as it is at the highest height. Kinetic energy is minimal (if not zero). Point B: Part of the potential energy was converted into kinetic energy. The cart is accelerating. Point C: Minimum potential energy, maximum kinetic energy (highest speed of the cart). Point D: Kinetic energy is being converted back into potential energy as the cart rises again.
b. What happens to the rollercoaster’s kinetic energy between Points B and C? What happens to its potential energy between these points? Kinetic energy increases because potential energy is being converted. Potential energy decreases as the cart moves downwards.
c. Why is it important for Point A to be higher than Point C? To ensure that the initial potential energy is sufficient for the cart to complete the entire journey without needing an additional energy source.
Figure 6: Different points in a roller coaster’s motion.
Record your observed forces for each distance the spring was pulled. Then calculate the average force between the measurements. Use this average to find the work it took to pull the spring for each step and record this in the final column.
Table 1. Spring Scale Force Data
Force (N) Distance, x (m) ForceAverage (N) Δ Distance, Δx (m) Work (J)
0 0
0.75 0.01 0.
1.5 0.
1.95 0.01 0.
2.4 0.
2.85 0.01 0.
3.3 0.
3.75 0.01 0.
4.2 0.
4.6 0.01 0.
5 0.
Insert a photo of the spring being pulled back for each step (5 in total) with your handwritten name in the background. The photos must clearly demonstrate the reading on the spring when pulled back to the distances in the table. To do so, the spring must be next to the ruler as specified in the procedure. The distances and forces must match those recorded in Table 1. Submissions that do not include photos that meet these requirements will be rejected.
- Create a graph similar to the one in Figure 5 that depicts each distance on the X axis, and the force on the Y axis. Your handwritten name must be included in your graph for credit.
- Using the result of Question 1 for the experiment introduction, calculate the work done by the spring.
K= F/x= 5N/0.05m= 100N/m
W= 1/2(100)(0.05)^2= 0.125J
- In your table and graph, the work done by the spring is broken down by the work done by each 1 cm stretch. How does this compare to the work done by the spring calculated in Question 2, above? The work calculated using the average force in each 1 cm increment adds up to approximately the same total work calculated using W=1/2kx^2. Any small differences are due to rounding errors or the incremental approach approximating the area under the curve of the Force vs. Distance graph.
EXPERIMENT 2: CONSERVATION OF ENERGY
Introduction Questions
- Consider the ball example in the introduction for the lab course, where a ball is dropped from 3 meters. After the ball bounces, it rises to a height of 2 meters. The mass of the ball is 0.5 kg. a. Calculate the speed of the ball right before the bounce
b. How much energy was converted into heat after the ball bounced off the ground? (Hint: Thermal Energy (TE) will now need to be included in your conservation of energy equation and you will now need to know the mass of the ball) TE = mghinitial − mghfinal
TE=0.5(9.81)(3)−0.5(9.81)(2)
TE=14.72J−9.81J=4.91J
handwritten name must appear in the background. Submissions without a photo depicting these requirements will be rejected.
● the potential energy (PE) of the ball before the drop. Remember, you should use the equation PE=mgh.
● the kinetic energy (KE) of the ball right before it bounces. Remember, total energy is the sum of kinetic and potential energy. Right before the bounce, the potential energy has all been transferred into kinetic energy.
● the potential energy at the new height using PE=mgh.
● the thermal energy (TE) lost during the bounce, which is the difference between the original PE and the PE after the bounce.
● the kinetic energy after the bounce. Remember, this should be the difference between the KE just before the bounce and the lost TE.
Table 4. State of Energy at Various Points in Motion
Ball Type PE0.5 meters KEbefore bounce PEnew max height TE KEafter bounce
Ping Pong Ball 0.0132 0.0132 0.0074 0.0058 0.
Golf Ball 0.221 0.221 0.156 0.065 0.
Volleyball 1.278 1.278 0.476 0.802 0.
- Calculate the speed of the ball right before and right after the bounce. -Ping Pong Ball:
Speed Before Bounce: 3.12 m/s
Speed After Bounce: 2.34 m/s
-Golf Ball:
Speed Before Bounce: 3.13 m/s
Speed After Bounce: 2.64 m/s
-Volleyball:
Speed Before Bounce: 3.14 m/s
Speed After Bounce: 2.07 m/s
EXPERIMENT 3: CONSERVATION OF ENERGY - DATA ANALYSIS
Introduction Questions
- In this experiment, you are given a set of data from an experiment carried out by someone else. Explain the experiment with enough detail to demonstrate your understanding. The experiment measures the variation in potential and kinetic energy as an object falls, allowing us to verify whether total energy is conserved. It will be calculated based on the conservation of energy, based on a given set of data. The data in Table 5 will be analyzed to understand the position and distance traveled by the ball. The ball has a mass of 0.5 kg and is dropped from a height of 5 meters from rest, i.e., the initial distance is 5 meters.
- The analysis method this experiment utilizes is called the “leap-frog method”. Why do you think this is? The method uses successive approximations to calculate speeds and positions in small increments of time, similar to the movement of a leapfrog.
- What are the limitations of the leap-frog method? It may introduce small numerical errors due to approximations, it depends on the accuracy of the input data, and may not capture air resistance effects well.
- Carefully graph the potential energy, kinetic energy, and total energy of the ball on one graph. The easiest way to do this is to copy the data into a spreadsheet program, but a hand-drawn graph is also acceptable. If you decide to draw a graph by hand, it must be accurate. Include your name in the title of the graph, ensuring to use the same font and font size, if it is generated with graphing software, or handwrite it if your graph is generated by hand. Submissions with graphs that do not clearly reflect the data in Table 5, or that lack a name that is properly incorporated into the graph, will be rejected.
- Clearly describe the shape of each graph in detail.
● Potential Energy Graph : This graph decreases smoothly from a maximum of 24.5 J to a minimum near 2.8 J as the ball falls. It shows a downward sloping curve, consistent with the loss of height.
● Kinetic Energy Graph : This graph increases as the ball accelerates, starting from 0 and rising to over 19 J. It mirrors the potential energy graph, increasing as PE decreases.
● Total Energy Graph : The total energy remains nearly constant throughout the fall, fluctuating slightly around 24.5 J. This flat line demonstrates the conservation of mechanical energy, confirming minimal energy loss.
- Did the leapfrog method affect any of the values in the graph? If so, which ones? How do you know? Yes, the leapfrog method affects the velocity values, which then impact kinetic energy calculations. The method uses estimated differences in position before and after each time step, which introduces slight rounding or numerical errors. These errors are visible as minor fluctuations in the total energy graph, where the total energy is not perfectly flat but close—this shows the effect of approximation.
