PHY250L Lab 6 Exam (2026 / 2027) | Work & Conservation of Energy | StraighterLine (PDF), Exams of Physics

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PHY250L

LAB 6 EXAM

Work & Conservation of Energy

Actual Questions & Verified Answers

Straighterline

Student Name: Shear Jashub

Access Code (located on the underside of the lid of your lab kit): AC-1FVKJN

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

1. 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 the energy transferred by a force causing displacement, defined mathematically as W=Fdcos(θ), where F is force, d is displacement, and θ is the angle between them. Potential energy is stored energy due to an object's position or state, with gravitational potential energy defined as PE=mgh, where m is mass, g is gravity, and h is height. Kinetic energy is the energy of motion, defined as KE=(1/2)mv^2, where m is mass and v is speed.

EXPERIMENT 1: WORK DONE BY A SPRING

Introduction Questions

1. In Experiment 1, you will stretch a spring at varying distances and calculate the work required to do so. The force associated with compressing or stretching a spring is variable and is quantified by F = kx, where k is the spring constant and x is the displacement.

Given the graph of the force versus displacement graph for a spring in Figure 5, derive an equation for the amount of work done by the spring. Do not simply state a final equation. Show the mathematical steps you will take to derive this equation. You must show all work for credit. The area under the force vs. displacement graph is the work done.For a spring, W=12kx2W = \frac{1}{2} k x^2W=21kx2, where kkk is the spring constant and xxx is the displacement.

Figure 5: Force versus displacement of a spring.

Data and Observations

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 0.4N 0.01 0.004J 0.8N 0. 1.25N 0.01 0.0125J 1.7N 0. 2.15N 0.01 0.0215J 2.6N 0. 2.95N 0.01 0.0295J 3.3N 0. 3.75N 0.01 0.0375J 4.2N 0.

1. 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? When I add up all the interval work values from my table, the total is almost the same as the value from the equation in Question 2. The small difference is because the table uses averages for each segment, while the equation uses a continuous calculation. Both methods closely agree, which shows the experiment matches the theory for a spring.

EXPERIMENT 2: CONSERVATION OF ENERGY

Introduction Questions

1. 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 To find the speed just before hitting the ground, use energy conservation: mgh = (1/2)mv² 0.5 × 9.8 × 3 = (1/2) × 0.5 × v² (0.5 cancels out) 9.8 × 3 = v² 29.4 = v² v = √29.4 ≈ 5.42 m/s

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) Initial potential energy (drop height): E₁ = mgh₁ = 0.5 × 9.8 × 3 = 14.7 J Final potential energy (bounce height): E₂ = mgh₂ = 0.5 × 9.8 × 2 = 9.8 J Energy lost to heat (thermal energy, TE): TE = E₁ - E₂ = 14.7 J - 9.8 J = 4.9 J

c. What is the speed of the ball immediately after the ball bounces off the ground? Again use energy conservation for the bounce up: mgh = (1/2)mv² 0.5 × 9.8 × 2 = (1/2) × 0.5 × v² (0.5 cancels out) 9.8 × 2 = v² 19.6 = v² v = √19.6 ≈ 4.43 m/s

Include a photo of the 2 items you used with your handwritten name in the background. Note: One of those items must be a ping pong ball. All five items must be shown, and they must match your entries in Table 5. Submissions without a photo depicting these requirements will be rejected.

EXPERIMENT 3: CONSERVATION OF ENERGY - DATA ANALYSIS

Introduction Questions

1. 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. In this experiment, we analyze data from an experiment that examines the conservation of energy using a moving object (such as a ball or cart). The original experiment involves measuring the position, velocity, and energy of the object at different points in time as it moves. By studying the data, we can see how potential and kinetic energy change, and whether the total mechanical energy is conserved as the object moves. Our goal is to use this data to understand the principles of energy conservation.
2. The analysis method this experiment utilizes is called the “leap-frog method”. Why do you think this is? The “leap-frog method” is used because it calculates velocities at points halfway between the measured positions (the “leap” between time steps). This helps make the velocity calculations more accurate and better matches the real motion of the object, especially when analyzing changes in energy.
3. What are the limitations of the leap-frog method? The main limitation of the leap-frog method is that it only provides an estimate of the velocity and energy at intermediate points, not at the exact measurement points. This can introduce small errors, especially if the time intervals are large or the object’s speed is changing rapidly. It is also less accurate if the data has significant measurement errors or if there is not enough data collected.

Data and Observations

Here, we provide the data and observations obtained from the experiment. Conduct the calculations necessary to complete the table. Table 5. Dropped Ball Data

• 0.00 5. Time (s) Ball Position(m) Ball Velocity(m/s) Potential Energy(J) Kinetic Energy(J) Total Energy(J)
• 0.05 4.99 -0.40 24.45 0.04 24.
• 0.10 4.96 -1.00 24.30 0.25 24.
• 0.15 4.89 -1.80 24.02 0.81 24.
• 0.20 4.78 -2.00 23.41 1.00 24.
• 0.25 4.69 -2.40 22.99 1.44 24.
• 0.30 4.54 -2.90 22.25 2.10 24.
• 0.35 4.40 -3.20 21.56 2.56 24.
• 0.40 4.22 -4.00 20.68 4.00 24.
• 0.45 4.00 -4.20 19.60 4.41 24.
• 0.50 3.80 -5.00 18.62 6.25 24.
• 0.55 3.50 -5.40 17.15 7.29 24.
• 0.60 3.26 -5.70 16.00 8.12 24.
• 0.65 2.93 -6.60 14.36 10.89 25.
• 0.70 2.60 -7.00 12.74 12.25 24.
• 0.75 2.23 -7.20 10.93 12.96 23.
• 0.80 1.88 -7.70 9.21 14.83 24.
• 0.85 1.46 -8.30 7.15 17.22 24.
• 0.90 1.05 -8.80 5.15 19.36 24.
• 0.95 0.58 -9.40 2.84 22.09 24.
• 1.00 0.