phys172_rec07_echinitz.ipynb - Colaboratory

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2/22/23, 1:19 PM phys172_rec07_echinitz.ipynb - Colaboratory https://colab.research.google.com/drive/1ePCiptKxBSzpuwcFNOyH6z2nvxOxﬂWT#scrollTo=5QSI51vGW-b2&printMode=true 1/3 Chinitz Chinitz W 12:30 12 Caitlyn Bowerman, Aliya Carmon, Tatum LeMaire Part 1: How much work is done on the crate by the gravitational force from the initial to ±nal position? Part 2: How much work is done on the crate by the tension force from the cable from initial to ±nal position? Problem 1: An initially stationary crate, mass, kg , is pulled by a cable a distance, m up a smooth ramp to height, m where it ±nally stops. [Use ] 1.1 What principle(s)/concept(s) will you need to help solve the problem? energy princple, work princple, kintetic energy 1.2 What assumption(s)/approximation(s) do you need to make to better help you solve the problem? Gravity on earth is 10 m/s^2 friction and air resistance are negliable. 1.3 Identify your system (i.e. objects experiencing a change) and surroundings (i.e. objects causing the change). system: crate surroundings: ramp, cable, earth.

2/22/23, 1:19 PM phys172_rec07_echinitz.ipynb - Colaboratory https://colab.research.google.com/drive/1ePCiptKxBSzpuwcFNOyH6z2nvxOxﬂWT#scrollTo=5QSI51vGW-b2&printMode=true 2/3 Write your answer to Part 1. -300 J Write your answer to Part 2. 300 J 2.1 Are there other ways to solve this problem? Explain how or why not. Yes, we could use the momentum princple to ±nd the ±nal momentum then use that to ±nd the work. 2.2 Explain and justify why the work done by gravitational force depends on the vertical displacement and NOT the horizontal displacement. The horizontal displacement does not affect the gravitational force because it is perpendicular to the force so it is cancelled out in the dot product when ±nding work done. 2.3 Explain and justify what would happen to the work done by the cable and magnitude of tension force as the crate was lifted the same height but with a longer ramp. The work done by the cable would stay the same because the displacement is greater but the smaller angle cancels out the change in displacement meaning that the height is the only distance that changes the work done. 2.4 Describe another problem you have seen or previously solved that has a similar solution strategy? How are these problems similar? Finding the force of gravity on an item on an angled ramp is similar to ±nding the work done by gravity on the crate in this problem. For both you need to use the mass and gravitational constant and both the vertial and horizontal components of gravity. STUDENT A: To ±nd the work done by the gravitational force, I consider the block as the system, and the Earth and string as the surrounding. I would use the formula that Work done is Force times displacement. The displacement is and the force due to gravity is the weight, . So, I would multiply the mg times the displacement , or work done by gravity is . The work done by tension must just cancel out the work done by gravity because tension works against gravity, so work by tension is . STUDENT B: First, your system is ±ne, but surroundings must also include the ramp, in addition to the Earth and the rope. Yes, I agree that work done by the gravitational force is the gravitational force times the displacement, but we should use displacement in the direction of the gravitational force, which is the vertical displacement, . So, the work done by gravity is . But for ±nding the work done by tension, we need to ±rst ±nd the force of tension, . After that we must multiply the force of tension by the displacement in the direction of the tension, which is . So, work done by tension is . STUDENT C: The system is the block and the surroundings includes the ramp, Earth and rope. Actually, the answer to both questions can be found much more easily than that. Basically, you have to notice that the block was at rest at the beginning and at the end, so the change in kinetic energy of the block is zero. This means that the work done by any force is zero. Consider below, three different hypothetical solution strategies suggested by students. Utilize the , , and methods you've been using on previous recitations. Justify the various decisions of the person whose solution strategy you agree with. Incorporate why the chosen principle(s)/concept(s) and assumption(s)/approximation(s) are relevant to correctly solving the problem. 3.1 In words, construct an argument to explain and justify which of the three strategies described you prefer, or if there is a completely different strategy that you prefer.

2/22/23, 1:19 PM phys172_rec07_echinitz.ipynb - Colaboratory https://colab.research.google.com/drive/1ePCiptKxBSzpuwcFNOyH6z2nvxOxﬂWT#scrollTo=5QSI51vGW-b2&printMode=true 3/3 Student B has a mostly correct approach; however, they forgot to include the cosine component in their calculations. This approach assumes that the crate is moving on a ²at surface which means that the force of gravity found using their method is higher than the actual situiation. Using the work done by gravity was the correct approach, but they did not do so correctly. They did the same when ±nding the force of tension. The correct method would have included cosine in the multipication. ψ Student B has a mostly correct approach; however, they forgot to include the cosine component in their calculations. This approach assumes that the crate is moving on a flat surface which means that the force of gravity found using their method is higher than the actual situiation. Using the work done by gravity was the correct approach, but they did not do so correctly. They did the same when finding the force of tension. The correct method would have included cosine in the multipication.

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