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--- 183_projects:problem10b_fall2024 [2024/10/28 15:07] – hallstein
+++ 183_projects:problem10b_fall2024 [2025/03/28 18:51] (current) – hallstein
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-====== Project 10: Part B: Post-Apocalypse Now, Part 2 ======
+====== Project 12: Part a: Post-Apocalypse Now, Part 2 ======
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-==== Project 10B: Learning goals ====
+==== Project 12A: Learning goals ====
   * For single-particle systems where little or no heat is exchanged with the surroundings, use conservation of energy ( $\Delta E_{\rm sys}=W_{\rm ext}$ ) to explain and/or predict the final state of the system (this includes choosing a system, and setting up initial and final states consistent with that system).
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 <WRAP info>
-==== Project 10B: Learning Concepts ====
+==== Project 12A: Learning Concepts ====
   * Energy Conservation
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 The spring-loaded harpoon launchers are detachable and can easily be moved from floor to floor, or to the bottom of the elevator shaft. The plan is to drop the concrete blocks down the elevator shaft onto the spring to compress the spring.  Design the defense system to find the minimum angle for the boulder to fall down the elevator shaft and the range/locations outside the defensive wall that your system can reach with the required specifications. Indicate your supply needs to meet the Aunty Entity's requirements to keep Thunderdome safe.
-=== **Project broken into parts - mini-problems to use as an exam 2 review** ===
+Notes on the diagram: The five ramps with the spherical objects resting on them are inclined planes that can be adjusted to any angle. The idea here is to get the boulder to slide off the ramp and into the elevator shaft. The square box with the coil attached to it represents the harpoon launcher that can be removed and place aligned horizontally on any of the floors or the roof to fire harpoons; or it can be anchored vertically at the bottom of the elevator shaft where you can drop boulders onto it and compress the spring.  You may assume the spring and harpoon launcher are sturdy enough to withstand the impact of the boulder.
+==== Project broken into parts - mini-problems to use as an exam 2 review ====
 **Overall general idea**
 The general idea is to drop a block into the elevator shaft such that it lands on a vertically aligned harpoon launcher (spring), compressing the spring with the spring latching in place. The launcher can then be brought up to any of the five launcher supports on floors 2 through the roof. The harpoon launcher (spring) is anchored in place here and is horizontally aligned. A harpoon is placed in the launching mechanism where it can be fired at approaching zombies.
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 **Part 1: Finding the angle of the platform**
-We would like to increase the angle of the inclined plane so that the block slides off of the plane and into the elevator shaft. Assume the plane is constructed of steel.
+We would like to increase the angle of the inclined plane so the block begins to slide on the plane(ramp). The idea here is we want it to fall into the elevator shaft so you can start the next part. Assume the plane is constructed of steel.
   - Do we want to use static or kinetic friction?
   - Draw a free-body diagram of the block on the inclined plane.
   - Find components of each force parallel and perpendicular to the plane.
-  - In terms of variables, what are the normal force and the frictional force?
+  - In terms of variables, what are the normal and frictional forces?
   - What is the angle of the plane?
-**Part 2: finding the spring compression**
+**Part 2: Finding the energy stored in the spring**
 The most straightforward distance to find is finding the maximum possible distance a harpoon can reach. This will occur when the block is dropped over the greatest distance (from the roof) and launched from the highest elevation (also from the roof). So, let's work with this first.
-  - We want to use the energy principle to find the energy stored in the spring. What are you including in your system include in our system?
+  - We want to use the energy principle to find the energy stored in the spring. What are you including in your system?
   - We'd like to use the simplest model, with this in mind what assumptions can we make to simplify this process?
   - What, if anything does work on your system? If any work is done, calculate this work.
   - Apply the energy principle to find the energy stored in your spring.  Make your life easier - keep this in variable form!
+**Part 3: Checking the harpoon speed**
+  - The minimum speed needed is at the instant the harpoon hits a zombie.
+  - In order to find the speed, we need to use energy considerations. What is in your system?
+  - What, if anything does work on your system? If any work is done, calculate this work.
+  - Keeping your work in variables until the final step (you'll thank us later), apply the energy principle to find the speed.
+  - We also will need the launch speed of the arrow so we can find out if it clears the wall. Apply steps 2 through 4 to get this speed, again keep this in variables.
+**Part 4: Does it clear the wall?**
+  - Does the time of fall of the horizontally-launched harpoon depend on the launch speed?
+  - Is this constant force motion? If so, we can use kinematics here.
+  - How much time does it take the harpoon to reach the horizontal location of the wall? Again, keep in variables.
+  - What is the elevation of the harpoon at the time found in the previous step - now, use your known quantities to get a numerical value. Does it clear the wall?
-**Post-Solution questions:**
+**Part 5: What is the range/ total horizontal distance of the launched harpoon?**
-  * A 90 kg zombie is moving 1 m/s directly toward Thunderdome.  If a harpoon launched with the maximum possible velocity strikes this zombie and embeds in the zombie’s flesh, what is the velocity of the zombie immediately after being struck with the harpoon?
+  - Use a similar procedure here as you used in part 4 to find the range with a slight modification.
-  * Willard suggests you can increase the range of the harpoons if the harpoon launcher is not anchored to the floor, and thereby would recoil.  Would this work?  Use the lowest workable launch speed to confirm your prediction.  What is the new launch speed, and what is the recoil speed of the launcher/support?  The anchor and spring launcher have a mass of 400 kg (excluding the harpoon).
+  - Start with the vertical direction to find the time it takes the harpoon to reach the level of the zombies (hit the zombie).
-  * Draw a free-body diagram of the harpoon launcher as it slides along the concrete floor. What is the frictional force acting on the launcher during this slide, and using forces how far does it slide.  After all, you don’t want it to fall into the elevator shaft.
+  - Use the horizontal direction and the time from the previous step to get the range.
+**Part 6: Amount of ice**
+  - This is the non-review part of this problem.
+  - We'll use the energy principle here. What is in your system?
+  - For your given system, what are W and Q?
+  - Calculate the amount of ice needed.
+**Wrap up questions:**
+  * A 90 kg zombie is moving 1 m/s directly toward Thunderdome.  If a harpoon launched with the maximum possible velocity strikes this zombie and embeds in the zombie’s flesh, what is the velocity of the zombie immediately after being struck with the harpoon?
+    * The zombie slides with this velocity and friction causes it to come to a stop. What is the work done by friction during this slide? Also, the coefficients of friction between the zombie and the horizontal surface are  $\mu_s = 0.3$  and  $\mu_k = 0.2$ . How far does the zombie slide before coming to a stop?
+  * Willard suggests you can increase the range of the harpoons if the harpoon launcher is not anchored to the floor, and thereby would recoil.  Would this work?  Check your prediction by calculation.  What is the new launch speed, and what is the recoil speed of the launcher/support?  The anchor and spring launcher have a mass of 400 kg (excluding the harpoon).
+  * Draw a free-body diagram of the harpoon launcher as it slides along the concrete floor. What is the frictional force acting on the launcher during this slide? How far does it slide?  After all, you don’t want it to fall into the elevator shaft.
   * Sketch the trajectory of one of the launched harpoons. For a point halfway from where it is launched to where it strikes a zombie, draw a free-body diagram showing all forces acting on the harpoon. In the past when objects were in freefall, we used a vertical-horizontal coordinate system. Here, we'd like to investigate what the parallel and perpendicular components of the net force look like, and how they affect the motion. With this in mind, sketch the parallel and perpendicular components of the net force acting on the arrow.
+  * Assume you accidentally place a boulder at the top of the adjustable ramp, at the most distant point form the elevator shaft and the coefficient of sliding friction is half of what you used earlier. What is the magnitude of the acceleration as the boulder slides down the plane after the angle of the plane has been made large enough to get the boulder to move down the plane?
 We can use the momentum principle to express the net force as:
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   * Which term is the parallel component of the net force, and which term is the perpendicular component of the net force?
   * Which component causes the direction of the momentum to change, and which component causes its magnitude to change?
+  * Now, find the minimum distance your defending mechanism can reach and still hit a zombie. If you took our suggestions above and kept everything in variables, this is where you thank us.
+  * What would be the minimum distance of a harpoon if Willard's scheme of not anchoring a launcher were employed?