Gizmo Inclined Plane - Rolling Objects

Name: Max Gunther Date: 3-4-26 Student Exploration: Inclined Plane – Rolling Objects Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. [Note to teachers and students: This Gizmo was designed as a follow-up to the Inclined Plane – Sliding Objects Gizmo. We recommend doing that activity before trying this one.] Vocabulary: moment of inertia, rotational kinetic energy, translational kinetic energy Prior Knowledge Question (Do this BEFORE using the Gizmo.) A boy rolls an old car tire down a hill. It goes pretty fast, but he wants the tire to go even faster. So, the boy climbs inside and rolls down the hill inside the tire. Assuming there are no crashes, how do you think the speed of the tire with the boy inside will compare to the speed of the empty tire? Explain your answer. With more weight, the tire speeds up, but a tire with no boy will be the same or faster than the tire with the boy in it. Gizmo Warm-up Do all round objects roll at the same rate, or does their distribution of mass make a difference? You can explore this question with the Inclined Plane – Rolling Objects Gizmo. On Ramp 1, select a Ring of Steel on a Frictionless ramp. On Ramp 2, select a Disk of Steel on a Frictionless ramp. Check that each ramp has an Angle of 20°.​ 1.​ Click Play ( ).What was the result of the race to the bottom? Both landed at the same time 2.​ On a frictionless ramp, neither object will roll. Instead, they will slide. Click Reset ( material of each ramp to Wood. Click Play. Which object wins the race this time? 3.​ Which object is similar to an empty tire? ), and change the disk of steel ring of steel Which is similar to a tire with a person inside of it? disk of steel Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved Activity A: Ring vs. block Get the Gizmo ready: ●​ Click Reset. ●​ For Ramp 1, choose a Block of Steel on an Ice ramp. ●​ For Ramp 2, choose a Ring of Steel on an Ice ramp. Introduction: A sliding object has a type of kinetic energy, called translational kinetic energy, which is equal to half the object’s mass multiplied by the square of its velocity. A rotating object, such as a spinning top, has a different type of kinetic energy, called rotational kinetic energy. A rolling object has both translational and rotational kinetic energy. Question: How is potential energy converted to kinetic energy for a rolling object? 1.​ Predict: Which object do you think will reach the bottom of the ramp first? Explain your choice: the ring because is a circle and is more faster than a block 2.​ Observe: Click Play. Which object reached the bottom first? block How did the motion of the ring differ from that of the block? glide 3.​ Record: Select the ENERGY tab and turn on Show values. Complete the table below. Object KE (translational) KE (rotational) Energy lost Block 73 0 27 Ring 49 49 2 4.​ Analyze: Compare the energy distribution of each object at the bottom of the ramp. ​ A.​ Which object lost more energy to friction? block B.​ Which object had more translational kinetic energy at the bottom? block C.​ If the ring lost so much less energy to friction than the block, why did it lose the race? because much of its potential energy is converted to rotational kinetic energy rather than translational kinetic energy 5.​ Investigate: Does the angle of the ramp affect the results of a race between the block and the ring? Use the Gizmo to find out. Describe the results of your investigation below. no, the result will remain the same because the block slides faster Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved ​ Get the Gizmo ready: Activity B: ●​ ●​ ●​ ●​ The fastest rollers Click Reset. For Ramp 1, choose a Disk of Steel on an Ice ramp. For Ramp 2, choose a Ball of Steel on an Ice ramp. Set the Angle of both ramps to 20°. Introduction: In activity A, you discovered that a ring can lose a race with a block because much of its potential energy is converted to rotational kinetic energy rather than translational kinetic energy. In this activity, you will compare the translational and rotational kinetic energies for a variety of rolling objects. Question: What are the fastest rolling objects? 1.​ Predict: The Gizmo allows you to experiment with a disk, a ring, a solid ball, and a hollow sphere. Predict which will be the slowest and fastest objects by ranking them below. Slowest sphere ring disk ball Fastest disk ball Fastest 2.​ Experiment: Use the Gizmo to find the actual order: Slowest ring sphere 3.​ Gather data: For each object, list the percentage of potential energy that was converted to translational kinetic energy, converted to rotational kinetic energy, and lost to friction. Object KE (translational) KE (rotational) Energy lost Disk 65 32 3 Ring 49 49 2 Solid ball 69 28 3 Hollow sphere 58 39 3 4.​ Analyze: Look at the results in the data table and from your racing experiment. A.​ How does the final percentage of translational kinetic energy relate to the speed of the object? ​ dont really know about this one B.​ In general, which rolls faster, hollow objects like the ring and sphere or solid objects like the disk and ball? The hollow cylinder or ring or hoop has all its mass a a distance r away from its ax is of rotation C.​ Why do you think this is the case? Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved ​ is for the distance and the mass Activity C: ​ Moment of Inertia Get the Gizmo ready: ●​ For Ramp 1, choose a Disk of Steel on an Ice ramp. ●​ For Ramp 2, choose None. Introduction: The moment of inertia (I) of an object is a value that represents the object’s resistance to rotating. The moment of inertia for many objects is given by the formula: I = kmr 2 In this formula, m is the mass, r is the radius, and k is a constant that represents how far the mass is distributed away from the axis of rotation. Question: How does an object’s distribution of mass relate to how fast it rolls? 1.​ Calculate: The value of k for a rolling object can be found by determining the ratio of its rotational kinetic energy (RKE) to its translational kinetic energy (TKE): Calculate the value of k for each rolling object in the Gizmo. (Note: You can use the data you collected for each object in activity B, or collect new data.) Disk: .49 Ring: 1 Ball: .40 Sphere: .67 2.​ Analyze: Look at the moment of inertia equation, the values of k listed above, and the results of the races between objects in activity B. A.​ How do you think the value of k relates to the moment of inertia for each object? kinetic energy of a rotating rigid body is directly proportional to the moment of inert ia and the square of the angular velocity. B.​ How does the value of k affect how fast each object rolls? always roll down the ramp faster than a hollow object of the same shape (sphere or cylinder)—regardless of their exact mass or diameter. 3.​ Find a pattern: Suppose a ring and a disk have the same mass and radius. A.​ Which object has its mass distributed as far as possible from the axis of rotation? the block will arrive faster because it is smooth and more veils than the ring B.​ Which object has a greater moment of inertia? ring Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved ​ C.​ Which object will roll down a ramp most quickly? block Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved ​ 4.​ Make a rule: In general, how does the distribution of mass affect the moment of inertia, the translational kinetic energy, and the speed of a rolling object? Explain your rule in detail. Nope. Moment of Inertia depends on both the mass and the distribution of the mass. Further away from the axis of rotation, a unit of mass will cause a greater moment of inertia 5.​ Explain: Why does a solid ball roll faster than a hollow sphere? the solid sphere will have more of its mass at a smaller distance from the axis of rotation 6.​ Challenge: Suppose two rings are at the top of a ramp. The rings have the same mass, but one ring has a much larger radius than the other. Which ring will win the race to the bottom, and why? (Hint: Consider the potential energy, translational kinetic energy, and rotational kinetic energy of each ring.) Based on the equation above, the velocity of each ring will only be based on the gravitational constant and height of the ramp. Since the radius doesn't determine the velocity ,both rings will hit the bottom at the same time. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved