Student Exploration: Inclined Plane Sliding Objects
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1 Name: Date: Student Exploration: Inclined Plane Sliding Objects Vocabulary: acceleration, coefficient of friction, conservation of energy, friction, gravitational potential energy, inclined plane, kinetic energy, potential energy, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Two skiers are at the top of a mountain. Amanda decides to go down a steep trail that leads directly to the bottom. Brandon decides to take a longer, more gradual trail. 1. Assuming neither skier tries to slow down, who will reach the bottom first? 2. Who will be going faster at the bottom? Explain. Gizmo Warm-up The two ski trails are examples of inclined planes. As objects move from the top of an inclined plane to the bottom, their potential energy, or energy of position, is converted into kinetic energy, or energy of motion. This process is explored in the Inclined Plane Sliding Objects Gizmo. To begin, check that Ramp 1 has a block on a Frictionless ramp with an Angle of Click Play ( ). How does the block s speed change as it slides? 2. Select the TABLE tab and scroll to the bottom of the table. A. What is the final velocity (v) of the block? B. What is the acceleration (a) of the block? The acceleration of the block is equal to how much its velocity increases each second. 3. Click Reset ( ). On the CONTROLS tab, change the Angle of Ramp 1 to 60. Select the TABLE tab and click Play. What is the final velocity and acceleration of the block this time? Final velocity: Acceleration: Did the steepness of the plane affect the final velocity of the block?
2 Activity A: Potential and kinetic energy Get the Gizmo ready: Click Reset. Check that the Angle of Ramp 1 is 60. Introduction: Potential energy is energy of position or shape. In this Gizmo, the block at the top of the ramp has gravitational potential energy, which is equal to the product of the block s weight and height: GPE = wh. The weight of an object is equal to the product of its mass and gravitational acceleration, which is 9.8 m/s 2 on Earth s surface. So, GPE = 9.8 m/s 2 m h. Question: How is potential energy converted into kinetic energy? 1. Predict: As the block slides down the ramp, how do you expect the gravitational potential energy and kinetic energy of the block to change? 2. Observe: Select the ENERGY tab, and turn on Show values. Click Play. A. What happens to the potential energy (PE) over time? B. What happens to the kinetic energy (KE) over time? C. Click Reset. Click Play, and then click Pause ( ) when the block is about halfway down the plane. What is the sum of the potential and kinetic energy percentages? PE %: KE %: PE % + KE %: 3. Observe: Click Reset. Select the GRAPH tab, and check that the graph shows Energy vs. Time. Click Play. What do you notice? 4. Confirm: Repeat the experiment with ramps of varying steepness. Does the same pattern hold true? Explain. This demonstrates the law of conservation of energy, which states that in a closed system, energy is neither created nor destroyed. (Activity A continued on next page)
3 Activity A (continued from previous page) 5. Manipulate: The kinetic energy (KE) of an object is equal to half of its mass (m) multiplied by the square of its velocity (v): 1 KE mv 2 2 Rearrange the terms in this equation to solve for velocity: v = 6. Calculate: If you know the kinetic energy and mass of an object, you can use this formula to calculate the velocity of the object. Click Reset. Change the graph to Kinetic energy vs. Time, and click Play. A. What is the approximate final kinetic energy of the block? B. If the block had a mass of 1.0 kg, what is the final velocity of the block? Show your work. (Note: The units of velocity are meters per second (m/s).) C. Select the TABLE tab. What is the actual final velocity of the block? 7. Apply: A 3-kg block sits at the top of a frictionless ramp that has a height of 6.4 meters. The weight of the block is 29.4 newtons. A. What is the initial gravitational potential energy of the block? B. What will be the block s kinetic energy at the bottom of the ramp? C. What will be the block s velocity at the bottom of the ramp? 8. Think and discuss: Why doesn t the steepness of a frictionless ramp affect the velocity of the block at the bottom of the ramp? (Hint: Discuss conservation of energy in your answer.)
4 Activity B: Friction Get the Gizmo ready: Click Reset. On the CONTROLS pane, select a block on a ramp for Ramp 1. Select a block on a ramp for Ramp 2. Set the Angle of both ramps to 45. Introduction: Friction is a force that opposes motion. The coefficient of friction (μ) is a value that represents how much friction exists between an object and a surface. Question: How does friction affect a block sliding down an inclined plane? 1. Predict: Which block do you think will slide down the ramp most quickly? 2. Observe: Select the ENERGY tab. Click Play. A. Which block reached the bottom first? B. For the steel block, what percentage of its potential energy was converted into kinetic energy? What percentage was lost due to friction? C. For the rubber block, what percentage of its potential energy was converted into kinetic energy? What percentage was lost due to friction? D. Which block was more affected by friction? Explain. 3. Observe: Click Reset. Change the Angle of both ramps to 20. Click Play. What happens? In some cases, the friction is so great that the object doesn t move at all! 4. Gather data: On the CONTROLS pane, turn on Show coefficient of friction for each ramp. Use the Gizmo to find the smallest ramp angle that still allows each block to slide. Use a calculator to find the sine (sin), cosine (cos), and tangent (tan) of that angle. Block Ramp Angle Sine Cosine Tangent μ (Activity B continued on next page)
5 Activity B (continued from previous page) 5. Analyze: What pattern do you notice? You can use this relationship to calculate an unknown coefficient of friction. 6. Apply: Click Reset. Turn off Show coefficient of friction for each ramp. For each combination of materials, use the Gizmo to find the smallest ramp angle that still allows each block to slide. Use a calculator to find each coefficient of friction. Then, turn on Show coefficient of friction and record the actual values. Block Ramp Angle μ (calculated) μ (actual) Ice Ice 7. Interpret: Which combination resulted in the greatest friction? Which combination had the least friction? 8. Analyze: Based on your results, which factors do you think are most important in determining the amount of friction between two surfaces? 9. Think and discuss: When an object slides down a ramp with friction, the kinetic energy at the bottom of the ramp is not equal to the potential energy at the top. Why doesn t this situation violate the law of conservation of energy?
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= 1 2 kx2 dw =! F! d! r = Fdr cosθ. T.E. initial. = T.E. Final. = P.E. final. + K.E. initial. + P.E. initial. K.E. initial =
Practice Template K.E. = 1 2 mv2 P.E. height = mgh P.E. spring = 1 2 kx2 dw =! F! d! r = Fdr cosθ Energy Conservation T.E. initial = T.E. Final (1) Isolated system P.E. initial (2) Energy added E added
Dynamics Review Checklist
Dynamics Review Checklist Newton s Laws 2.1.1 Explain Newton s 1 st Law (the Law of Inertia) and the relationship between mass and inertia. Which of the following has the greatest amount of inertia? (a)