Inclined Plane – Simple Machine Answer Key Vocabulary: coefficient of friction, efficiency, force, free-body diagram, friction, inclined plane, mechanical advantage, mechanical energy, normal force, resultant force, simple machine, vector, work, work-energy theorem Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is to activate prior knowledge and get students thinking. Students are not expected to know the answers to the Prior Knowledge Questions.] Jan is moving to a new apartment. She needs to load her sofa and other large furniture into a moving van. The rear of the moving van is 1.5 meters high. 1. What could Jan use to make loading furniture on the van easier? Answers will vary. Sample answer: Jan could use a ramp to load the furniture. 2. Why would this help? Answers will vary. Sample answer: By using a ramp, Jan would not have to directly lift the furniture into the back of the truck. Gizmo Warm-up A simple machine can be used to make tasks like lifting heavy weights easier. One example of a simple machine is a ramp, or inclined plane. You can use the Inclined Plane – Simple Machine Gizmo to see how inclined planes can help to lift objects. On the CONTROLS pane, make sure the Angle is 30°, the Coeff. of friction is 0.00, and the Weight is 300 N. 1. The brick has a weight of 300 newtons (N). How much force would it take to lift the brick straight up? Slightly more than 300 N 2. Set the External force to On. Set the Applied force to 100 N and click Play ( ). What happens? The brick and car slide down the ramp. 3. Click Reset ( ). Using the Gizmo, find the smallest force that is required to push the block up the 30° ramp. What is the smallest force required? 151 N [The nearest slider setting is 155 N.] Activity A: Redirection of force Get the Gizmo ready:  Turn Off the External force. Click Reset.  Set the Angle to 30° and the Weight to 300 N. Question: How does an inclined plane redirect a force? 1. Observe: Select the FREE-BODY DIAGRAM tab. Make sure Magnitude is on. A free-body diagram is a picture that uses vectors to show the different forces acting on an object. What does the purple arrow pointing down represent? The weight of the brick The inclined plane breaks this force down into two components: one parallel to the inclined plane (W||) and one perpendicular to the inclined plane (W ). 2. Infer: Which force (W|| or W ) will cause the brick to slide down the plane? W|| 3. Calculate: To calculate a ratio, divide the two numbers being compared. A. What is the ratio of W|| to the Weight of the brick? 0.5 B. What is the ratio of W to the Weight of the brick? 0.8667 C. Sine (sin), cosine (cos), and tangent (tan) are ratios of the lengths of a right triangle’s sides. Use a calculator to find the sin, cos, and tan of the inclined plane’s Angle. Sin: 0.5 Cos: 0.866 Tan: 0.577 4. Synthesize: Describe any relationships you see between the ratios you calculated and the sine, cosine, and/or tangent of the inclined plane’s angle. The ratio of W|| to the weight of the brick equals the sine of the plane’s angle, and the ratio of W to the weight of the brick equals the cosine of the plane’s angle 5. Make a rule: Use the relationships you found to write a formula for W|| and W in terms of weight (W) and angle (θ): W = W(cos θ) W|| = W(sin θ) 6. Apply: If the brick’s weight is 500 N and the plane’s angle is 40°, what will W|| and W be? Use the Gizmo to check your answer. W = 383.02 N W|| = 321.39 N