Student Exploration: Inclined Plane – Simple Machine (ANSWER KEY)

Student Exploration: Inclined Plane – Simple Machine
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.
What could Jan use to make loading furniture on the van easier?
Why would this help?.
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.
The brick has a weight of 300 newtons (N).
How much force would it take to lift the brick straight up?
Set the External force to On. A car appears, ready to push on the brick. Set the Applied force to 100 N and click Play (). What happens?
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?

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?

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 inclined plane breaks this force down into two components: one parallel to the inclined plane (W||) and one perpendicular to the inclined plane (W).
Infer: Which force (W|| or W) will cause the brick to slide down the plane?
Calculate: To calculate a ratio, divide the two numbers being compared.
What is the ratio of W|| to the Weight of the brick?
What is the ratio of Wto the Weight of the brick?
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:                                  Cos:                                      Tan:
Synthesize: Describe any relationships you see between the ratios you calculated and the sine, cosine, and/or tangent of the inclined plane’s angle.
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||=
Apply: If the brick’s weight is 500 N and the plane’s angle is 40°, what will W||and Wbe? Use the Gizmo to check your answer.
W=                                             W||=
Solve: As the weight of the brick pushes down on the inclined plane, the inclined plane pushes up against the brick. This upward force is called the normal force.
What is the relationship between the normal force and W?
The net force on the brick is the resultant force. What is its value?
What force is equal to the resultant force?
Select the SIMULATION tab. What is the mass of the brick?
The formula for force is: Force = mass × acceleration. Use this formula to calculate what the brick’s acceleration should be:
Use the Gizmo to check your answer. (Click Play, and then select the TABLE tab and look at the a (m/s2) column. Downward accelerations are negative.)
Make connections: Click Reset. On the CONTROLS tab, switch the External force to On. Set the Applied force to 100 N. Select the FREE-BODY DIAGRAM tab. The green vector represents the force the car exerts on the brick.
How does the direction of the applied force compare to the direction of W||?
Is the applied force enough to push the brick up the ramp? Explain.
What is the minimum applied force needed to push the brick up the ramp?
Use the Gizmo to check your answer. What applied force did you use?
Activity C:

Friction and efficiency
Get the Gizmo ready:
  • Click Reset. Set the Angle to 37°, Coeff. of friction (μ) to 0.25 and the Weight to 450 N.
  • Switch the External force to Off.
 

Introduction: Wherever two surfaces meet, the force of friction acts to oppose any motion.

Question: How does friction affect an inclined plane?
Observe: Select the FREE-BODY DIAGRAM tab. The teal blue vector represents friction.
How does the friction vector relate to the direction of movement?
What is the magnitude of the friction force?
Divide the magnitude of the friction by the normal force. How does this ratio compare to the coefficient of friction?
Calculate: The coefficient of friction (μ) is the ratio of the force of friction (Ff)to W:
 μ = Ff ÷ W
If μ = 0.42 and W= 563 N, what would be the force of friction?
Explain: Switch the External force to On. Set the Applied force to 400 N and observe the Friction vector.
Why do you think the friction vector changed direction
What are the magnitudes of Ff, W||, and the applied force?
Ff:                                     W||:                                  Applied force:
How is the resultant force calculated, and what is its value?
What happens if the applied force is greater than W|| but less than W|| + Ff?

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