Machines

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Science Simulations, Technology Simulations, Engineering Simulations, Mathematics Simulations

Lesson 13: Inclined Plane Factors

Inclined planes are simple machines that provide a way to increase the mechanical advantage of a given system. Inclined planes reduce the amount of force required to complete work; however, they do so at the expense of having to move an object a longer distance. Can you determine how these machines work?

Doing the science

Part I. The Plane

Start the Machines Simulation by clicking on the “Simulation” tab.
Click the “Inclined Planes” button at the bottom of the screen.
Make sure that the inclined plane angle is set on 0º and the 1.0-kilogram mass is attached to the Force device.
Click the “Pull” button on the Force Device. Note and record in Table 1 the force value after the mass is moving.
Click the “Reset” button.
Change the inclined plane angle to 10º by using the red up and down arrows.
Repeat step 4, making sure to note and record your data in Table 1.
Repeat steps 6 and 7 for inclined plane angles of 20 º, 30 º, and 40 º.
Repeat the Part I experiment using the 2.0-kilogram mass. Make sure to record your data in Table 2.

Part II. Friction

Make sure that the inclined plane angle is set on 0º and the 1.0-kilogram mass is attached to the Force device.
Select the “Pull” button on the Force device. Note and record in Table 3 the initial force value displayed in the Force Device before the mass begins to move (Max) and the force value after the mass is moving (Current).
Select the “Reset” button.
Select on the 2.0-kilogram mass to replace the 1.0-kilogram mass on the inclined plane.
Repeat step 11, making sure to note and record your data in Table 3.

Part III. Coefficient of Friction

Use the following equation to convert the masses (m) (1.0 and 2.0 kilograms) from Part II into weight, which is the force (fg) due to gravity (in newtons). Record the forces in Table 4.

fg = mg where (g = 9.80 m/s2)
Copy the data from Table 3 for the columns of Force Before Mass Begins Moving (fb) and Force While Mass Is Moving (fm) into Table 4 below.
To find the coefficient of static friction (µ_s), divide f_b by _fg. This value is called the static friction coefficient because the mass is not yet moving. Calculate and record µ_s for each mass (1.0 and 2.0-kg) in Table 5.
To find the coefficient of kinetic friction (µ_s), divide f_b by _fg. This value is called the kinetic friction coefficient because the mass is not yet moving. Calculate and record µ_s for each mass (1.0 and 2.0-kg) in Table 5.

Table 1. Inclined Plane Angle and Moving Forces for 1.0-Kg

Angle (º)	Force While Mass Is Moving (Current Force in Newtons)
0
10
20
30
40

Table 2. Inclined Plane Angle and Moving Forces for 2.0-Kg

Angle (º)	Force While Mass Is Moving (Current Force in Newtons)
0
10
20
30
40

Table 3. Frictional Forces

Mass (kg)

Force Before Mass Begins Moving (Max Force in Newtons)

Force While Mass Is Moving

(Current Force in Newtons)

1.0

2.0

Table 4. Gravitational and Frictional Forces

Mass (kg)

Force Due to Gravity (fg)

(Newtons)

Force Before Mass Begins Moving (fb)

(Newtons)

Force While Mass Is Moving (fm)

(Newtons)

1.0

2.0

Table 5. Coefficients of Friction

Mass (kg)	μs	μk
1.0
2.0

Do You Understand?

How did the distance the mass traveled along the inclined plane compare to the height the mass moved above the tabletop?

Which inclined plane angle required the smallest force to move the mass to the top of the inclined plane?

How much force (in newtons) would have been required if no inclined plane was used to lift the mass up to the same height as the top of the inclined plane? Explain how the inclined plane made the task easier?

A direct relationship is when one variable increases, the other variable also increases. An inverse relationship is when one variable increases the other variable decreases. What is the relationship between the inclined plane angle and the force required to lift the mass up the incline plane? Please support your answer with evidence.

Work in is defined as the effort force times the distance the mass moves along the inclined plane. Work out is the load force (force on the mass due to gravity) times the height the mass was lifted. Imagine a 2.00-kilogram mass moved 2.00 meters up along an inclined plane with an effort force of 13.80 newtons. The mass reaches a final height of 1.40 meters straight up above the tabletop.

a. What is the work out for this system?

b. What is the work in for this system?

c. How does the work out compare to the work in for this system?

A student stated that an inclined plane is capable of multiplying the amount of work a person can do. Discuss whether you agree or disagree with this student’s statement. Please support your response with evidence.

What is the value of the force of friction for the 1.0-kg mass while moving for Part II of this investigation?

How did the force required to start the mass moving up the inclined plane compare to the force required to keep the mass moving? Provide a reason for this difference in required forces.

If the inclined plane surface was significantly rougher, how would the forces required to move the masses have changed? Please provide a reason for your answer.

Which coefficient was larger, µ_s or µ_k? Provide a possible explanation for this observation.

Does the size of the mass on the surface affect the value of µ_s or µ_k? Provide a possible explanation for your response and support your response with evidence.