Download Inclined Plane Sliding Objects Answer Key

Inclined Plane – Sliding Objects
Answer Key
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.)
[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.]
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? Amanda
2. Who will be going faster at the bottom? Explain. Answers will vary.
[If there was no friction and neither skier tries to slow down, both skiers will theoretically be
going the same speed at the bottom. With friction, Amanda will be going faster.]
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 Steel block on a
Frictionless ramp with an Angle of 20°.
1. Click Play (
). How does the block’s speed change as it slides? The block speeds up.
2. Select the TABLE tab and scroll to the bottom of the table.
A. What is the final velocity (v) of the block? 4.43 m/s
B. What is the acceleration (a) of the block? 3.36 m/s2
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: 4.43 m/s
Acceleration: 8.50 m/s2
Did the steepness of the plane affect the final velocity of the block? No
Activity A:
Get the Gizmo ready:
Potential and
kinetic energy
Click Reset.
Check that Ramp 1 is a Frictionless ramp.
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/s2 on Earth’s surface. So, GPE = 9.8 m/s2·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?
Predictions will vary.
2. Observe: Select the ENERGY tab, and turn on Show values. Click Play.
A. What happens to the potential energy (PE) over time? Decreases
B. What happens to the kinetic energy (KE) over time? Increases
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 %: Values will vary.
KE %: Values will vary.
PE % + KE %: 100%
3. Observe: Click Reset. Select the GRAPH tab, and check that the graph shows Energy vs.
Time. Click Play. What do you notice?
The total energy of the block does not change as it slides down the inclined plane.
4. Confirm: Repeat the experiment with ramps of varying steepness. Does the same pattern
hold true? Explain.
Yes. No matter how steep the ramp is, the total energy of the block always remains the
same, around 10 joules.
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)
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):
KE
1 2
mv
2
Rearrange the terms in this equation to solve for velocity:
v=
2 KE
m
6. Demonstrate: If you know an object’s mass and height, you can determine its gravitational
potential energy. You can then use conservation of energy to determine the object’s kinetic
energy when it slides to the bottom of a frictionless ramp. Finally, you can determine the
object’s final velocity because you know its kinetic energy and mass.
Click Reset. In the Gizmo, the object has a mass of 1 kg and an initial height of 1 m.
A. What is the initial gravitational potential energy of the block? 9.8 J
B. Based on conservation of energy, what will be the kinetic energy of the block when it
gets to the bottom? 9.8 J
C. What will be the final velocity of the block? 4.43 m/s
Show your work:
v
2 KE
m
2 9.8
1
19.6 = 4.43 m/s
D. Click Play and select the TABLE tab. What is the block’s final velocity? 4.43 m/s
E. How does this experiment demonstrate conservation of energy?
The block’s final velocity was 4.43 m/s, which meant that its final kinetic energy (and
total energy) was 9.8 J. This is equal to the block’s potential energy (and total
energy) at the top of the ramp. No energy was lost or gained in the experiment.
7. 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.)
Because energy is conserved, the kinetic energy of a block at the bottom of a frictionless
ramp is equal to the gravitational potential energy of the block at the top of the ramp. This
value is proportional to the square of the block’s velocity at the bottom of the ramp.
Therefore, the block’s final velocity depends on the height of the ramp but not the steepness
of the ramp.
Get the Gizmo ready:
Activity B:
Click Reset. On the CONTROLS pane, select a
Steel block on a Wood ramp for Ramp 1. Select
a Rubber block on a Wood ramp for Ramp 2.
Set the Angle of both ramps to 45°.
Friction
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? Answers will vary.
2. Observe: Select the ENERGY tab. Click Play.
A. Which block reached the bottom first? The steel block
B. For the steel block, what percentage of its potential energy was converted into kinetic
energy? 50%
What percentage was lost due to friction? 50%
C. For the rubber block, what percentage of its potential energy was converted into
kinetic energy? 10%
What percentage was lost due to friction? 90%
D. Which block was more affected by friction? Explain.
The rubber block lost 40% more energy to friction than the steel block. Therefore, the
rubber block was affected more by friction.
3. Observe: Click Reset. Change the Angle of both ramps to 20°. Click Play. What happens?
Neither block moves.
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
Steel
Wood
27°
0.454
0.891
0.510
0.500
Rubber
Wood
42°
0.669
0.743
0.900
0.900
(Activity B continued on next page)
Activity B (continued from previous page)
5. Analyze: What pattern do you notice?
In each experiment, the coefficient of friction is close to the tangent of the minimum angle
required for the block to slide.
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
Rubber
<20°
<0.36
0.250
Rubber
Steel
59°
1.66
1.600
Wood
Ice
<20°
<0.36
0.100
Steel
Steel
37°
0.75
0.750
Wood
Wood
22°
0.40
0.400
Rubber
Rubber
55°
1.43
1.400
7. Interpret: Which combination resulted in the greatest friction? Rubber on steel
Which combination had the least friction? Wood on ice
8. Analyze: Based on your results, which factors do you think are most important in
determining the amount of friction between two surfaces?
Answers will vary. Sample answer: All the materials are fairly smooth, but softer materials
such as rubber seem to have more friction than harder materials such as steel and wood.
Ice had the least friction because it typically has a thin layer of water on its surface, which
acts as a lubricant.
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?
Sample answer: When friction is present, some potential energy is converted into sound and
heat rather than kinetic energy. The total energy of the system is still the same.