conservation of energy at the skate park lab answers

Section Scholarship Objectives

By the end of this section, you will comprise able to do the following:

• Explain the constabulary of conservation of energy in terms of mechanics and P.E.
• Perform calculations incidental kinetic and latent energy. Apply the law of nature of conservation of energy

Teacher Support

Teacher Support

The learning objectives in this section wish assistance your students master the following standards:

• (6) Science concepts. The student knows that changes occur inside a somatogenetic system and applies the laws of law of conservation of energy and momentum. The student is supposed to:
  • (B) investigate examples of kinetic and potential energy and their transformations;
  • (D) shew and apply the Pentateuch of conservation of Department of Energy and conservation of impulse in one dimension.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Work and Energy, as well as the undermentioned standards:

• (6) Science concepts. The scholarly person knows that changes go on within a physical system and applies the laws of law of conservation of energy and momentum. The student is expected to:
  • (B) investigate examples of moving and P.E. and their transformations;
  • (D) demonstrate and apply the Torah of preservation of energy and conservation of momentum in one dimension.

Segment Distinguish Terms

conservation of energy

Teacher Support

Teacher Support

[BL] [OL] Begin away distinguishing mechanical energy from other forms of energy. Excuse how the general definition of energy as the ability to do piece of work makes perfect sense in terms of either descriptor of mechanical energy. Discuss the law of conservation of energy and dispel any misconceptions correlative to this law, such is the idea that soul-stirring objects evenhanded slow bolt down naturally. Discover heat generated by friction as the usual explanation for apparent violations of the law.

[AL] Start a treatment about how different useful forms of energy also end up as wasted ignite, such American Samoa light, sound, and electricity. Try to get students to understand heat and temperature at a unit level. Explain that energy lost to rubbing is actually transforming kinetic energy at the small level to K.E. at the atomic level.

Mechanical Energy and Preservation of Energy

We saw earlier that mechanical energy can live either potency Beaver State kinetic. In this section we wish see how energy is transformed from one of these forms to the other. We will too see that, in a closed system of rules, the sum of these forms of energy cadaver constant.

Quite a spot of potential energy is gained by a roller coaster car and its passengers when they are raised to the top of the first hill. Remember that the possible part of the condition means that energy has been stored and can be utilized at another metre. You testament see that this stored energy can either be wont to work or tin can be transformed into K.E.. E.g., when an object that has gravitational P.E. falls, its energy is regenerate to K.E.. Think back that both work and energy are expressed in joules.

Refer back to Estimate 9.3. The amount of work required to produce the TV from point A to point B is equal to the measure of gravitational potential energy the TV gains from its height above the ground. This is generally true for some aim increased above the ground. If all the work done on an object is used to rear the objective above the ground, the amount turn equals the object's gain in gravitational potential energy. However, note that because of the work done by friction, these energy–work transformations are never perfect. Rubbing causes the loss of some useful energy. In the discussions to follow, we will use the bringing close together that transformations are frictionless.

Now, Lashkar-e-Tayyiba's look at the roller coaster in Fig 9.6. Work was done on the roller coaster to obtain information technology to the top of the first rise; at this point, the roller coaster has gravitational potential energy. IT is moving slowly, so it also has a small amount of K.E.. As the gondola descends the archetypical slope, its PE is reborn to KE. At the low point much of the originative PE has been changed to KE, and speed is at a supreme. As the car moves up the next slope, any of the KE is transformed back into PE and the railroad car slows down.

Figure 9.6 During this big dipper ride, there are conversions between potential drop and dynamic energy.

Teacher Support

Instructor Support

[OL] [AL] Ask if definitions of energy make up sense to the class, and try to bring unconscious whatever expressions of confusions or misconceptions. Help them make the logical leap that, if energy is the power to do work, information technology makes common sense that it is expressed by the same unit. Ask over students to constitute each the forms of energy they can. Ask if this helps them pose a finger for the nature of energy. Ask if they have a problem seeing how some forms of energy, such as sunlight, can do work.

[BL] [OL] You may want to introduce the concept of a reference point as the opening taper of motion. Relate this to the origin of a coordinate gridiron.

[BL] Get in clear that energy is a different property with different units than either force or power.

[OL] Help students understand that the speed with which the TV is delivered is not part of the calculation of PE. It is assumed that the stop number is constant. Whatever KE due to increases in delivery pelt along will glucinium lost when motion Chicago.

[BL] Be destined in that respect is a clear understanding of the preeminence between energising and potential drop energy and between velocity and acceleration. Explain that the word potential means that the vitality is available but information technology does not mean that it has to be used or will be used.

Virtual Physics

DOE Skate Park Bedroc

This model shows how kinetic and potency energy are related, in a scenario similar to the roller coaster. Find the changes in KE and PE by clicking on the legal community graph boxes. Also try the three other than shaped skate parks. Drag the skater to the dog to start the life.

Grasp Check

This simulation (HTTP://phet.CO.edu/nut/pretending/energy-skate-park-rudiments) shows how moving and potential energy are paternal, in a scenario similar to the roller coaster. Follow the changes in KE and PE by clicking along the bar chart boxes. Also hear the three otherwise formed skate parks. Drag the skater to the track to start the vivification. The ginmill graphs show how KE and PE are transformed rearmost and away. Which statement best explains what happens to the mechanical Energy Department of the system arsenic speed is increasing?

1. The mechanical Energy Department of the system increases, provided there is no red ink of muscularity imputable friction. The energy would transform to K.E. when the speed is increasing.
2. The mechanical Department of Energy of the system remains constant provided there is no passing of energy due to friction. The vim would transform to kinetic energy when the speed is increasing.
3. The mechanical energy of the system increases provided in that respect is no red ink of energy payable to friction. The muscularity would transform to P.E. when the speed is increasing.
4. The mechanical energy of the system clay constant provided there is no loss of energy cod to rubbing. The vigour would transform to potential energy when the speed is increasing.

Instructor Supporting

Teacher Support

This aliveness shows the transformations betwixt KE and PE and how speed up varies in the process. Advanced we can refer indorse to the animation to see how friction converts some of the mechanical energy into rut you said it total vitality is conserved.

Happening an current roller coaster, there are many ups and downs, and each of these is accompanied by transitions 'tween dynamic and potential zip. Assume that no vigour is cursed to friction. At any point in the ride, the total mechanical energy is the same, and information technology is equal to the energy the car had at the top of the 1st rise. This is a result of the law of first law of thermodynamics, which says that, in a closed arrangement, total energy is preserved—that is, IT is constant. Using subscripts 1 and 2 to represent first and final energy, this law is definite American Samoa

$$K{E}_1+P{E}_1=K{E}_2+P{E}_2\text{.}$$

Either side equals the totality mechanical energy. The phrase in a restricted system means we are forward no zip is lost to the environs ascribable friction and air resistance. If we are making calculations on dense falling objects, this is a advantageous assumption. For the roller coaster, this assumption introduces some inaccuracy to the reckoning.

Calculations involving Mechanical Energy and Preservation of Energy

Tips For Succeeder

When calculating figure out or energy, use units of meters for distance, newtons for force, kilograms for mass, and seconds for meter. This will assure that the ensue is express in joules.

Teacher Support

Teacher Support

[BL] [OL] Impress upon the students the momentous amount of knead compulsory to stick a roller coaster car to the top of the first, highest full stop. Compare IT to the amount of play it would go for walk to the elevation of the roller coaster. Ask students why they may feel tired if they had to walk or climb to the top of the roller coaster (they have to use energy to exert the force compulsory to relocation their bodies up against the force of gravity). Check if students can aright prognosticate that the ratio of the slew of the car to a person's mass would be the ratio of work done and push gained (for example, if the railcar's mass was 10 multiplication a person's mint, the amount of work needed to move the gondola to the top of the hill would be 10 multiplication the work needed to pass up the James Jerome Hill).

Watch Physics

Preservation of Energy

This video discusses conversion of PE to KE and preservation of energy. The scenario is identical akin to the big dipper and the skate park. It is also a good account of the energy changes studied in the snap research laboratory.

Teacher Support

Instructor Support

Before viewing the video, review altogether the equations involving kinetic and possible vigour and preservation of energy. Likewise constitute sure the students have a qualitative understanding of the energy transformation taking place. Refer back to the snap lab and the simulation research laboratory.

Grok Check

Watch Physics: First law of thermodynamics. This video introduces the law of law of conservation of energy and explains how P.E. is converted to K.E..

Did you expect the speed at the bottom of the slope to be the same A when the object vanish straight down? Which statement best explains why this is non just the casing in real-life situations?

1. The zip was the similar in the scenario in the vitality because the object was sliding on the ice, where there is extended amount of rubbing. In realistic life, much of the mechanical energy is lost as heat caused by friction.
2. The speed was the same in the scenario in the animation because the object was sliding on the meth, where there is small amount of friction. In real life, much of the mechanical energy is lost as heat caused by friction.
3. The speed was the same in the scenario in the animation because the object was sliding on the ice, where there is large amount of friction. In genuine life, no mechanical push is lost due to conservation of the mechanical vigor.
4. The quicken was the same in the scenario in the animation because the object was sliding on the ice, where there is littler amount of friction. In factual biography, no more mechanical energy is lost ascribable conservation of the mechanical vim.

Worked Example

Applying the Practice of law of Preservation of Energy

A 10 kg rock falls from a 20 m cliff. What is the kinetic and potential zip when the rock has fallen 10 m?

Strategy

Choose the equation.

$$K{E}_1+P{E}_1=K{E}_2+P{E}_2$$

9.4

$$\begin{array}{cc}KE=\frac{1}{2}m{v}_{}^2;& PE=mgh\end{array}$$

9.5

$$\frac{1}{2}m{v}_1^2+mg{h}_1=\frac{1}{2}m{v}_2^2+mg{h}_2$$

9.6

List the knowns.

m = 10 kilogram, v ₁ = 0, g = 9.80

h ₁ = 20 m, h ₂ = 10 m

Identify the unknowns.

KE ₂ and PE ₂

Substitute the known values into the equation and solve for the dishonorable variables.

Discussion

Alternatively, first law of thermodynamics equation could follow solved for v ₂ and KE ₂ could cost calculated. Greenbac that m could also live eliminated.

Tips For Achiever

Note that we can solve many problems involving spiritual rebirth between KE and PE without lettered the lot of the objective in question. This is because kinetic and potential energy are both proportional to the mass of the object. In a situation where KE = PE, we recognize that m g h = (1/2)m v ².

Dividing some sides by m and rearranging, we have the relationship

2g h = v ².

Instructor Support

Teacher Support

Kinetic and potential Energy are both proportional to the mass of the objective. In a situation where KE = PE, we jazz that m g h = (1/2)m v ². Dividing both sides aside m and rearranging, we get the kinship 2g h = v ².

Practise Problems

5 .

A child slides down a playground glide. If the slip up is 3 m altitudinous and the child weighs 300 N, how much P.E. does the shaver have at the top of the slide? (Cumuliform g to $$10m/s^2.$$ )

1. 0 J
2. 100 J
3. 300 J
4. 900 J

6 .

A 0.2 kg apple on an Malus pumila tree has a P.E. of 10 J. Information technology waterfall to the ground, converting all of its PE to kinetic energy. What is the velocity of the orchard apple tree just before IT hits the ground?

1. 0 m/s
2. 2 m/s
3. 10 m/s
4. 50 m/s

Snap Research lab

Converting P.E. to Kinetic Energy

In that activity, you bequeath calculate the potential energy of an physical object and predict the object's speed when all that P.E. has been converted to kinetic energy. You will then check up on your prediction.

You will cost dropping objects from a height. Be sure to stay a safe distance from the edge. Don't pinched over the railing too far. Make a point that you do not throw objects into an area where people or vehicles overstep by. Make sure that dropping objects will not cause damage.

You leave need the following:

Materials for apiece pair of students:

• Four marbles (operating theater similar small, dense objects)
• Stopwatch

Materials for class:

• Metric measuring tape long enough to measure the chosen height
• A scale

Instructions

Procedure

1. Go with a partner. Find out and record the mass of four small, dense objects per group.
2. Choose a fix where the objects can equal safely dropped from a height of at least 15 meters. A bridge over water supply with a safe uninteresting paseo will work well.
3. Measure the distance the object leave recede.
4. Bet the P.E. of the object before you drop it using PE = m g h = (9.80)mh.
5. Predict the K.E. and velocity of the objective when it lands using PE = KE and so, $mgh=\frac{m{v}^2}{2};v=\sqrt{2(9.80)h}=4.43\sqrt{h}\text{.}$
6. Matchless partner drops the object piece the other measures the time information technology takes to downslop.
7. Take turns being the dropper and the timer until you have made quaternary measurements.
8. Average your drop increased by and calculate the velocity of the object when information technology landed using v = a t = g t = (9.80)t.
9. Comparison your results to your forecasting.

Teacher Support

Instructor Financial support

Ahead students begin the lab, find the nearest location where objects can be dropped safely from a height of at least 15 m.

As students go through the lab, encourage lab partners to discuss their observations. Encourage them to discuss differences in results between partners. Ask if in that location is any confusion about the equations they are using and whether they seem binding settled happening what they have already knowing about mechanic energy. Ask them to discuss the effect of breeze resistance you said it density is related to that effect.

Grasp Check

Galileo's experiments tried that, contrary to popular belief, heavy objects behave not fall behind faster than light objects. How do the equations you used support this fact?

1. Heavy objects do non fall faster than the light objects because while preserving the mechanical energy of the system, the mass term gets cancelled and the velocity is independent of the volume. In real life, the variation in the velocity of the different objects is observed because of the not-zilch air electric resistance.
2. Heavy objects do not fall quicker than the ignite objects because while conserving the mechanical energy of the system, the mass terminus does not pay off off and the velocity is dependent on the mass. In sincere life history, the mutant in the velocity of the different objects is determined because of the cardinal aura electric resistance.
3. Heavy objects do not fall faster than the light objects because while conserving the natural philosophy vim the system, the people condition gets cancelled and the velocity is separatist of the the great unwashed. In real world, the variation in the velocity of the unusual objects is observed because of zero air resistance.
4. Heavy objects exercise not light quicker than the incandescent objects because spell preserving the mechanized energy of the system of rules, the mass terminus does not suffer cancelled and the speed is dependent on the multitude. In real life, the variation in the speed of the different objects is observed because of zero transmit resistance.

Check Your Understanding

7 .

Describe the transformation between forms of machine push that is happening to a down skydiver before her parachute opens.

1. Dynamical push is being changed into potential energy.
2. Potential energy is being transformed into K.E..
3. Work is being transformed into K.E..
4. K.E. is being changed into work on.

8 .

True or false—If a rock is tangled into the air, the increase in the pinnacle would increase the rock's kinetic muscularity, and so the increase in the speed as it waterfall to the ground would increase its potential energy.

1. True
2. False

9 .

Identify equivalent terms for stored Energy and energy of motion.

1. Stored vigor is potential muscularity, and energy of motion is kinetic energy.
2. Energy of motion is P.E., and stored muscularity is kinetic get-up-and-go.
3. Stored push is the potential besides as the kinetic energy of the system.
4. Energy of motion is the potential too as the kinetic energy of the system.

Teacher Support

Teacher Support

Utilisation the Check Your Understanding questions to assess students' achievement of the section's learning objectives. If students are struggling with a proper objective, the Delay Your Reason wish help identify which one and direct students to the applicable content.

conservation of energy at the skate park lab answers

Source: https://openstax.org/books/physics/pages/9-2-mechanical-energy-and-conservation-of-energy