The principle of the conservation of mechanical energy and its application

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Zasada zachowania energii mechanicznej i jej zastosowanie

You will learn

to apply the principle of the conservation of mechanical energymechanical energymechanical energy to describe natural phenomena and to make calculations in English.

Exercise 1

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Source: GroMar, licencja: CC BY 3.0.

nagranie abstraktu

A small flowerpot with the mass of 0,5 kg is falling down (as a result of inattention) from the edge of the balcony which is at the height of 20 m. Assume that no resistance force is working on the flowerpot. The flowerpot is moving with acceleration of $10 \frac{m}{s^{2}}$ .

Rewrite to your notebook and complete the table below by inserting the appropriate values of height, velocity, potential energy, kinetic energy and mechanical energymechanical energymechanical energy in the SI system.


$h [m]$	$v [\frac{m}{s}]$	$E_{p} [J]$	$E_{k} [J]$	$E_{m} [J]$
10	0	50	0
9,2	4
8,2	6
		34	16
		25	25
2,8			36
0,2			49


$h [m]$	$v [\frac{m}{s}]$	$E_{p} [J]$	$E_{k} [J]$	$E_{m} [J]$
10	0	50	0	50
9,2	4	46	4	50
8,2	6	41	9	50
6,8	8	34	16	50
5	10	25	25	50
2,8	12	14	36	50
0,2	14	1	49	50

Exercise 2

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nagranie abstraktu

The flowerpot fell down just next to John. He was very upset by this fact and he threw this pot vertically up from the ground level. As a result, the pot had the vertical upward velocity of $15 \frac{m}{s}$ .


$h [m]$	$v [\frac{m}{s}]$	$E_{p} [J]$	$E_{k} [J]$	$E_{m} [J]$
0	15	0	56,25
2,8	13	14	42,25
	11	26
	9	36
8,8			12,25
10			6,26
10,8	3
11,25


$h [m]$	$v [\frac{m}{s}]$	$E_{p} [J]$	$E_{k} [J]$	$E_{m} [J]$
0	15	0	56,25	56,25
2,8	13	14	42,25	56,25
5,2	11	26	30,25	56,25
7,2	9	36	20,25	56,25
8,8	7	44	12,25	56,25
10	5	50	6,26	56,25
10,8	3	54	2,25	56,25
11,25	0	56,25	0	56,25

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Source: GroMar, licencja: CC BY 3.0.

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nagranie abstraktu

On the basis of the results from both tables, formulate the principle of the conservation of mechanical energymechanical energymechanical energy.

The principle of the conservation of mechanical energymechanical energymechanical energy is one of the most important principles in physics. According to this principle in case of the system of bodies on which no external and resistance forces work, the total mechanical energymechanical energymechanical energy of the system remains constant.

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What does the jumper have to do to start jumping on the trampoline?
What energy does a deflected trampoline have?
What kind of energy does the jumper have when the trampoline is straight?
Describe energy conversions from the start of the jump to the moment of re‑landing on the trampoline.
Draw a diagram showing the energy conversion during the jump.
Does the total mechanical energymechanical energymechanical energy change during the jumps?

Justify your answer.

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nagranie abstraktu

Compare your answers with the model ones.

The jumper has to do work.
The deflected trampoline has the energy of elasticityenergy of elasticityenergy of elasticity.
Then the jumper has kinetic energy.
Elastic energy -> kinetic energy -> potential energy of gravity -> kinetic energy -> elastic energy.
As in point 4.
If we ignore the resistance of the jumper's movement, the total mechanical energymechanical energymechanical energy remains constant.

Exercises

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Exercise 3

A car with the mass of 1000 kg parked in the car park has started its route. What work did the engine of the car do to increase its velocity to 30 $\frac{m}{s}$ ?

15000 J
900000 J
30000 J
450000 J

Exercise 4

Solve tasks.

Over the distance of 100 m the car obtained the kinetic energy of 120000 J. Calculate the resultant force acting on the car.
Zakopane is located at the altitude of 837 m above the sea level, Świnica peak - at 2,306 m above the sea level. What work did a tourist do climbing from Zakopane to Świnica? The mass of the tourist is 60 kg.

Exercise 5

Experiment

Construct a self‑made slingshot using available items.

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Ilustracja przedstawia procę — Source: GroMar, licencja: CC BY 3.0.

Design and perform an experiment which will provide the answer to the following question: „How does the velocity of the flying stone depend on the stretching of the rubber bands of the slingshot?”

Warning: always shoot with extreme caution! The slingshot is considered as melee weapon.

Note: If you shoot horizontally, the throwing range is proportional to the initial velocity of the stone.

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Exercise 6

Indicate which pairs of expressions or words are translated correctly.

energia potencjalna grawitacji - potential energy of gravity
zachowanie energii - energy conservation
energia mechaniczna - mechanical energy
zmiana energii - change of energy
energia sprężystości - principle of energy conservation
zasada zachowania energii - energy of elasticity

zadanie

Source: GroMar, licencja: CC BY 3.0.

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Match Polish terms with their English equivalents.

energy conservation
zachowanie energii
mechanical energy
energia mechaniczna
energia potencjalna grawitacji
potential energy of gravity

Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

change of energy

zmiana energii

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wymowa w języku angielskim: change of energy

energy conservation

zachowanie energii

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wymowa w języku angielskim: energy conservation

energy of elasticity

energia sprężystości

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wymowa w języku angielskim: energy of elasticity

mechanical energy

energia mechaniczna

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Source: GroMar, licencja: CC BY 3.0.

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wymowa w języku angielskim: mechanical energy

potential energy of gravity

energia potencjalna grawitacji

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Source: GroMar, licencja: CC BY 3.0.

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wymowa w języku angielskim: potential energy of gravity

Keywords

energy conservationenergy conservationenergy conservation

mechanical energymechanical energymechanical energy

potential energy of gravitypotential energy of gravitypotential energy of gravity

Scenariusz

Exercises

Glossary

Keywords