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Mechanical energy is one of the most mentioned concepts in the Physics 10 program. So what is mechanical energy? How is the law of conservation of energy stated? Nguyễn Tất Thành will summarize all the necessary knowledge in the following article.

What is mechanical energy?

What is mechanical energy? Mechanical energy is a physical quantity that represents the ability of any object to do work. Understand specifically, an object has mechanical energy when it has the ability to perform mechanical work. In physics, mechanical energy is equal to the sum of potential and kinetic energy. The greater the work done by an object, the greater its mechanical energy.

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• The symbol for mechanical energy is W.

Example: Place a brick on a glass plate. Initially, the brick is not capable of doing work on the glass. However, when it is raised to a height h above the glass and dropped, the brick can break the glass. At that time, we say the brick has the ability to generate work. Therefore, when the brick is raised to height h, the brick has mechanical energy.

How many types of mechanical energy are there?

Mechanical energy consists of two main forms: potential energy and kinetic energy.

About potential energy

The mechanical energy of an object placed at a certain height is called potential energy. Gravitational potential energy is the mechanical energy of an object at a height h above the ground or compared to another location chosen as a landmark. When the object is on the ground, the distance from the object to the ground is 0, so the gravitational potential energy is 0. The higher the object is and the greater the mass, the greater the value of gravitational potential energy.

Besides, elastic potential energy is also defined as a form of mechanical energy of an object, it depends on the deformation of the spring. To determine whether an object has elastic potential energy or not, we will consider whether the object is deformed or elastic.

For example: When we pull the bowstring, we change the shape of the bowstring, which means we give the bow elastic potential energy.

About kinetic energy

The mechanical energy of an object created by motion is called kinetic energy. The faster an object moves and the more mass it has, the greater its kinetic energy. If the object is at rest, the kinetic energy is 0.

The conversion between kinetic energy and potential energy

Kinetic energy and potential energy are two basic forms of energy in objects, and they can be converted to each other. Specifically:

• Kinetic energy can be converted into potential energy. For example: When a ball is thrown high, the ball’s kinetic energy will gradually decrease and be converted into gravitational potential energy.
• Potential energy can be converted into kinetic energy. For example: When a ball falls from a height, the ball’s gravitational potential energy will gradually decrease and convert into kinetic energy.

The conversion between kinetic energy and potential energy occurs continuously during the movements of objects. For example, when a spring pendulum oscillates, the kinetic energy and potential energy of the pendulum are converted back and forth into each other.

In reality, because there is always friction and other resistance forces, some energy will be lost in the form of heat. However, in mechanical problems, we often ignore resistance forces to simplify the problem.

Law of conservation of mechanical energy

Law of conservation of mechanical energy: Potential energy and kinetic energy of an object can change back and forth when the object moves inside gravity. However, because mechanical energy is equal to the sum of potential and kinetic energy, this total always remains constant.

We have the formula to calculate mechanical energy:

Consequences:

• When an object moves in gravity, the object’s kinetic energy will increase if the object’s potential energy decreases and vice versa.
• At the position where the potential energy is at its minimum, the kinetic energy is at its maximum, and conversely, when the potential energy is at its maximum, the kinetic energy will be at its minimum.

Note: The law of conservation of mechanical energy (or conservation of mechanical energy) only applies when the object moves in gravity and is not affected by friction but only by gravity or elastic force.

Mechanical energy of objects moving in gravity

What is the mechanical energy of an object moving in gravity? How to calculate? Let’s find out in the section below:

Define

When any object moves in gravity, the total potential energy and kinetic energy of the object is called mechanical energy.

Formula for calculating the mechanical energy of an object moving in gravity

Recipe:

Conservation of mechanical energy of objects moving in gravity

When any object moves under gravity and is only affected by gravity (ignoring friction, resistance, etc.), the mechanical energy of the object remains unchanged (a conserved quantity).

From there, we get:

The mechanical energy of an object is affected by elastic force

Conservation of mechanical energy of an object under the influence of elastic force

When only the effect of elastic force caused by the deformation of an elastic spring acts on the object, then during motion, the mechanical energy is determined by the sum of the object’s potential energy and elastic kinetic energy as a conserved quantity.

Note: The law of conservation of mechanical energy is only true when the object is affected by two forces, gravity and elasticity, and is not affected by any other force such as resistance, friction,…

Formula for calculating the mechanical energy of an object subjected to elastic force

Answer questions about potential and kinetic energy

1. When is potential energy equal to mechanical energy?

When does mechanical energy equal potential energy? Potential energy equals mechanical energy when an object has only potential energy and no kinetic energy. Because the mechanical energy of an object is the sum of potential energy and kinetic energy (W = Wt + Wd), when the object’s kinetic energy is 0, the object’s mechanical energy is equal to its potential energy.

For example: A ball is suspended at a height h above the ground. When the ball is released, the ball’s potential energy will gradually decrease and convert into kinetic energy. When the ball hits the ground, the ball’s potential energy is zero and the ball’s kinetic energy reaches its maximum value.

2. Statement about the law of conservation of kinetic energy:

In a closed system, if there is no friction or other resisting forces acting on the objects in the system, the kinetic energy of the system will be conserved. However, in reality, because there is always friction and other resistance forces, the kinetic energy of the system is not completely conserved.

See more: What is kinetic energy? Kinetic energy expressions & application exercises (Physics grade 10)

Functional exercises (Physics grade 10)

Below are some exercises in the topic Mechanical Functions, with detailed explanations to help you check and compare results after completion.

Question 1: A small object is thrown up from a point M above the ground; The object reaches point N then stops and falls down. Ignore air resistance. During MN process

A. Kinetic energy increases

B. Potential energy decreases

C. Maximum mechanical energy at N

D. Mechanical energy remains unchanged

Answer: Choose D.

Explanation: Because air resistance is ignored, mechanical energy remains constant during the MN process.

Question 2: From point M (0.8m above the ground), throw an object with an initial velocity of 2m/s. Knowing the mass of the object is 0.5kg, take g= 10m/s^2. What is the mechanical energy of an object?

A. 4J

B. 1J

C. 5J

D. 8J

Answer: Choose C

Explain:

Select potential energy landmarks at ground level. At the throwing point M we get:

So the mechanical energy of the object is equal to 5J

Question 3: The mechanical energy of an object with a mass of 2kg falling from a height of 5m to the ground is:

A. 10J

B. 100J

C. 5J

D. 50J

Answer: Choose B

Explain:

Because the mechanical energy of the system is conserved, the mechanical energy is equal to the initial potential energy, or:

W = W( t = 0 ) = Wđ + Wt = mgh = 100 (J).

Question 4: An object is thrown vertically upward at a speed of 6 m/s. Take g = 10 m/s^2. Calculate its maximum altitude.

A. h = 1.8 m.

B h = 3.6 m.

C. h = 2.4 m

D h = 6 m

Answer: Choose A

Explain:

When the object reaches its maximum height, v = 0.

Law of conservation of mechanical energy for the two starting positions and maximum height:

W1 = W2 ⇔ Wd1 + Wt1 = Wd2 + Wt2.

Question 5: An object m slides without initial velocity from the top to the bottom of an inclined plane with a length of 5m, and an angle of 30° with the horizontal plane. The friction force between the object and the inclined plane is equal to one-fourth the weight of the object. Take g=10m/s^2. The magnitude of the velocity of the object at the base of the inclined plane is:

A. 4.5 m/s. B. 5 m/s. C. 3.25 m/s. D. 4 m/s.

Answer: Choose B

Explain:

Applying the kinetic energy change theorem to the two positions where the object starts moving and when the object stops, we have:

Question 6: An athlete weighing 650N jumps with an initial speed v0 = 2 m/s from a diving board at a height of 10 m into the water in a vertical downward direction. Taking g = 10 m/s^2, after touching the water the person moves another 3m vertically in the water and then stops. The change in mechanical energy of that person is:

A. – 8580 J

B. – 7850 J

C. – 5850 J

D. – 6850 J

Answer: Choose A

Explain:

Choose the origin of potential energy at the interface between water and air.

The body’s abilities at the beginning of the dance are:

At the stopping position, the coordinates are h’ = -3 m.

The mechanical energy when the person stops is:

Wsau = – mgh’ = -1950 (J)

Mechanical energy change: ΔW = Wafter – Wbefore = – 8580 (J).

Question 7: An object is dropped freely, in the process of falling

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A. The object’s kinetic energy remains unchanged.

B. The object’s potential energy remains unchanged.

C. The total kinetic and potential energy of the object does not change.

D. The total kinetic and potential energy of an object always changes.

Answer: Choose C.

Explanation: An object is dropped freely. During the fall, the object’s velocity and height change, so its potential and kinetic energy change, but the total potential and kinetic energy of the object does not change.

Question 8: A skier slides down from a cliff, his sliding speed increasing each time. Ditto for athletes

A. Kinetic energy increases, potential energy increases.

B. Kinetic energy increases, potential energy decreases.

C. Kinetic energy remains unchanged, potential energy decreases.

D. Kinetic energy decreases, potential energy increases.

Answer: Choose B.

Explanation: A skier slides down a cliff, so the height decreases and the speed increases. Therefore, potential energy decreases and kinetic energy increases.

Question 9: During the oscillation of a simple pendulum, it is at the equilibrium position

A. kinetic energy reaches its maximum value.

B. potential energy reaches its maximum value.

C. mechanical energy is zero.

D. potential energy equals kinetic energy.

Answer: Choose A.

Explanation: During the oscillation of a simple pendulum, at the equilibrium position, the simple pendulum has the lowest altitude coordinates, so the potential energy is the smallest and the kinetic energy is the largest.

Question 10: When you drop an object that slides without initial velocity on an inclined plane with friction

A. The mechanical energy of an object is equal to the maximum value of its kinetic energy.

B. the change in kinetic energy is equal to the work of the friction force.

C. the decrease in potential energy is equal to the work of gravity.

D. the decrease in potential energy equals the increase in kinetic energy.

Answer: Choose C.

Explanation: When an object is dropped without initial velocity on an inclined plane, the potential energy of friction decreases due to the work done by gravity. Therefore, the reduction in potential energy is equal to the work of gravity.

Question 11: An object is dropped freely from a height of 3m. The height of the object when the kinetic energy is twice the potential energy is

A. 1.5 m.

B. 1.2 m.

C. 2.4 m.

D. 1.0 m.

Answer: Choose D

Explanation: Select the potential energy landmark at ground level.

The object falls freely so mechanical energy is conserved: W1 = W2

⇒ W1 = Wđ2 + Wt2 = 2.Wt2 +Wt2 ⇒ h2 = h/3 = 1 (m).

Question 12: An object is thrown vertically upward from the ground with an initial velocity of 4 m/s. Ignore air resistance. The speed of an object when its kinetic energy equals its potential energy is

A. 2√2 m/s.

B. 2 m/s.

C. √2 m/s.

D. 1 m/s.

Answer: Choose A

Explanation: Select the potential energy landmark at ground level.

Ignoring air resistance, mechanical energy is conserved: W1 = W2

Wd1+0 = Wd2+Wt2=2.Wd2

v2=v12=42=22 (m/s)

Conclusion:

Hopefully the information about Mechanical Energy and the law of conservation of mechanical energy that Nguyễn Tất Thành has provided will help you in the learning process and solving related Physics exercises. Besides, you can also refer to many other useful articles at the website monkey.edu.vn.

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