Name: finding force from potential energy
Uploaded: 2023-04-30T10:57:22.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physics

Energy

PS.Phy.6.2

force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

Korunumlu kuvvetler potansiyel enerji cinsinden ifade edilebilir.
Konumun bir fonksiyonu olan korunumlu bir kuvvet nedeniyle düz bir çizgi boyunca hareket eden bir cisim düşünün.
Şimdi, korunumlu kuvvet tarafından yapılan iş, potansiyel enerjisindeki değişimin negatifine eşittir.
Yapılan iş aynı zamanda kuvvetin çarpımına ve kuvvetin neden olduğu yer değiştirmeye eşittir.
Bu nedenle, cisim üzerindeki kuvvet, potansiyel enerjideki değişimin negatifinin yer değiştirmeye bölünmesine eşittir. 
Negatif işaret, korunumlu kuvvetin sistemi daha düşük bir potansiyel enerjiye sürüklediğini gösterir.
Çok küçük yer değiştirmeler için, bir boyutta kuvvet ve potansiyel enerji ifadesi oluşturulabilir.
Kuvvet ve potansiyel enerji ilişkisinin doğrulanması için elastik potansiyel enerji örneğini göz önünde bulundurun. Kuvvet ve enerji ilişkisinin yerine konduğunda, Hooke yasasının formülü kurulur.

tek boyutta kuvvet ve potansiyel enerji

Potansiyel enerji için pozisyona bağlı bir fonksiyon olan ifadeden kuvvet hesaplanabilir. Bir kor conservatif kuvvetin, belirli bir yönde, pozisyona bağlı potansiyel enerjinin bu yöndeki yer değiştirmeye göre negatif türeviden oluşan bileşeni. Potansiyel enerjinin yer değiştirmeye göre hızlı bir şekilde değiştiği bölgelerde, yapılan iş ve kuvvet maksimumdur. Ayrıca, kuvvet pozitif koordinat ekseni boyunca uygulandığında, potansiyel enerji yer değiştirmenin artmasıyla azalır. Dolayısıyla, kuvvet ve yer değiştirmeye göre potansiyel enerjinin türevi, zıt işaretlere sahiptir.

Örneğin, x-ekseni boyunca tek boyutlu hareket eden bir parçacığın potansiyel enerjisi şu şekilde ifade edilirse,

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_1.png" style="height: 32px;" />

Potansiyel enerji = cx^3 (burada c = 8 N/m^3)

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_2.png" style="height: 32px;" />

verilen potansiyel enerji için kuvvet ne olur? Burada, bilinen miktar potansiyel enerjidir. Bilinmeyen miktar olan kuvvet hesaplanmalıdır.

Yukarıdaki ifadeye potansiyel enerji değerini dahil ederek, x-yönündeki kuvvet -cx^3 olarak hesaplanır. c değerinin yerine konmasıyla, kuvvet -8x^3 olarak hesaplanır.

Diatomik bir moleküldeki iki atom arasındaki kuvvet için potansiyel enerji fonksiyonu yaklaşık olarak şöyle verilir:

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_3.png" style="height: 32px;" />

Potansiyel enerji = a/x^12 - b/x^6 (burada a ve b sabitlerdir ve x atomlar arasındaki mesafedir)

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_4.png" style="height: 14px;" />

D'nin değeri nedir? Burada bilinen nicelik potansiyel enerjidir. Bilinmeyen nicelik ise molekülün ayrışma enerjisidir. Potansiyel enerji fonksiyonunu yerine koyduğumuzda kuvvet ifadesini elde ederiz. Net kuvvet dengede sıfır olduğundan, şunu elde ederiz

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_5.png" style="height: 32px;" />

Şimdi, x6 değeri potansiyel enerji ifadesine eklenecektir. Sonsuzdaki potansiyel enerji sıfır olduğundan, molekülün ayrışma enerjisi b2/4a olarak hesaplanır.

Bu metin, <a href="https://openstax.org/books/university-physics-volume-1/pages/8-4-potential-energy-diagrams-and-stability">Openstax, "University Physics Volume 1, Section 8.4: Potential Energy Diagrams and Stability'den"</a> uyarlanmıştır.

Tek Boyutta Kuvvet ve Potansiyel Enerji

Kuvvet, konumun bir fonksiyonu olan potansiyel enerji ifadesinden hesaplanabilir. Muhafazakar bir kuvvetin bileşeni, belirli bir ...

Education

JoVE Core

Fizik

Unit 1

Ünite 1

Potential Energy and Energy Conservation

Potansiyel Enerji ve Enerjinin Korunumu

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

finding force from potential energy

Force can be found from potential energy when the energy is written as a function of position. For a conservative force, the force component in a given direction equals the negative derivative of the matching potential energy with respect to displacement. This means force and the slope of potential energy have opposite signs.

Where potential energy changes quickly with displacement, the force and the work done are largest. When a force acts along the positive coordinate axis, potential energy decreases as displacement increases. In one-dimensional motion, this relationship is often used to move from a known potential energy function to the force it produces.

For example, if a particle moves along the x-axis and its potential energy is given with c = 8 N/m^3, the force can be calculated from that expression. The potential energy is the known quantity, and the force is the unknown quantity. Differentiating the energy function gives the x-direction force as -cx^3, which becomes -8x^3 after substituting the value of c.

The same idea also applies to the force between two atoms in a diatomic molecule. Their potential energy can be written approximately as a function of distance x, with a and b as constants. If the dissociation energy is needed, the force is first found from the potential energy, and the equilibrium point is used because the net force is zero there. Then the value of x^6 is substituted into the energy expression, and since the potential energy at infinity is zero, the dissociation energy is b^2/4a.

Finding Force from Potential Energy

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force and potential energy in one dimension

Force can be found from potential energy when the energy is written as a function of position. For a conservative force, the force component in a given direction equals the negative derivative of the matching potential energy with respect to displacement. This means force and the slope of potential energy have opposite signs. Where potential energy changes quickly with displacement, the force and the work done are largest. When a force acts along the positive coordinate axis, potential energy...

force and potential energy in three dimensions

force-and-potential-energy-in-three-dimensions

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Learn how to calculate force from potential energy in one dimension, including the sign rule, a particle example, and dissociation energy for atoms.

Finding Force from Potential Energy | JoVE K12

physics

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Pennsylvania State Academic Standards

Physical Science

3.2.9-12.S

Louisiana Student Standards for Science

High School

HS-PS3-5

Tennessee Academic Standards

PHYS.PS3.3

PHYS.PS3.8

Virginia  Standards of Learning

HIgh School

PH.4

PH.4.b

Alabama Course of Study Science

9-12.P.2.3.b

Next Generation Science Standards

HS-PS3-2

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South Carolina College and Career Ready Science Standards

P-PS3-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-2.

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Finding Force from Potential Energy

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