Name: lawn roller force calculation
Uploaded: 2023-09-22T11:49:31.000Z
Duration: 1 min 17 s
Channel: JoVE

100 kg kütleli ve yarıçapı 25 cm olan bir çim silindiri düşünün. Makara kolu, yatay eksene otuz derecelik bir açıyla uzanır.
Aksta gelişen sürtünmeyi ihmal ederek, yuvarlanma direnci katsayısının 25 mm olması koşuluyla, silindiri sabit bir hızda hareket ettirmek için hangi kuvvet gereklidir?
Sapa etki eden bileşke itici kuvvetin kol boyunca uygulandığı varsayılarak, silindirin ağırlığı, normal kuvveti ve itici kuvveti gösteren bir serbest cisim diyagramı çizilir.
İtici güç, yatay ve dikey bileşenlerine ayrılabilir.
Sistemin geometrisi, normal kuvvet ile dikey eksen arasındaki açıyı belirlemek için kullanılabilir.
Moment denge koşulu daha sonra O temas noktasına uygulanır. Ağırlık değerlerini, itici kuvvetin bileşenlerini ve karşılık gelen dik mesafeleri değiştirerek, itici gücü tahmin eder.
İtici kuvvetten çok daha küçük bir büyüklükte bir kuvvet uygulanırsa, silindir hareket etmez.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 452 \u2012 453.</li>
	<li>Meriam, J.L.; Kraige, L.G. ve Bolton, J.N. (2020). Mühendislik Mekaniği \u2012 Statik. Hoboken, New Jersey: John Wiley. sayfa 373.</li>
	<li>Bira, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. ve Öz, B.P. (2019). Mühendisler için Vektör Mekaniği \u2012 Statik ve Dinamik. New York: McGraw-Tepesi. sayfa 463</li>
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yuvarlanma direnci: hataları giderme

Yuvarlanma direnci, yuvarlanan bir nesnenin, örneğin bir tekerlek, lastik veya topun hareketine direnç gösteren kuvvettir. Bu, nesnenin yüzeyle temas ettiğinde deforme olmasından ve yüzey arasındaki diğer faktörlerden dolayı oluşur. Yuvarlanma direnci, nesnenin hareketine karşı çıkar ve onu aşmak ve hareketi sürdürmek için ek enerji gerektirir. Uygulamalarda yuvarlanma direncini en aza indirerek enerji verimliliği arttırılabilir ve hem yuvarlanan nesne hem de yüzeyin aşınması azaltılabilir.

Kütlesi 100 kg, yarıçapı 25 cm ve yuvarlanma direnç katsayısı 25 mm olan bir çim silindiri düşünelim. Silindir kolunun yatay eksene 30Â°lik bir açıyla uzandığını varsayalım. Silindiri sabit bir hızda hareket ettirmek için gereken kuvvet, ekseni yoksayıldığında belirlenebilir.

Eğer sürücü kuvvetin etki yaptığı yön, kol boyunca uygulanan sonuçta olursa, silindirin serbest cisim diyagramı çizilebilir ve ağırlık (W), normal kuvvet (N) ve sürücü kuvvet (F) dahil edilebilir. Sürücü kuvveti yatay (Fh) ve dikey (Fv) bileşenlerine ayrılabilir.

<img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;" />

Daha sonra, sistemin geometrisi kullanılarak normal kuvvet (N) ile dikey eksen arasındaki açı θ¸1 belirlenebilir. Ardından, nokta O'da moment denge şartı uygulanır.

<img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Silindirin kütlesiyle yerçekimi ivmesi çarpımıyla eşit olan silindirin ağırlığı 98.1 N olarak hesaplanır. Ağırlık, sürücü kuvvetin yatay ve dikey bileşenleri ve ilgili dik mesafelerin değerleri yerine konularak, sürücü kuvveti F 120.86 N olarak hesaplanır.

Sabit bir hızda kalmak için, sürücü kuvvetin yatay bileşeni yuvarlanma direncini aşmalıdır. Sürücü kuvvetin büyüklüğünden çok daha küçük bir kuvvet uygulandığında silindir hareket etmez. Bu ilişkinin anlaşılması, farklı kuvvetlerin silindirin hareketi üzerindeki etkisini ve çim silindirlerinin tasarımı ve kullanımında çeşitli faktörlerin dikkate alınmasının önemini anlamamıza yardımcı olur.

Yuvarlanma Direnci: Hataları Giderme

Yuvarlanma sürtünmesi olarak da bilinen yuvarlanma direnci, tekerlek, lastik veya top gibi yuvarlanan bir nesnenin hareketine direnen kuvvettir.

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Friction

Sürtünme

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

Rolling Resistance: Problem Solving

lawn roller force calculation

Rolling resistance is the force that makes a rolling object harder to move across a surface. It is also called rolling friction. It comes from deformation in the object and the surface that touch each other. Internal friction, hysteresis, and other energy losses in the materials also play a role. Because of this force, extra energy is needed to keep a wheel, tire, or ball moving.

The video applies this idea to a lawn roller. The roller has a mass of 100 kg, a radius of 25 cm, and a coefficient of rolling resistance of 25 mm. The roller arm is set at a 30º angle to the horizontal axis. To find the force needed to move the roller at constant speed, axle friction is ignored. The driving force is assumed to act along the arm.

A free-body diagram is used to show the forces on the roller. These include the weight, the normal force, and the driving force. The driving force is split into horizontal and vertical parts. The geometry of the setup is then used to find the angle θ1 between the normal force and the vertical axis. Next, moment equilibrium is applied at the contact point O.

The weight of the roller is found by multiplying mass by gravitational acceleration. This gives 98.1 N. After the weight, the force components, and the perpendicular distances are substituted into the equilibrium equation, the driving force is calculated as 120.86 N. To keep the roller moving at a constant speed, the horizontal part of the driving force must overcome rolling resistance. If the applied force is much smaller than this value, the roller does not move. This makes the problem useful for understanding how force balance affects the motion of a lawn roller and why rolling resistance matters in design and use.

Lawn Roller Force Calculation

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collar bearings

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rolling resistance: problem solving

Rolling resistance is the force that makes a rolling object harder to move across a surface. It is also called rolling friction. It comes from deformation in the object and the surface that touch each other. Internal friction, hysteresis, and other energy losses in the materials also play a role. Because of this force, extra energy is needed to keep a wheel, tire, or ball moving. The video applies this idea to a lawn roller. The roller has a mass of 100 kg, a radius of 25 cm, and a coefficient...

key terms and concepts

Solve a lawn roller force problem using rolling resistance, free-body diagrams, and moment equilibrium. See how the required force is calculated step by step.

Lawn Roller Force Calculation | JoVE K12

JoVE Core Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Lawn Roller Force Calculation

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