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

Considere um rolo de grama de massa 100 kg e raio 25 cm. O braço do rolo se estende em um ângulo de trinta graus em relação ao eixo horizontal.
Negligenciando o atrito desenvolvido no eixo, que força é necessária para mover o rolo a uma velocidade constante, desde que o coeficiente de resistência ao rolamento seja de 25 mm?
Supondo que a força motriz resultante que atua na alça seja aplicada ao longo do braço, um diagrama de corpo livre do rolo indicando o peso, a força normal e a força motriz é desenhado.
A força motriz pode ser resolvida em seus componentes horizontais e verticais.
A geometria do sistema pode ser usada para determinar o ângulo entre a força normal e o eixo vertical.
A condição de equilíbrio de momento é então aplicada ao ponto de contato O. Substituindo os valores de peso, componentes da força motriz e as distâncias perpendiculares correspondentes, estima a força motriz.
Se uma força com uma magnitude muito menor que a força motriz for aplicada, o rolo não se move.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 452 - 453.</li>
	<li>Oliveira, J.L.; Kraige, L.G. e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. pág. 373.</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. 463</li>
</ol>

resistência ao rolamento: resolução de problemas

A resistência ao rolamento, também conhecida como atrito de rolamento, é a força que resiste ao movimento de um objeto que rola, como uma roda, um pneu ou uma bola, quando ele se movimenta sobre uma superfície. Ela é causada pela deformação do objeto e da superfície que estão em contato um com o outro, assim como outros fatores, como atrito interno, histerese e perdas de energia nos materiais. A resistência ao rolamento se opõe ao movimento do objeto, exigindo energia adicional para superá-la e manter o movimento. Em aplicações práticas, minimizar a resistência ao rolamento pode melhorar a eficiência energética e reduzir o desgaste tanto do objeto que rola quanto da superfície.

Considere um rolo de grama com uma massa de 100 kg, um raio de 25 cm e um coeficiente de resistência ao rolamento de 25 mm. O braço do rolo se estende em um ângulo de 30° em relação ao eixo horizontal. A força necessária para mover o rolo a uma velocidade constante pode ser determinada, desde que o atrito desenvolvido no eixo seja negligênciado.

Supondo que a força de tração resultante atuando na alça seja aplicada ao longo do braço, um diagrama de corpo livre do rolo pode ser desenhado, incluindo o peso (W), a força normal (N) e a força de tração (F). A força de tração pode ser decomposta em suas componentes horizontal (Fh) e vertical (Fv).

<img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;" />

Em seguida, a geometria do sistema pode ser usada para determinar o ângulo θ1 entre a força normal (N) e o eixo vertical. A condição de equilíbrio de momentos é então aplicada ao ponto de contato O.

<img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

O peso do rolo, que é igual à massa multiplicada pela aceleração devido à gravidade, é calculado como 98,1 N. Substituindo os valores do peso, das componentes horizontal e vertical da força de tração e das distâncias perpendiculares correspondentes, a força de tração F é calculada como 120,86 N.

Para manter uma velocidade constante, a componente horizontal da força de tração deve superar a resistência ao rolamento. Se uma força com magnitude muito menor do que a força de tração for aplicada, o rolo não se move. Entender essa relação ajuda a valorizar o impacto das diferentes forças no movimento do rolo e a importância de considerar diversos fatores ao projetar e usar rolos de grama.

Resistência ao rolamento: resolução de problemas

A resistência ao rolamento, também conhecida como atrito de rolamento, é a força que resiste ao movimento de um objeto rolante, como uma roda, pneu ou bola, quando ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Friction

Atrito

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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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

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mechanical engineering

Lawn Roller Force Calculation

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