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

Considere un rodillo de césped de 100 kg de masa y radio de 25 cm. El brazo del rodillo se extiende en un ángulo de treinta grados con respecto al eje horizontal.
Dejando de lado la fricción desarrollada en el eje, ¿qué fuerza se requiere para mover el rodillo a una velocidad constante, siempre que el coeficiente de resistencia a la rodadura sea de 25 mm?
Suponiendo que la fuerza motriz resultante que actúa sobre el mango se aplica a lo largo del brazo, se dibuja un diagrama de cuerpo libre del rodillo que indica el peso, la fuerza normal y la fuerza motriz.
La fuerza motriz se puede resolver en sus componentes horizontales y verticales.
La geometría del sistema se puede utilizar para determinar el ángulo entre la fuerza normal y el eje vertical.
A continuación, se aplica la condición de equilibrio de momento al punto de contacto O. Sustituyendo los valores de peso, componentes de la fuerza motriz y las distancias perpendiculares correspondientes, se estima la fuerza motriz.
Si se aplica una fuerza con una magnitud mucho menor que la fuerza motriz, el rodillo no se mueve.

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	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 452 \u2012 453.</li>
	<li>Meriam, J.L.; Kraige, L.G. y Bolton, J.N. (2020). Ingeniería Mecánica \u2012 Estática. Hoboken, Nueva Jersey: John Wiley. Págs. 373.</li>
	<li>Cerveza, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. y Self, B.P. (2019). Mecánica vectorial para ingenieros: estática y dinámica. Nueva York: McGraw-Hill. págs. 463</li>
</ol>

resistencia a la rodadura: resolución de problemas

La resistencia a la rodadura, también conocida como fricción de rodadura, es la fuerza que se opone al movimiento de un objeto rodante, como una rueda, un neumático o una bola, cuando se desplaza sobre una superficie. Se produce debido a la deformación del objeto y la superficie en contacto, así como otros factores como la fricción interna, la histéresis y las pérdidas de energía en los materiales. La resistencia a la rodadura se opone al movimiento del objeto, requiriendo energía adicional para superarla y mantener el movimiento. En aplicaciones prácticas, minimizar la resistencia a la rodadura puede mejorar la eficiencia energética y reducir el desgaste tanto del objeto rodante como de la superficie. Consideremos un rodillo de césped con una masa de 100 kg, un radio de 25 cm y un coeficiente de resistencia a la rodadura de 25 mm. El brazo del rodillo se extiende a un ángulo de 30° con respecto al eje horizontal. La fuerza requerida para mover el rodillo a una velocidad constante puede ser determinada, siempre y cuando se ignore la fricción desarrollada en el eje. Suponiendo que la fuerza de tracción resultante que actúa sobre el mango se aplica a lo largo del brazo, se puede dibujar un diagrama de cuerpo libre del rodillo, incluyendo el peso (W), la fuerza normal (N) y la fuerza de tracción (F). La fuerza de tracción puede descomponerse en sus componentes horizontal (Fh) y vertical (Fv). <img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;"> A continuación, la geometría del sistema se puede utilizar para determinar el ángulo θ1 entre la fuerza normal (N) y el eje vertical. Luego se aplica la condición de equilibrio de momentos al punto de contacto O. <img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> El peso del rodillo, que es igual a la masa multiplicada por la aceleración debido a la gravedad, se calcula como 98.1 N. Sustituyendo los valores del peso, las componentes horizontal y vertical de la fuerza de tracción y las correspondientes distancias perpendiculares, se calcula la fuerza de tracción F como 120.86 N. Para mantener una velocidad constante, la componente horizontal de la fuerza de tracción debe superar la resistencia a la rodadura. Si se aplica una fuerza con una magnitud mucho menor que la fuerza de tracción, el rodillo no se mueve. Comprender esta relación ayuda a apreciar el impacto de las diferentes fuerzas en el movimiento del rodillo y la importancia de considerar diversos factores al diseñar y utilizar rodillos de césped.

Resistencia a la rodadura: Resolución de problemas

La resistencia a la rodadura, también conocida como fricción de rodadura, es la fuerza que resiste el movimiento de un objeto rodante, como una rueda, un neumático o una bola, cuando ...

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TÉRMINOS Y CONCEPTOS CLAVE

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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Lawn Roller Force Calculation

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