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

Considérons un rouleau à gazon de masse 100 kg et de rayon 25 cm. Le bras du rouleau s’étend à un angle de trente degrés par rapport à l’axe horizontal.
Si l’on néglige le frottement développé au niveau de l’essieu, quelle force est nécessaire pour déplacer le rouleau à vitesse constante, à condition que le coefficient de résistance au roulement soit de 25 mm ?
En supposant que la force motrice résultante agissant sur la poignée est appliquée le long du bras, un schéma du corps libre du rouleau indiquant le poids, la force normale et la force motrice est dessiné.
La force motrice peut être résolue en ses composantes horizontales et verticales.
La géométrie du système peut être utilisée pour déterminer l'angle entre la force normale et l'axe vertical.
La condition d’équilibre du moment est ensuite appliquée au point de contact O. En substituant les valeurs du poids, des composantes de la force motrice et des distances perpendiculaires correspondantes, on estime la force motrice.
Si une force d’une amplitude bien inférieure à la force motrice est appliquée, le rouleau ne bouge pas.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. pp 452 à 453.</li>
	<li>Meriam, J.L. ; Kraige, L.G. et Bolton, J.N. (2020). Génie mécanique \u2012 Statique. Hoboken, New Jersey : John Wiley. p. 373.</li>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. p. 463</li>
</ol>

résistance au roulement: résolution de problèmes

La résistance au roulement, également connue sous le nom de frottement de roulement, est la force qui s'oppose au mouvement d'un objet roulant, tel qu'une roue, un pneu ou une balle, lorsqu'il se déplace sur une surface. Elle est causée par la déformation de l'objet et de la surface en contact l'un avec l'autre, ainsi que par d'autres facteurs tels que le frottement interne, l'hystérésis et les pertes d'énergie dans les matériaux. La résistance au roulement s'oppose au mouvement de l'objet, nécessitant une énergie supplémentaire pour la surmonter et maintenir le mouvement. Dans les applications pratiques, minimiser la résistance au roulement peut améliorer l'efficacité énergétique et réduire l'usure à la fois de l'objet roulant et de la surface. Considérons un rouleau de pelouse avec une masse de 100 kg, un rayon de 25 cm et un coefficient de résistance au roulement de 25 mm. Le bras du rouleau s'étend selon un angle de 30 degrés par rapport à l'axe horizontal. La force nécessaire pour déplacer le rouleau à une vitesse constante peut être déterminée, à condition que la friction développée à l'axe soit négligée. En supposant que la force d'entraînement résultante agissant sur la poignée soit appliquée le long du bras, on peut dresser un diagramme des forces du rouleau, comprenant le poids (W), la force normale (N) et la force d'entraînement (F). La force d'entraînement peut être résolue en ses composantes horizontales (Fh) et verticales (Fv). <img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;"> Ensuite, la géométrie du système peut être utilisée pour déterminer l'angle θ1 entre la force normale (N) et l'axe vertical. La condition d'équilibre des moments est ensuite appliquée au point de contact O. <img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> Le poids du rouleau équivalant à la masse multipliée par l'accélération due à la gravité est calculé à 98,1 N. En substituant les valeurs du poids, des composantes horizontales et verticales de la force d'entraînement, ainsi que des distances perpendiculaires correspondantes, la force d'entraînement F est calculée à 120,86 N. Pour maintenir une vitesse constante, la composante horizontale de la force d'entraînement doit surmonter la résistance au roulement. Si une force d'une magnitude beaucoup plus faible que la force d'entraînement est appliquée, le rouleau ne bouge pas. Comprendre cette relation permet d'apprécier l'impact des différentes forces sur le mouvement du rouleau et l'importance de prendre en compte divers facteurs lors de la conception et de l'utilisation des rouleaux de pelouse.

Résistance au roulement: résolution de problèmes

La résistance au roulement, également connue sous le nom de frottement de roulement, est la force qui résiste au mouvement d’un objet roulant, tel qu’une roue, un pneu ou une balle, lorsqu’il ...

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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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