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

Considera un rullo da prato di massa 100 kg e raggio 25 cm. Il braccio del rullo si estende con un angolo di trenta gradi rispetto all'asse orizzontale.
Trascurando l'attrito sviluppato sull'asse, quale forza è necessaria per muovere il rullo a velocità costante, a condizione che il coefficiente di resistenza al rotolamento sia di 25 mm?
Supponendo che la forza motrice risultante che agisce sull'impugnatura sia applicata lungo il braccio, viene disegnato un diagramma a corpo libero del rullo che indica il peso, la forza normale e la forza motrice.
La forza motrice può essere risolta nelle sue componenti orizzontali e verticali.
La geometria del sistema può essere utilizzata per determinare l'angolo tra la forza normale e l'asse verticale.
La condizione di equilibrio del momento viene quindi applicata al punto di contatto O. Sostituendo i valori di peso, le componenti della forza motrice e le corrispondenti distanze perpendicolari, stima la forza motrice.
Se viene applicata una forza con un'entità molto inferiore alla forza motrice, il rullo non si muove.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pp 452 \u2012 453.</li>
	<li>Meriam, J.L.; Kraige, LG e Bolton, JN (2020). Ingegneria Meccanica \u2012 Statica. Hoboken, New Jersey: John Wiley. 373.</li>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P. (2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. pagine 463</li>
</ol>

resistenza al rotolamento: risoluzione del problema

La resistenza al rotolamento, nota anche come attrito di rotolamento, è la forza che si oppone al movimento di un oggetto che rotola, come una ruota, uno pneumatico o una pallina, quando si muove su una superficie. È causata dalla deformazione dell'oggetto e della superficie fra loro in contatto, così come da altri fattori come l'attrito interno, l'isteresi e le perdite energetiche nei materiali. La resistenza al rotolamento si oppone al movimento dell'oggetto, richiedendo energia aggiuntiva per superarla e mantenere il movimento. Nelle applicazioni pratiche, minimizzare la resistenza al rotolamento può migliorare l'efficienza energetica e ridurre l'usura sia dell'oggetto che della superficie di rotolamento.

Consideriamo un rullo per il prato con una massa di 100 kg, un raggio di 25 cm e un coefficiente di resistenza al rotolamento di 25 mm. Il braccio del rullo si estende di un angolo pari a 30° rispetto all'asse orizzontale. La forza necessaria per far muovere il rullo a velocità costante può essere determinata, a condizione che l'attrito sviluppato all'asse venga trascurato.

Assumendo che la forza di guida risultante che agisce sulla maniglia sia applicata lungo il braccio, è possibile disegnare un diagramma del corpo libero del rullo, includendo il peso (W), la forza normale (N) e la forza di guida (F). La forza di guida può essere risolta nelle sue componenti orizzontale (Fh) e verticale (Fv).

<img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;" />

Successivamente, è possibile utilizzare la geometria del sistema per determinare l'angolo θ1 tra la forza normale (N) e l'asse verticale. La condizione di equilibrio del momento viene quindi applicata al punto di contatto O.

<img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Il peso del rullo, che corrisponde alla massa, moltiplicata per l'accelerazione di gravità, viene calcolato come 98,1 N. Sostituendo i valori del peso, dei componenti orizzontali e verticali della forza di guida e delle corrispondenti distanze perpendicolari, la forza di guida F viene calcolata come 120,86 N.

Per mantenere una velocità costante, la componente orizzontale della forza di guida deve superare la resistenza al rotolamento. Se viene applicata una forza con una magnitudine molto inferiore alla forza di guida, il rullo non si muove. Comprendere questa relazione aiuta a comprendere l'impatto delle diverse forze sul movimento del rullo e l'importanza di considerare vari fattori nella progettazione e nell'uso dei rulli per il prato.

Resistenza al rotolamento: risoluzione del problema

La resistenza al rotolamento, nota anche come attrito volvente, è la forza che resiste al movimento di un oggetto che rotola, come una ruota, uno pneumatico o una palla, quando ...

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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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