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

Stellen Sie sich eine Rasenwalze mit einer Masse von 100 kg und einem Radius von 25 cm vor. Der Rollenarm fährt in einem Winkel von dreißig Grad zur horizontalen Achse aus.
Welche Kraft ist erforderlich, um die Rolle bei konstanter Geschwindigkeit zu bewegen, wenn der Rollwiderstandskoeffizient 25 mm beträgt, wenn die an der Achse entstehende Reibung abgesehen wird?
Unter der Annahme, dass die resultierende Antriebskraft, die auf den Griff wirkt, entlang des Arms ausgeübt wird, wird ein Freikörperdiagramm der Rolle gezeichnet, das das Gewicht, die Normalkraft und die Antriebskraft angibt.
Die treibende Kraft kann in ihre horizontalen und vertikalen Komponenten aufgelöst werden.
Anhand der Geometrie des Systems kann der Winkel zwischen der Normalkraft und der vertikalen Achse bestimmt werden.
Die Momentengleichgewichtsbedingung wird dann auf den Kontaktpunkt O angewendet. Durch Ersetzen der Werte des Gewichts, der Komponenten der Antriebskraft und der entsprechenden senkrechten Abstände wird die Antriebskraft geschätzt.
Wenn eine Kraft aufgebracht wird, die viel kleiner ist als die Antriebskraft, bewegt sich die Rolle nicht.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seiten 452 \u2012 453.</li>
	<li>Meriam, J.L.; Kraige, L.G. und Bolton, J.N. (2020). Technische Mechanik \u2012 Statik. Hoboken, New Jersey: John Wiley. S. 373.</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seite 463</li>
</ol>

rollwiderstand: problemlösung

Rollwiderstand, auch als Rollreibung bekannt, ist die Kraft, die der Bewegung eines rollenden Objekts wie einem Rad, Reifen oder Ball entgegenwirkt, wenn es über eine Oberfläche bewegt wird. Er wird durch die Verformung des Objekts und der Fläche, die miteinander in Kontakt stehen, sowie andere Faktoren wie innere Reibung, Hysteresis und Energieverluste in den Materialien verursacht. Der Rollwiderstand widersetzt sich der Bewegung des Objekts's und erfordert zusätzliche Energie, um ihn zu überwinden und die Bewegung aufrechtzuerhalten. In der praktischen Anwendung kann eine Minimierung des Rollwiderstands die Energieeffizienz verbessern und den Verschleiß sowohl des rollenden Objekts als auch der Oberfläche verringern. Betrachten Sie eine Rasenwalze mit einer Masse von 100 kg, einem Radius von 25 cm und einem Rollwiderstandskoeffizienten von 25 mm. Der Walzenarm erstreckt sich unter einem Winkel von 30° zur horizontalen Achse. Die zur Bewegung der Walze mit konstanter Geschwindigkeit erforderliche Kraft kann bestimmt werden, vorausgesetzt, die am Achsenpunkt entwickelte Reibung wird vernachlässigt. Unter der Annahme, dass die resultierende Antriebskraft, die auf den Griff wirkt, entlang des Arms aufgebracht wird, kann eine Freikörperdarstellung der Walze gezeichnet werden, einschließlich des Gewichts (W), der Normalkraft (N) und der Antriebskraft (F). Die Antriebskraft kann in ihre horizontalen (Fh) und vertikalen (Fv) Komponenten aufgelöst werden. <img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;"> Als nächstes kann die Geometrie des Systems verwendet werden, um den Winkel θ1 zwischen der Normalkraft (N) und der vertikalen Achse zu bestimmen. Die Momentengleichgewichtsbedingung wird dann auf den Kontaktpunkt O angewendet. <img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> Das Gewicht der Walze, das der Masse multipliziert mit der Erdbeschleunigung entspricht, wird als 98,1 N berechnet. Durch Einsetzen der Werte des Gewichts, der horizontalen und vertikalen Komponenten der Antriebskraft und der entsprechenden senkrechten Abstände wird die Antriebskraft F als 120,86 N berechnet. Um eine konstante Geschwindigkeit aufrechtzuerhalten, muss die horizontale Komponente der Antriebskraft den Rollwiderstand überwinden. Wenn eine Kraft mit einer viel geringeren Größe als die Antriebskraft angewendet wird, bewegt sich die Walze nicht. Das Verständnis dieser Beziehung hilft dabei, die Auswirkungen verschiedener Kräfte auf die Bewegung der Walze und die Bedeutung der Berücksichtigung verschiedener Faktoren bei der Gestaltung und Verwendung von Rasenwalzen zu erkennen.

Rollwiderstand: Problemlösung

Der Rollwiderstand, auch Rollreibung genannt, ist die Kraft, die der Bewegung eines rollenden Objekts wie eines Rades, Reifens oder Balls widersteht, wenn es ...

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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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