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

Consider a lawn roller of mass 100 kg and radius 25 cm. The roller arm extends at a thirty-degree angle to the horizontal axis.
Neglecting the friction developed at the axle, what force is required to move the roller at a constant speed, provided the coefficient of rolling resistance is 25 mm?
Assuming that the resultant driving force acting on the handle is applied along the arm, a free-body diagram of the roller indicating the weight, normal force, and driving force is drawn.
The driving force can be resolved into its horizontal and vertical components.
The system&#39;s geometry can be used to determine the angle between the normal force and the vertical axis.
The moment equilibrium condition is then applied to contact point O. By substituting the values of weight, components of the driving force and the corresponding perpendicular distances, estimates the driving force.
If a force with a magnitude much lesser than the driving force is applied, the roller does not move.

rolweerstand: probleemoplossing

Rolweerstand, ook bekend als rolwrijving, is de kracht die de beweging van een rollend object, zoals een wiel, band of bal, weerstaat wanneer het over een oppervlak beweegt. Het wordt veroorzaakt door de vervorming van het object en het oppervlak dat met elkaar in contact staat, evenals andere factoren zoals interne wrijving, hysterese en energieverliezen binnen de materialen. Rolweerstand werkt in tegen de beweging van het object en vereist extra energie om het te overwinnen en de beweging te behouden. In praktische toepassingen kan het minimaliseren van rolweerstand de energie-efficiëntie verbeteren en slijtage verminderen van zowel het rollende object als het oppervlak. Stel dat we een grondwals hebben met een massa van 100 kg, een straal van 25 cm en een rolweerstandscoëfficiënt van 25 mm. De walsarm strekt zich uit onder een hoek van 30° ten opzichte van de horizontale as. De kracht die nodig is om de wals met constante snelheid te verplaatsen kan worden bepaald, op voorwaarde dat de wrijving bij de as wordt verwaarloosd. Als we aannemen dat de resulterende aandrijfkracht die op het handvat werkt langs de arm wordt toegepast, kan er een vrijlichaamsdiagram van de wals worden getekend, inclusief het gewicht (W), de normaalkracht (N) en de aandrijfkracht (F). De aandrijfkracht kan worden opgesplitst in zijn horizontale (Fh) en verticale (Fv) componenten. <img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;"> Vervolgens kan de geometrie van het systeem worden gebruikt om de hoek θ1 te bepalen tussen de normaalkracht (N) en de verticale as. De momentevenwichtsvoorwaarde wordt dan toegepast op het contactpunt O. <img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> Het gewicht van de wals dat gelijk is aan de massa maal de versnelling door zwaartekracht wordt berekend als 98,1 N. Door de waarden van het gewicht, de horizontale en verticale componenten van de aandrijfkracht en de overeenkomstige loodrechte afstanden te substitueren, wordt de aandrijfkracht F berekend als 120,86 N. Om een constante snelheid te behouden, moet de horizontale component van de aandrijfkracht de rolweerstand overwinnen. Als er een kracht met een veel kleinere magnitude dan de aandrijfkracht wordt toegepast, beweegt de wals niet. Het begrijpen van deze relatie helpt bij het waarderen van de invloed van verschillende krachten op de beweging van de wals en het belang van het overwegen van verschillende factoren bij het ontwerpen en gebruiken van grondwalsen.

Rolweerstand: Probleemoplossing

Rolling resistance, also known as rolling friction, is the force that resists the motion of a rolling object, such as a wheel, tire, or ball, when it ...

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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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mechanical engineering

Lawn Roller Force Calculation

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