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

Rozważ wałek do trawy o masie 100 kg i promieniu 25 cm. Ramię rolki wysuwa się pod kątem trzydziestu stopni do osi poziomej.
Pomijając tarcie powstające na osi, jaka siła jest potrzebna do przesuwania rolki ze stałą prędkością, pod warunkiem, że współczynnik oporu toczenia wynosi 25 mm?
Zakładając, że wypadkowa siła napędowa działająca na uchwyt jest przyłożona wzdłuż ramienia, rysowany jest schemat swobodnego korpusu rolki wskazujący masę, siłę normalną i siłę napędową.
Siłę napędową można podzielić na składowe poziome i pionowe.
Geometria systemu może być wykorzystana do wyznaczenia kąta między siłą normalną a osią pionową.
Warunek równowagi momentu jest następnie stosowany do punktu kontaktowego O. Podstawiając wartości masy, składowych siły napędowej i odpowiadających im odległości prostopadłych, szacuje siłę napędową.
Jeśli zostanie przyłożona siła o wielkości znacznie mniejszej niż siła napędowa, rolka nie porusza się.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 452 \u2012 453.</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley. str. 373.</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strona 463</li>
</ol>

opór toczenia: rozwiązywanie problemów

Opór toczenia, znany również jako tarcie toczenia, to siła, która hamuje ruch toczącego się obiektu, takiego jak koło, opona lub piłka, gdy porusza się po powierzchni. Powstaje w wyniku odkształcenia obiektu i powierzchni stykającej się ze sobą, a także innych czynników, takich jak tarcie wewnętrzne, histereza i straty energii w materiałach. Opór toczenia przeciwdziała ruchowi obiektu, co wymaga dodatkowej energii do pokonania go i utrzymania ruchu. W praktycznych zastosowaniach minimalizacja oporu toczenia może poprawić efektywność energetyczną i zmniejszyć zużycie zarówno toczącego się obiektu, jak i powierzchni.

Rozważ walec do trawnika o masie 100 kg, promieniu 25 cm i współczynniku oporu toczenia wynoszącym 25 mm. Ramię wałka rozciąga się pod kątem 30° do osi poziomej. Siła wymagana do utrzymania wałka w stałej prędkości może być ustalona, o ile zignorujemy tarcie rozwijające się na osi.

Zakładając, że działająca siła napędowa na uchwyt jest stosowana wzdłuż ramienia, można narysować diagram sił swobodnych walca, obejmujący wagę (W), siłę normalną (N) oraz siłę napędową (F). Siłę napędową można rozłożyć na jej składowe poziomą (Fh) i pionową (Fv).

<img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;" />

Następnie geometria systemu może zostać wykorzystana do ustalenia kąta θ1 między siłą normalną (N) a osią pionową. Następnie można zastosować równowagę momentów do punktu kontaktu O.

<img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Wagi wałka, które wynoszą masę razy przyspieszenie ziemskie, oblicza się jako 98,1 N. Podstawiając wartości wagi, składowych poziomej i pionowej siły napędowej oraz odpowiadających odległości prostopadłych, siła napędowa F wynosi 120,86 N.

Aby utrzymać stałą prędkość, składowa pozioma siły napędowej musi pokonać opór toczenia. Jeśli zastosuje się siłę o znacznie mniejszej wartości niż siła napędowa, walec nie porusza się. Zrozumienie tej zależności pozwala docenić wpływ różnych sił na ruch wałka i znaczenie rozważenia różnych czynników podczas projektowania i stosowania walców.

Opór toczenia: rozwiązywanie problemów

Opór toczenia, znany również jako tarcie toczne, to siła, która opiera się ruchowi toczącego się obiektu, takiego jak koło, opona lub piłka, gdy ...

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Inżynieria mechaniczna

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Kluczowe terminy i pojęcia

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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