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

考虑一个质量为 100 kg、半径为 25 cm 的草坪滚压器。滚压器的手柄与水平轴成 30 度角延伸。
忽略轴处产生的摩擦，若滚动阻力系数为 25 mm，使滚轮以恒定速度移动所需的力是多少？
假设作用在手柄上的合力沿臂的方向施加，则绘制出表示滚轮所受重力、法向力和驱动力的受力分析图。
驱动力可以分解为水平分量和垂直分量。
可以通过系统的几何结构来确定法向力与垂直轴之间的夹角。
随后将力矩平衡条件应用于接触点 O。通过代入重量、驱动力分量及其相应的垂直距离的数值，估算驱动力。
如果施加的力远小于驱动力，则滚轮不会移动。

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	<li>梅里亚姆，JL;Kraige， LG 和 Bolton， JN （2020）。工程力学 \u2012 静力学。新泽西州霍博肯:约翰·威利。第 373 页。</li>
	<li>比尔，F.P.;约翰斯顿，ER;马祖克，DF;克伦威尔，PJ 和塞尔夫，BP（2019 年）。工程师的矢量力学 \u2012 静力学和动力学。纽约:麦格劳-希尔。页码 463</li>
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滚动阻力：问题求解

滚动阻力，也被称为滚动摩擦力，是当滚动的物体（例如车轮、轮胎或球）在表面上发生移动时阻碍其运动的力。它是由物体和与之接触表面的变形以及其他因素（如内摩擦、滞后和材料内的能量损失）所引起的。滚动阻力与物体的运动是相反的，需要额外的能量来克服它并保持其运动。在实际的应用中，使滚动阻力最小化可以提高其能源效率，以此来减少滚动物体表面的磨损。 假设有一个质量为100kg，半径为25cm，滚动阻力系数为25mm的草坪辊。辊臂与水平轴成30°角。以此可以确定将辊子以恒定的速度来移动所需的力，前提是忽略轴上所发生的摩擦。 假设施加在手柄上的合力是沿着辊臂的方向，从而绘制出辊子的受力分析图，其中包括重力（W）、法向力（N）和牵引力（F）。牵引力可以分解为水平分量（Fh）和垂直分量（Fv）。 <img alt="Figure 1" src="/files/ftp_upload/14329/14329_PT_Fig_1v2.svg" style="text-align: center; height: 200px;"> 接下来，系统的几何形状可以用来确定法向力（N）与垂直轴之间的角度θ1。然后，将力矩的平衡条件应用于接触点O。 <img alt="Equation 1" src="/files/ftp_upload/14329/14329_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> 滚筒的重量等于质量与重力加速度的乘积，其计算结果为98.1N。通过替换重量、牵引力在水平方向和垂直方向的分量以及相应垂直距离的数值，可以计算出牵引力F为120.86N。 要保持其恒定速度，牵引力的水平分量必须要克服其中的滚动阻力。如果其中施加的力小于牵引力，那么滚筒将不会移动。了解这种关系有助于人们理解不同的力对滚筒的运动所产生的影响，以及在设计和使用草坪辊时能够考虑到各种因素的重要性。

滚动阻力，也称为滚动摩擦，是当一个滚动物体（如车轮、轮胎或球体）在表面滚动时，阻碍其运动的力。

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Friction

摩擦

KEY TERMS AND CONCEPTS

关键术语与概念

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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Lawn Roller Force Calculation

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