Name: dry friction in crate, ladder, and frame problems
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 27 s
Channel: JoVE

乾式摩擦の問題は、3つのタイプに分類できます。
最初のタイプは、明らかな差し迫った動きがないことです。木枠に加えられる力を考えてみましょう。
未知数が3つあり、3つの平衡方程式から評価できます。したがって、発生した摩擦力を決定できます。
2番目のタイプは、すべての接触点、たとえば滑らかな壁に対して配置されたはしごでの差し迫った動きです。
4つの未知数は、接触点に適用される3つの平衡方程式と1つの静摩擦方程式から決定できます。
次に、はしごを滑らずに配置できる最小角度を評価します。
3番目のタイプは、いくつかの接触点での差し迫った動きです。未知の水平力を受ける 2 部材フレームについて考えてみます。
7つの未知数、6つの平衡方程式、および2つの可能な静摩擦方程式のうちの1つがあります。これらを解くと、移動を引き起こすために必要な水平方向の力を決定できます。
力を大きくすると、左端で滑って右端ではなく左端で滑る、またはその逆の2つの可能性があります。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。406-412ページ。</li>
	<li>メリアム、JL、クレイジ、LGおよびボルテン、JN(2016)。エンジニアリングメカニクス:静力学とダイナミクス。第8版、シンガポール:John Wiley & Sons。337ページ。</li>
</ol>

摩擦問題の種類

Types of Friction Problems

摩擦は物理学、工学、日常生活において重要な概念です。摩擦は、接触している二つの表面間の相対的な運動またはその傾向に反対する力です。様々な応用で遭遇する最も一般的な摩擦の種類は、乾燥摩擦です。乾燥摩擦問題は、独自の特徴と課題を持つ三つのタイプに大きく分類されます。

最初のタイプの乾燥摩擦問題は、明らかな運動の兆候がない状況に関わるものです。これの典型的な例は、力がクレートに加えられるがクレートが静止している場合です。床とクレートの間で発生する摩擦力は、加えられた力に反対し、クレートを静止させます。

このタイプの問題を解決するには、三つの未知数を考慮する必要があります。それは、法線力、摩擦力、および加えられた力です。これらの未知数は、システムを支配する三つの平衡方程式を使用して評価することができます。これらの未知数が決定されると、発生する摩擦力を計算することができ、クレートの安定性に影響を与える要因についての洞察が得られます。

二番目のタイプの乾燥摩擦問題は、接触点全てで運動が起こる場合に関わるものです。この問題の例としては、滑らかな壁に置かれたはしごがあります。このシナリオでは、はしごは滑り落ちる寸前であり、はしごが滑り落ちない最小の角度を決定しなければなりません。

この問題を解決するためには、最初に次の四つの未知数を特定する必要があります。それは、両方の接触点での法線力、はしごの底部の摩擦力、および角度です。これらの未知数は、接触点で適用される三つの平衡方程式と一つの静摩擦方程式を使用して決定することができます。これらの値を計算すると、はしごを滑り落ちない最小の角度を評価することができます。

三番目のタイプの乾燥摩擦問題は、一部の接触点で運動が起こる場合に関わります。このタイプの問題の例としては、未知の水平力がかかる二部材フレームがあります。この場合、フレームは一方の端で滑り落ちるかのようにするが他方の端は静止するかもしれません。

この問題を解決するためには、次の七つの未知数を特定する必要があります。それは、両方の接触点での法線力、両端での摩擦力、適用された水平力、および支持部の反力です。これらの未知数を決定するためには、六つの平衡方程式と二つの可能な静摩擦方程式のうちの一つが使用できます。これらの方程式を解くことで、フレームの運動に必要な水平力を求めることができます。

フレームに加えられる力が増加すると、二つの可能性が発生する場合があります。一つは、左端で滑り落ちるのに右端は静止したままというケースです。これらの可能性を分析することで、フレームの運動に影響を与える要因と滑り落ちる条件をよりよく理解することができます。

摩擦は、物理学、工学、そして日常生活において不可欠な概念です。それは、そのような運動の相対的な運動または傾向に対抗する力です...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Friction

摩擦

KEY TERMS AND CONCEPTS

主要用語と概念

dry friction in crate, ladder, and frame problems

Dry friction problems often focus on crates, ladders, and frames that are close to slipping. Dry friction is the force that resists relative motion, or the tendency for motion, between two surfaces in contact. In many physics and engineering problems, this force helps keep an object still or defines the point where motion is about to begin.

One common case has no clear impending motion. A force may be applied to a crate, but the crate stays at rest. The friction force between the floor and the crate opposes the applied force and keeps the crate stationary. To solve this kind of problem, the normal force, the friction force, and the applied force are the three unknowns. They can be found using the three equilibrium equations for the system.

A second type of problem reaches impending motion at every contact point. A ladder against a smooth wall is a good example. The ladder is just about to slip, and the goal is to find the smallest angle that still keeps it from sliding. This setup has four unknowns: the normal forces at both contact points, the friction force at the base, and the angle. The three equilibrium equations and one static friction equation are used to solve for these values.

A third type involves impending motion at some contact points, but not at others. A two-member frame with an unknown horizontal force is one example. The frame may slip at one end while the other end remains stationary. This case has seven unknowns, including the normal forces, the friction forces at both ends, the applied horizontal force, and the reaction forces at the supports. Six equilibrium equations and one of the two possible static friction equations are used to determine the force needed to start movement. As the applied force increases, the frame may slip on the left while the right side stays fixed, or the reverse may happen.

Dry Friction in Crate, Ladder, and Frame Problems

dry-friction-in-crate-ladder-and-frame-problems

dry friction

Dry Friction in Crates and Everyday Motion

Dry friction appears when two solid surfaces touch and try to move past each other. Students can see it when they walk, slide a box across a table, or rub their hands together. Even though it is common, the forces behind it are not easy to see. A simple crate on a rough horizontal floor helps explain the idea. When an external force pushes the crate sideways, two main forces act on it. The normal force acts perpendicular to the surface and helps balance the crate’s weight, while the frictional...

static friction

Static Friction at the Point of Slip

Static friction is the force that keeps two surfaces from starting to slide past each other. It acts when there is a tendency for motion, but not yet actual slipping. This force helps explain everyday actions like walking on the ground and driving a car. A towing example shows how static friction changes as force is applied. A truck pulls a car with a rope, and the car stays still at first. The car is in static equilibrium, which means the forces on it are balanced. Gravity and the normal...

kinetic friction

Sliding Friction Between Moving Surfaces

Kinetic friction is the sliding friction that acts when two surfaces move against each other. It opposes relative motion and acts parallel to the contact surface, in the opposite direction of travel. In the truck and car example, the car first stays still because static friction holds it in place. When the truck’s force becomes greater than the limiting static frictional force, the friction at the contact surface drops to a lower value. The car then begins to slide, and its speed increases. At...

characteristics of dry friction

Static and Kinetic Dry Friction

Dry friction is the resistance between two solid surfaces that move against each other without lubrication or any fluid. A common example is a gardener pushing a wheelbarrow across the ground. The wheel and the ground create dry friction that slows the motion. Before the wheelbarrow starts to move, static friction acts at the contact surface. Static friction is the force that opposes motion before slipping begins, and it helps keep the wheelbarrow stable. It is present only when there is no...

types of friction problems

Dry friction problems often focus on crates, ladders, and frames that are close to slipping. Dry friction is the force that resists relative motion, or the tendency for motion, between two surfaces in contact. In many physics and engineering problems, this force helps keep an object still or defines the point where motion is about to begin. One common case has no clear impending motion. A force may be applied to a crate, but the crate stays at rest. The friction force between the floor and the...

friction: problem solving

Friction on a Banked Road

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

wedges

Wedges and Self-Locking Stability

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort. One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force. To analyze wedge...

frictional forces on screws

Square-Thread Screw Mechanics and Friction

Square-threaded screws use a helical thread to turn force into lifting motion. They are common fasteners, but they are also useful for transmitting power and motion in machines. A jack with a square-threaded screw lifts heavy loads when force is applied at the handle and the screw turns. A screw can be viewed as a cylindrical shaft with an inclined square ridge wrapped around it. The distance between two neighboring threads is called the pitch. The lead is the distance the screw advances in...

upward impending motion

Screw Jack Force and Friction Analysis

A square-threaded screw jack lifts heavy loads by turning handle force into a twisting moment. Its upward motion depends on overcoming static friction between the screw threads and the jack. To study this motion, the thread can be treated as if it were a block on the groove of the jack after the thread is completely unraveled. A free-body diagram helps show the forces acting on this simplified system. The force at the handle creates a horizontal force that pushes the movable thread up the...

self-locking screw

Screw Jack Self-Locking Behavior

A square-threaded screw jack can hold a heavy load because of its self-locking behavior. This feature makes the device more reliable when it is used to lift large weights or apply a strong force. If the screw keeps its position after the turning moment is removed, the jack is self-locking. Self-locking happens because friction changes the way the forces act on the thread. The friction force reverses direction, and the reaction force moves to the other side of the thread’s normal. In this case,...

screw: problem solving

Screw Torque and Self-Locking

Screw torque and self-locking are analyzed by looking at a threaded screw shaft and a plate gear. The shaft has a mean radius and a lead. The plate gear also has a mean radius. The coefficient of static friction between the screw and the gear is part of the setup. The first step is to find the static friction angle, φ. This angle is defined by the coefficient of static friction. Next, the lead angle is calculated from the lead and the mean radius of the shaft. It gives the screw geometry...

frictional forces on flat belts

Flat Belt Tension and Friction

Flat belt tension and friction control how power moves from one pulley to another. Flat belts are used in many industrial systems to transmit power between pulleys. As the belt wraps around the pulleys, the tension changes because of friction between the belt and the pulley surface. When a pulley turns counterclockwise, the belt side moving away from the pulley has the higher tension, called T2. The side moving toward the pulley has the lower tension, called T1. To estimate these tensions, the...

flat belts: problem solving

Flat Belt Forces and Pulley Moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system. As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β,...

pivot bearings

Axial Load Support in Pivot Bearings

Pivot bearings support axial loads on a rotating shaft. A bearing helps two parts move relative to each other while reducing friction and wear. In this design, the pivot is placed at the end of the shaft to carry the axial thrust. The pivot surface can be flat, conical, or truncated, depending on the application. In a flat pivot bearing, the axial load is spread over the bearing area. The pressure is uniform and can be found by dividing the load by the area. To study the forces more closely,...

collar bearings

Friction Torque in Collar Bearings

Collar bearings support axial loads on rotating shafts, and their friction helps determine the torque needed to start motion. They are used in many machines and may have a single collar or multiple collars, depending on the application and load needs. For a single collar bearing under an axial load, the contact area is the ring-shaped region between the external radius and the internal radius of the collar. If the bearing is assumed to support the load evenly, the uniform normal pressure is...

journal bearings

Friction Moment in Journal Bearings

Journal bearings support rotating shafts and axles while helping keep them stable. They are used in machines such as engines, turbines, and pumps. Their job is to reduce friction, wear, and vibration. A journal bearing works by keeping a thin film of lubricant between the bearing surface and the rotating shaft. This film limits direct contact and lowers frictional force. The video uses a rope winch with dry or only partly lubricated journal bearings to show the idea. As the spool turns...

bearings: problem solving

Double-Collar Bearing Torque Calculations

Double-collar bearing torque calculations show how friction and axial force affect bearing performance. Engineers use these calculations to test whether the bearing can handle the forces and moments it experiences during operation. This helps them choose and design bearings for specific applications and setups. For a double-collar bearing with set dimensions and an axial force applied, the maximum frictional moment can be found with a standard expression. The equation is rearranged, and the...

rolling resistance

Tire Deformation and Rolling Resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

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...

key terms and concepts

Explore dry friction through crate, ladder, and frame problems. Learn how equilibrium and static friction equations help predict when slipping begins.

Dry Friction in Crate, Ladder, and Frame Problems | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Dry Friction in Crate, Ladder, and Frame Problems

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