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

건조 마찰 문제는 세 가지 유형으로 분류할 수 있습니다.
첫 번째 유형은 명백한 임박한 움직임이 없는 것입니다. 상자에 가해지는 힘을 생각해 보십시오.
세 가지 미지수가 있으며, 이는 세 가지 평형 방정식에서 평가할 수 있습니다. 따라서 개발된 마찰력을 측정할 수 있습니다.
두 번째 유형은 모든 접점에서 임박한 움직임입니다(예: 매끄러운 벽에 배치된 사다리).
4개의 미지수는 접촉점에 적용되는 3개의 평형 방정식과 1개의 정적 마찰 방정식으로 결정할 수 있습니다.
그런 다음 사다리가 미끄러지지 않고 배치될 수 있는 가장 작은 각도를 평가합니다.
세 번째 유형은 일부 접촉 지점에서 임박한 움직임입니다. 알 수 없는 수평력의 영향을 받는 2멤버 프레임을 고려하십시오.
7개의 미지수, 6개의 평형 방정식 및 2개의 가능한 정적 마찰 방정식 중 하나가 있습니다. 이를 해결하면 움직임을 일으키는 데 필요한 수평력을 결정할 수 있습니다.
힘을 증가시킴에 따라 두 가지 가능성이 발생하는데, 오른쪽 끝이 아닌 왼쪽 끝에서 미끄러지거나 그 반대의 경우도 마찬가지입니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 406-412쪽.</li>
	<li>Meriam, J.L., Kraige, L.G. 및 Bolten, J.N.(2016). Engineering Mechanics: Statics and Dynamics(정역학 및 동역학). 여덟 번째 판, 싱가포르 : John Wiley & Sons. 337쪽.</li>
</ol>

마찰 문제의 유형

Types of Friction Problems

마찰은 물리학, 공학 및 일상생활에서 필수적인 개념입니다. 접촉하는 두 표면 사이의 상대적인 운동 또는 그러한 운동 경향에 반대하는 힘입니다. 다양한 응용 분야에서 직면하는 가장 일반적인 유형 중 하나는 건식 마찰입니다. 건식 마찰 문제는 크게 세 가지 유형으로 분류될 수 있으며, 각각 고유한 특성과 도전 과제를 가지고 있습니다.
첫 번째 유형의 건식 마찰 문제는 명백하게 임박한 움직임이 없는 상황을 포함합니다. 그 대표적인 예는 상자에 힘이 가해지지만 정지 상태를 유지하는 것입니다. 바닥과 상자 사이에 발생한 마찰력은 가해지는 힘에 반대하고 상자를 정지 상태로 유지합니다. 
이런 종류의 문제를 해결하려면 관련된 세 가지 미지의 힘, 즉 수직력, 마찰력, 가해진 힘을 고려해야 합니다. 이 미지들은 시스템을 지배하는 세 가지 평형방정식을 사용하여 평가할 수 있습니다. 이 미지들이 결정되면 개발된 마찰력이 계산되어 상자의 안정성에 영향을 미치는 요인에 대한 통찰력을 제공할 수 있습니다.
두 번째 유형의 건식 마찰 문제는 모든 접촉점에서 임박한 움직임이 발생하는 상황을 포함합니다. 이 문제의 예는 매끄러운 벽에 기대어 배치되는 사다리입니다. 이 시나리오에서는 사다리가 미끄러지기 직전이며, 사다리가 미끄러지지 않고 배치될 수 있는 가장 작은 각도를 결정해야 합니다.
이 문제를 해결하기 위해서는 먼저 두 접점에서의 수직력, 사다리 밑면에서의 마찰력, 각도 등 네 가지 미지수를 확인해야 합니다. 이들 미지수는 세 개의 평형방정식과 접점에서 적용되는 하나의 정마찰방정식을 이용하여 결정할 수 있습니다. 이 값이 계산되면 사다리가 미끄러지지 않고 놓일 수 있는 가장 작은 각도를 평가할 수 있습니다.
세 번째 유형의 건식 마찰 문제는 임박한 움직임이 모든 것은 아니지만 일부 접촉점에서 발생하는 상황을 포함합니다. 이러한 유형의 문제의 예는 알려지지 않은 수평력의 영향을 받는 2부재 골조입니다. 이 경우, 골조는 다른 쪽에서 정지 상태를 유지하면서 한쪽 끝에서 미끄러지는 것을 경험할 수 있습니다.
이 문제를 해결하기 위해서는 두 접점에서의 수직력, 양 끝에서의 마찰력, 가해진 수평력, 지지대에서의 반력 등 7가지 미지의 힘을 알아내야 합니다. 이 미지의 값은 6개의 평형방정식과 2개의 가능한 정적 마찰력 중 하나로 구할 수 있습니다. 이 방정식들을 풀면 골조에 작용하는 수평력을 구할 수 있습니다. 
골조에 가해지는 힘이 증가함에 따라 왼쪽 끝에서 미끄러지는 경우와 오른쪽 끝이 정지 상태를 유지하는 경우, 또는 그 반대의 경우 두 가지 가능성이 발생할 수 있습니다.

마찰은 물리학, 공학 및 일상 생활에서 필수적인 개념입니다. 그러한 운동의 상대적인 운동 또는 경향에 반대하는 힘입니다 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Friction

마찰

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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

Dry Friction in Crate, Ladder, and Frame Problems

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