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

干摩擦问题可分为三种类型。
第一种类型是无明显即将发生的运动。考虑对一个箱子施加一个力。
存在三个未知数，可通过三个平衡方程求解，因此可确定产生的摩擦力。
第二种类型是所有接触点均处于即将发生运动的状态，例如，一个&#160;靠在光滑墙壁上的梯子。
四个未知量可通过三个平衡方程以及适用于接触点的一个静摩擦方程来确定。
然后，评估梯子在不打滑的情况下所能放置的最小角度。
第三种类型是接触点处的即将发生运动的情况。考虑一个受到未知水平力作用的两构件框架。
共有七个未知量、六个平衡方程以及两个可能的静摩擦力方程之一。通过求解这些方程，可确定引起运动所需的水平力。
当增大作用力时，会出现两种可能情况：左侧端点滑动而右侧端点不滑动，或者相反。

<ol>
	<li>希伯勒，RC（2016 年）。工程力学:静力学。第十四版，新泽西州:皮尔逊。第 406-412 页。</li>
	<li>Meriam， JL， Kraige， LG 和 Bolten， JN（2016 年）。工程力学:静力学和动力学。第八版，新加坡:John Wiley & Sons。第 337 页。</li>
</ol>

摩擦问题的类型

Types of Friction Problems

摩擦是物理学、工程学和日常生活中的一个基本概念。它是两个接触表面之间能够产生相对运动或具有趋势运动的力。在各种应用中能够遇到最常见的摩擦类型是干摩擦。干摩擦问题可以广泛分为三种类型，每种类型都有着独特的特点和挑战。 第一种类型的干摩擦问题涉及到没有明显即将发生运动的情况。一个典型的例子是当力施加到一个木箱上时，木箱会保持静止。地板和木箱之间所产生的摩擦力会抵抗施加在上面的力，并使木箱保持静止。 要解决这种类型的问题，必须考虑其中涉及到的三个未知数：法向力、摩擦力和所施加的力。可以使用三个控制系统的平衡方程来对这些未知数进行评估。一旦确定了这些未知数，就可以计算出其中所产生的摩擦力，从而由此来了解影响木箱稳定性的因素。 第二种类型的干摩擦问题涉及到即将发生运动的情况。这个问题的一个例子是将梯子放在光滑的墙上。在这种情况下，梯子即将会发生滑动，同时必须确定梯子可以放置的最小角度，以免使其产生滑动。 要解决这个问题，首先必须要确定存在的四个未知数：两个接触点的法向力，梯子底部的摩擦力和角度。可以使用适用于接触点的三个平衡方程和一个静摩擦方程来确定这些未知数。一旦计算出这些值，便可以对梯子可以放置的最小角度来进行评估。 第三种类型的干摩擦问题涉及到即将发生运动的情况，但不是所有的接触点都是如此。这种问题的一个例子是受到未知水平力的两个构件框架。在这种情况下，框架的一侧可能会发生滑动，而另一侧则会保持静止。 要解决这个问题，必须确定其中存在的七个未知数：两个接触点的法向力，两端的摩擦力，施加的水平力和反支撑力。可以使用六个平衡方程和两个可能的静摩擦方程之一来确定这些未知数。通过对这些方程进行求解，可以由此来确定使框架发生运动所需的水平力。 随着施加到框架上力的增加，可能会发生两种可能性：左端发生滑动而右端保持静止，反之亦然。通过对这些可能性进行分析，可以更好地理解影响框架运动的因素以及框架发生滑动的条件。

摩擦是物理学、工程学和日常生活中的一个基本概念。它是一种阻碍物体相对运动或相对运动趋势的力……

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

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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