6161103 4.4 principles of moments
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This document discusses the principle of moments, which states that the moment of a force about a point is equal to the sum of the moments of its components about that point. It provides examples of calculating the moment of a force about different points using both trigonometric methods and resolving the force into Cartesian components. In one example, the moment of a 200N force acting at an angle is calculated to be 14.1 Nm about point A. In another, the moment of a 400N force is found to be -98.6 Nm about point O.
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Module 4
This document contains lecture material on moments and couples from a engineering mechanics course. It includes:
- Definitions of moment as the turning effect of a force and how to calculate moment magnitude using the perpendicular distance from the axis (moment arm).
- Details on sign conventions and using the right hand rule to determine moment direction.
- An explanation of Varignon's theorem which states the sum of all individual moments equals the moment of the resultant force.
- Examples of calculating moments using scalar and vector methods, as well as resolving force systems into equivalent force-couple systems.
- The definition of a couple as two equal and opposite parallel forces separated by a perpendicular distance, and characteristics such as couple
6161103 4.6 moment of a couple
A couple is formed by two parallel forces of equal magnitude but opposite direction. The moment of a couple, called the couple moment, is the tendency of the couple to cause rotation. The couple moment is calculated as the perpendicular distance between the forces multiplied by the force magnitude. Unlike a moment of a force, the couple moment can be applied to any point as it is a free vector.
6161103 4.9 further reduction of a force and couple system
The document describes methods to reduce systems of forces and moments acting on a rigid body to an equivalent single resultant force and moment. It discusses reducing force systems that are concurrent, coplanar, or parallel to a single resultant force located at a point P. The location of P can be determined by satisfying the moment condition such that the resultant force and moment are perpendicular. Examples demonstrate applying these methods to solve for the magnitude, direction, and application point of the equivalent resultant force.
6161103 4.5 moment of a force about a specified axis
1) A moment is a rotational force that tends to cause rotation about an axis.
2) The moment of a force about an axis can be found using either scalar or vector analysis. Scalar analysis involves determining the perpendicular distance from the force to the axis, while vector analysis uses the cross product of the position vector and force vector.
3) No moment is produced about an axis if the force is parallel or passes through the axis, as there is no leverage. The maximum moment occurs when the force is applied at the maximum distance from the axis.
241 wikarta-kuliah-iii-momen-gaya
The document discusses moments (torques) of forces, moments of couples, and equivalent force-couple systems. It provides:
1) Definitions of the moment of a force as the tendency for rotation about a point, and the moment of a couple as two parallel forces with equal magnitude acting in opposite directions separated by a perpendicular distance.
2) Examples calculating moments of forces about a point using scalar analysis and resolving forces into components.
3) Discussion of replacing multiple forces and couples with an equivalent single force and couple moment at a point, in order to more easily understand their overall effect.
6161103 4.1 moment of a force – scalar formation
1) Moment of a force is a measure of the tendency of a force to cause rotation about a point or axis.
2) The magnitude of the moment of a force is equal to the product of the force and the perpendicular distance (moment arm) from the axis to the line of action of the force.
3) The direction of the moment vector is determined using the right hand rule, with the thumb pointing along the moment axis in the direction of rotation.
6161103 4.3 moment of force vector formulation
1) Moment of force is calculated using the cross product of the position vector r and force vector F.
2) The magnitude of the moment is equal to the force F multiplied by the perpendicular distance d between the line of action of F and the point of reference.
3) The direction of the moment is determined by the right-hand rule applied to r and F.
16201806 bahan-ajar-ptm117-mekanika-teknik
Here are the key differences between a particle and a rigid body in mechanics:
Particle:
- Has no size or internal structure, it is considered a point object.
- Cannot transfer or support moments/torques. Only forces can act on a particle.
Rigid Body:
- Has size, shape and internal structure. It is an extended object.
- Can transfer and support both forces and moments/torques at its different points.
Other differences:
- Equations of equilibrium for a particle involve only forces. Equations for a rigid body involve both forces and moments.
- Deformations are not considered for a particle as it has no internal structure. Deformations may need to be
Chapter 3
This document discusses equilibrium of particles and free body diagrams. It provides an example of drawing a free body diagram for a cylinder suspended by two cables, and using the equations of equilibrium to solve for the unknown tensions in the cables. It also discusses 3D equilibrium, giving an example problem of finding an unknown force on a particle given its position and four other forces.
Mekanika teknik
Three key concepts are discussed in the document:
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2) A free body diagram shows all external forces acting on a particle or rigid body and is essential for writing equations of equilibrium.
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Mekanikateknik 140330175907-phpapp01
This document discusses mechanics and statics concepts such as forces, moments, and couples. It begins by defining mechanics as the branch of physics dealing with motion and forces. It then discusses rigid bodies, deformable bodies, and fluids. The document reviews the international system of units and conversions between SI and US customary units. It introduces concepts of force systems, the parallelogram law, and the principle of transmissibility. Subsequent sections cover vector addition of forces, moments of forces, moments of couples, and developing equivalent force-couple systems. Examples are provided to demonstrate solving static mechanics problems by resolving forces into components and applying principles of moments.
6161103 3.4 three dimensional force systems
1) Three-dimensional force systems involve resolving forces into x, y, and z components and using the equations of equilibrium to solve for unknown forces.
2) Examples are provided of using free body diagrams and the equations of equilibrium to solve for tensions in cables, magnitudes of applied forces, and stretches of springs in static systems with multiple forces.
3) Unknown forces and stretches are determined by setting the vector sum of the forces in x, y, and z directions equal to zero and solving the resulting simultaneous equations.
dynamics and static for the advanced Moments 3D.ppt
1. The document discusses moments of forces about points and axes in 3D space. It defines the moment of a force about a point as the cross product of the position vector and the force vector.
2. An example problem is presented to calculate the moment of a 3000N force about a point. The shortest distance between the point and the line of action of the force is also determined.
3. The moment of the same 3000N force about the axis between two points is then calculated. Dot and cross products of vectors are used to solve for the moments.
6161103 4.8 resultants of a force and couple system
1) The document discusses calculating the resultant force and moment on a rigid body from a system of individual forces and couples.
2) It provides equations to calculate the total resultant force, FR, total resultant moment, MR, and components of each.
3) Examples are given to demonstrate calculating the equivalent resultant force and moment at a point by summing the forces and moments of the individual components.
ME 245_ 2.pptx
This document provides an overview of statics concepts including:
- Forces on particles in 2D and 3D space including addition and resolution of forces
- Equilibrium of particles and rigid bodies using free body diagrams
- Moments of forces about points and axes
- Force couples and equivalent force systems
- Example problems are provided to demonstrate applying concepts to determine tensions, components of forces, moments, and equivalent single forces.
Website friction
This document discusses frictional forces. There are two types of friction: static friction for stationary objects and kinetic friction for moving objects. Frictional forces always act opposite to the direction of motion and are calculated using coefficients of friction multiplied by the normal force. Free-body diagrams can be used to visualize the various forces acting on an object. The coefficient of friction and normal force allow calculation of the maximum static frictional force and actual kinetic frictional force in problems where net force equals acceleration or zero. Examples are provided to demonstrate calculating frictional forces in different scenarios.
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6161103 4.9 further reduction of a force and couple system
6161103 4.9 further reduction of a force and couple system
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6161103 4.8 resultants of a force and couple system
6161103 4.8 resultants of a force and couple system
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6161103 11.7 stability of equilibrium
The document discusses the stability of equilibrium for mechanical systems. It defines three types of equilibrium:
1) Stable equilibrium occurs when a small displacement causes the system to return to its original position with potential energy at a minimum.
2) Neutral equilibrium occurs when a small displacement does not change the potential energy, which remains constant.
3) Unstable equilibrium occurs when a small displacement causes the system to move farther away from the original position with potential energy at a maximum.
The stability of equilibrium depends on the potential energy function and its derivatives evaluated at the equilibrium position. A system is stable if the second derivative of the potential energy is positive and unstable if it is negative.
6161103 11.3 principle of virtual work for a system of connected rigid bodies
The document discusses using the principle of virtual work to solve for equilibrium in systems of connected rigid bodies. It explains that the number of degrees of freedom must first be determined by specifying independent coordinates. Virtual displacements are then related to these coordinates. Equating the virtual work done by external forces and couples to zero provides equations to solve for unknowns like force magnitudes or equilibrium positions. Examples show applying this process to determine values like joint angles or reaction forces.
6161103 11 virtual work
This chapter introduces the principle of virtual work and how it can be used to determine the equilibrium configuration of connected rigid bodies. It defines work and virtual work, and establishes the potential energy function. The chapter outlines applying the principle of virtual work to particles, rigid bodies, and connected systems to investigate equilibrium and stability, using the potential energy criterion.
6161103 10.9 mass moment of inertia
Mass moment of inertia measures an object's resistance to angular acceleration and is defined as the integral of the second moment of mass elements about an axis. It depends on the axis chosen and the distribution of mass. For composite objects, the total mass moment of inertia is found by summing the contributions of each component. The parallel axis theorem allows calculating mass moments of inertia about parallel axes.
6161103 10.8 mohr’s circle for moments of inertia
The document describes Mohr's circle, which is used to analyze the principal moments of inertia for a given cross-sectional area. It presents equations to determine the radius and center of the Mohr's circle based on the area's moments of inertia (Ix, Iy) and product of inertia (Ixy). An example problem is shown where these values are used to construct the circle and determine the maximum and minimum moments of inertia and their corresponding principal axes.
6161103 10.7 moments of inertia for an area about inclined axes
This document discusses calculating moments of inertia for an area about inclined axes. It provides transformation equations to relate moments of inertia with respect to x-y axes to moments with respect to inclined u-v axes. It also describes how to determine the principal axes, which are the orientations that produce the maximum and minimum moments of inertia. An example is provided to illustrate finding the principal moments of inertia for a beam cross-section.
6161103 10.6 inertia for an area
Moment of inertia and product of inertia are properties that depend on the orientation of the axes they are calculated around. The product of inertia, Ixy, of an area can be positive, negative, or zero depending on the location and orientation of the x and y axes. Ixy is calculated by taking the double integral of xy over the entire area or using the parallel axis theorem which relates Ixy to the product of inertia about the centroidal axes, Ix'y', plus the cross product of the distance from the centroidal axes to the x and y axes.
6161103 10.5 moments of inertia for composite areas
1) Moments of inertia for composite areas can be determined by dividing the area into its composite parts, finding the moment of inertia of each part about its centroidal axis and the reference axis using the parallel axis theorem, and taking the algebraic sum.
2) The procedure was demonstrated by calculating the moment of inertia of a composite area made of a rectangle and circle, and another made of three rectangles.
3) For the second example, the cross-sectional area was divided into three rectangles, the moment of inertia of each was found about the x and y axes using the parallel axis theorem, and summed to find the total moment of inertia.
6161103 10.4 moments of inertia for an area by integration
This document discusses calculating moments of inertia for planar areas using integration. It describes:
1) Choosing a differential element for integration that has size in only one direction to simplify the calculation.
2) The procedure involves specifying a rectangular differential element and orienting it parallel or perpendicular to the axis of rotation.
3) Moments of inertia are calculated through single or double integration, depending on whether the element has thickness in one or two directions.
6161103 10.10 chapter summary and review
The document summarizes key concepts relating to area moment of inertia including that it represents the second moment of area about an axis and is used in structural strength equations. It can be determined by integration for irregular shapes or found in tables for common shapes. The parallel axis theorem allows calculating it about other axes or for composite shapes. Product of inertia and principal moments of inertia can also be determined using formulas, Mohr's circle, or the parallel axis theorem. Mass moment of inertia measures rotational resistance and can be found using disk or shell elements for axially symmetric bodies.
6161103 9.2 center of gravity and center of mass and centroid for a body
This document discusses the center of gravity, center of mass, and centroid of rigid bodies. It defines these terms and presents methods to calculate them using integrals of differential elements. Examples are provided to demonstrate calculating the centroid for areas and lines using appropriate coordinate systems and differential elements. Centroids are found by taking moments of these elements and the document outlines the general procedure to perform these calculations.
6161103 9.6 fluid pressure
1) Pascal's law states that pressure in a fluid at rest acts equally in all directions. The pressure (ρ) at a point depends on the specific weight (γ) or density (ρ) of the fluid and the depth (z) of the point, where ρ = γz or ρgz.
2) For a submerged plate, the pressure at different points depends on the depth of each point. The resultant force on the plate acts through its center of pressure, not the plate's centroid.
3) For curved or variable width plates, integration is used to determine the total pressure distribution and locate the center of pressure.
6161103 9.3 composite bodies
This document discusses analyzing the center of gravity of composite bodies made up of simpler shapes. It provides the procedure for doing so which includes: [1] Dividing the body into composite parts; [2] Determining the coordinates of each part's center of gravity; [3] Using equations to calculate the total center of gravity by taking weight-weighted sums of the coordinate positions. Examples are provided to demonstrate locating the center of gravity for areas and volumes made of multiple components.
6161103 9.7 chapter summary and review
This document summarizes key concepts from a chapter including: center of gravity and centroid determination using moment balances; calculating body properties like surface area and volume using theorems of Pappus and Guldinus; fluid pressure distribution and determining resultants passing through the loading diagram's centroid.
6161103 8.4 frictional forces on screws
Screws are commonly used as fasteners to transmit power or motion between machine parts. A screw can be thought of as an inclined plane wrapped around a cylinder. When a screw is rotated, the nut moves along the inclined plane of the screw thread. The distance the nut moves in one revolution is called the lead of the screw. Large axial loads on a screw generate significant frictional forces on the threads. The moment required to turn a screw under an axial load depends on the frictional forces and can be calculated using force and moment equilibrium equations. A self-locking screw will remain locked in place through frictional forces alone when the applied moment is removed.
6161103 8.3 wedges
Wedges are simple machines that transform applied forces into larger forces directed at approximately right angles. They are used to give small adjustments to heavy loads by applying a smaller force. To analyze wedges, force and moment equilibrium equations are used along with frictional force equations, with unknown normal and frictional forces. Wedges can be self-locking if the frictional forces alone are enough to hold the load without any applied force needed.
6161103 8.2 problems involving dry friction
This document discusses problems involving dry friction. It describes three types of friction problems: equilibrium, impending motion at all points, and impending motion at some points. Examples are provided to demonstrate how to set up and solve static friction problems using free body diagrams, equilibrium equations, and frictional equations. The key steps are to determine the number of unknowns and equations, draw free body diagrams, apply the appropriate equilibrium and frictional equations, and solve the system of equations.
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6161103 11.3 principle of virtual work for a system of connected rigid bodies
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6161103 10.7 moments of inertia for an area about inclined axes
6161103 10.5 moments of inertia for composite areas
6161103 10.5 moments of inertia for composite areas
6161103 10.4 moments of inertia for an area by integration
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留信网认证的作用:
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3:国家专业人才认证中心颁发入库证书
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The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...
Leonardo DiCaprio, a name synonymous with Hollywood stardom and acting excellence. has captivated audiences for decades with his talent and charisma. But, the Leonardo DiCaprio haircut is one aspect of his public persona that has garnered attention. From his early days as a teenage heartthrob to his current status as a seasoned actor and environmental activist. DiCaprio's hairstyles have evolved. reflecting both his personal growth and the changing trends in fashion. This article delves into the many phases of the Leonardo DiCaprio haircut. exploring its significance and impact on pop culture.
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Leonardo DiCaprio Super Bowl: Hollywood Meets America’s Favorite Game
Introduction
Leonardo DiCaprio is synonymous with Hollywood stardom and acclaimed performances. has a unique connection with one of America's most beloved sports events—the Super Bowl. The "Leonardo DiCaprio Super Bowl" phenomenon combines the worlds of cinema and sports. drawing attention from fans of both domains. This article delves into the multifaceted relationship between DiCaprio and the Super Bowl. exploring his appearances at the event, His involvement in Super Bowl advertisements. and his cultural impact that bridges the gap between these two massive entertainment industries.
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Leonardo DiCaprio: The Hollywood Icon
Early Life and Career Beginnings
Leonardo Wilhelm DiCaprio was born in Los Angeles, California, on November 11, 1974. His journey to stardom began at a young age with roles in television commercials and educational programs. DiCaprio's breakthrough came with his portrayal of Luke Brower in the sitcom "Growing Pains" and later as Tobias Wolff in "This Boy's Life" (1993). where he starred alongside Robert De Niro.
Rise to Stardom
DiCaprio's career skyrocketed with his performance in "What's Eating Gilbert Grape" (1993). earning him his first Academy Award nomination. He continued to gain acclaim with roles in "Romeo + Juliet" (1996) and "Titanic" (1997). the latter of which cemented his status as a global superstar. Over the years, DiCaprio has showcased his versatility in films like "The Aviator" (2004). "Start" (2010), and "The Revenant" (2015), for which he finally won an Academy Award for Best Actor.
Environmental Activism
Beyond his film career, DiCaprio is also renowned for his environmental activism. He established the Leonardo DiCaprio Foundation in 1998, focusing on global conservation efforts. His commitment to ecological issues often intersects with his public appearances. including those related to the Super Bowl.
The Super Bowl: An American Institution
History and Significance
The Super Bowl is the National Football League (NFL) championship game. is one of the most-watched sporting events in the world. First played in 1967, the Super Bowl has evolved into a cultural phenomenon. featuring high-profile halftime shows, memorable advertisements, and significant media coverage. The event attracts a diverse audience, from avid sports fans to casual viewers. making it a prime platform for celebrities to appear.
Entertainment and Advertisements
The Super Bowl is not only about football but also about entertainment. The halftime show features performances by some of the biggest names in the music industry. while the commercials are often as anticipated as the game itself. Companies invest millions in Super Bowl ads. creating iconic and sometimes controversial commercials that capture public attention.
Leonardo DiCaprio's Super Bowl Appearances
A Celebrity Among the Fans
Leonardo DiCaprio's presence at the Super Bowl has noted several times. As a high-profile celebrity. DiCaprio attracts
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留信网认证的作用:
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2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Leonardo DiCaprio House: A Journey Through His Extravagant Real Estate Portfolio
Introduction
Leonardo DiCaprio, A name synonymous with Hollywood excellence. is not only known for his stellar acting career but also for his impressive real estate investments. The "Leonardo DiCaprio house" is a topic that piques the interest of many. as the Oscar-winning actor has amassed a diverse portfolio of luxurious properties. DiCaprio's homes reflect his varied tastes and commitment to sustainability. from retreats to historic mansions. This article will delve into the fascinating world of Leonardo DiCaprio's real estate. Exploring the details of his most notable residences. and the unique aspects that make them stand out.
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Leonardo DiCaprio House: Malibu Beachfront Retreat
A Prime Location
His Malibu beachfront house is one of the most famous properties in Leonardo DiCaprio's real estate portfolio. Situated in the exclusive Carbon Beach. also known as "Billionaire's Beach," this property boasts stunning ocean views and private beach access. The "Leonardo DiCaprio house" in Malibu is a testament to the actor's love for the sea and his penchant for luxurious living.
Architectural Highlights
The Malibu house features a modern design with clean lines, large windows. and open spaces blending indoor and outdoor living. The expansive deck and patio areas provide ample space for entertaining guests or enjoying a quiet sunset. The house has state-of-the-art amenities. including a gourmet kitchen, a home theatre, and many guest suites.
Sustainable Features
Leonardo DiCaprio is a well-known environmental activist. whose Malibu house reflects his commitment to sustainability. The property incorporates solar panels, energy-efficient appliances, and sustainable building materials. The landscaping around the house is also designed to be water-efficient. featuring drought-resistant plants and intelligent irrigation systems.
Leonardo DiCaprio House: Hollywood Hills Hideaway
Privacy and Seclusion
Another remarkable property in Leonardo DiCaprio's collection is his Hollywood Hills house. This secluded retreat offers privacy and tranquility. making it an ideal escape from the hustle and bustle of Los Angeles. The "Leonardo DiCaprio house" in Hollywood Hills nestled among lush greenery. and offers panoramic views of the city and surrounding landscapes.
Design and Amenities
The Hollywood Hills house is a mid-century modern gem characterized by its sleek design and floor-to-ceiling windows. The open-concept living space is perfect for entertaining. while the cozy bedrooms provide a comfortable retreat. The property also features a swimming pool, and outdoor dining area. and a spacious deck that overlooks the cityscape.
Environmental Initiatives
The Hollywood Hills house incorporates several green features that are in line with DiCaprio's environmental values. The home has solar panels, energy-efficient lighting, and a rainwater harvesting system. Additionally, the landscaping designed to support local wildlife and promote
Sara Saffari: Turning Underweight into Fitness Success at 23
Uncover the remarkable journey of Sara Saffari, whose transformation from underweight struggles to being recognized as a fitness icon at 23 underscores the importance of perseverance, discipline, and embracing a healthy lifestyle.
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Know about the five famous artists who have transitioned to Big Band Music from Swing Music. Here is a glimpse of their work and contributions.
Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspiration
Introduction
In the realm of entertainment, few names resonate as Orpah Winfrey Dwayne Johnson. Both figures have carved unique paths in the industry. achieving unparalleled success and becoming iconic symbols of perseverance, resilience, and inspiration. This article delves into the lives, careers. and enduring legacies of Orpah Winfrey Dwayne Johnson. exploring how their journeys intersect and what we can learn from their remarkable stories.
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Early Life and Backgrounds
Orpah Winfrey: From Humble Beginnings to Media Mogul
Orpah Winfrey, often known as Oprah due to a misspelling on her birth certificate. was born on January 29, 1954, in Kosciusko, Mississippi. Raised in poverty by her grandmother, Winfrey's early life was marked by hardship and adversity. Despite these challenges. she demonstrated a keen intellect and an early talent for public speaking.
Winfrey's journey to success began with a scholarship to Tennessee State University. where she studied communication. Her first job in media was as a co-anchor for the local evening news in Nashville. This role paved the way for her eventual transition to talk show hosting. where she found her true calling.
Dwayne Johnson: From Wrestling Royalty to Hollywood Superstar
Dwayne Johnson, also known by his ring name "The Rock," was born on May 2, 1972, in Hayward, California. He comes from a family of professional wrestlers, with both his father, Rocky Johnson. and his grandfather, Peter Maivia, being notable figures in the wrestling world. Johnson's early life was spent moving between New Zealand and the United States. experiencing a variety of cultural influences.
Before entering the world of professional wrestling. Johnson had aspirations of becoming a professional football player. He played college football at the University of Miami. where he was part of a national championship team. But, injuries curtailed his football career, leading him to follow in his family's footsteps and enter the wrestling ring.
Career Milestones
Orpah Winfrey: The Queen of All Media
Winfrey's career breakthrough came in 1986 when she launched "The Oprah Winfrey Show." The show became a cultural phenomenon. drawing millions of viewers daily and earning many awards. Winfrey's empathetic and candid interviewing style resonated with audiences. helping her tackle diverse and often challenging topics.
Beyond her talk show, Winfrey expanded her empire to include the creation of Harpo Productions. a multimedia production company. She also launched "O, The Oprah Magazine" and OWN: Oprah Winfrey Network, further solidifying her status as a media mogul.
Dwayne Johnson: From The Ring to The Big Screen
Dwayne Johnson's wrestling career took off in the late 1990s. when he became one of the most charismatic and popular figures in WWE. His larger-than-life persona and catchphrases endeared him to fans. making him a household name. But, Johnson had ambitions beyond the wrestling ring.
In the early 20
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6161103 4.4 principles of moments
- 1. 4.4 Principles of Moments Also known as Varignon’s Theorem “Moment of a force about a point is equal to the sum of the moments of the forces’ components about the point” For F = F1 + F2, MO = r X F1 + r X F2 = r X (F1 + F2) =rXF
- 2. 4.4 Principles of Moments The guy cable exerts a force F on the pole and creates a moment about the base at A MA = Fd If the force is replaced by Fx and Fy at point B where the cable acts on the pole, the sum of moment about point A yields the same resultant moment
- 3. 4.4 Principles of Moments Fy create zero moment about A MA = Fxh Apply principle of transmissibility and slide the force where line of action intersects the ground at C, Fx create zero moment about A MA = F yb
- 4. 4.4 Principles of Moments Example 4.6 A 200N force acts on the bracket. Determine the moment of the force about point A.
- 5. 4.4 Principles of Moments Solution Method 1: From trigonometry using triangle BCD, CB = d = 100cos45° = 70.71mm = 0.07071m Thus, MA = Fd = 200N(0.07071m) = 14.1N.m (CCW) As a Cartesian vector, MA = {14.1k}N.m
- 6. 4.4 Principles of Moments Solution Method 2: Resolve 200N force into x and y components Principle of Moments MA = ∑Fd MA = (200sin45°N)(0.20m) – (200cos45°)(0.10m) = 14.1 N.m (CCW) Thus, MA = {14.1k}N.m
- 7. 4.4 Principles of Moments Example 4.6 The force F acts at the end of the angle bracket. Determine the moment of the force about point O.
- 8. 4.4 Principles of Moments Solution Method 1 MO = 400sin30°N(0.2m)-400cos30°N(0.4m) = -98.6N.m = 98.6N.m (CCW) As a Cartesian vector, MO = {-98.6k}N.m
- 9. 4.4 Principles of Moments Solution Method 2: Express as Cartesian vector r = {0.4i – 0.2j}N F = {400sin30°i – 400cos30°j}N = {200.0i – 346.4j}N For moment, r r r i j k r r r M O = r XF = 0.4 − 0 .2 0 200.0 − 346.4 0 r { } = − 98.6k N .m