03 Forces Concept Overview
FORCES | CONCEPT OVERVIEW The TOPIC OF FORCES can be referenced on page 67 of the NCEES Supplied Reference Handbook, 9.4 version for Computer Based Testing.
CONCEPT INTRO: A FORCE represents the action of one body on another. It can be exerted by actual contact or at a distance, as in the case of gravitational forces and magnetic forces. The TOPIC OF FORCES can be referenced under the topic of STATICS on page 67 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing.
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A FORCE is a vector quantity that is characterized by its: • Magnitude – The magnitude of a vector is specified by a positive number and a unit having appropriate dimensions. No unit is stated if the dimensions are those of a pure number. • Line of Action – The line of action of a vector is hypothetical straight line that is collinear with the vector. The linear of actions helps to exaggerate or demonstrate the direction at which the force is acting. • Point of Action – The point of action of a vector is the exactly location or point about which the vector is acting on the define body of analysis. You can think of the point of action as the place or location that a forces acts, such that a point load would act directly on one point of action on a rigid body. • Direction – The direction of the vector is the orientation about which the force acts on the body at the point of action, relative to a define coordinate system and origin. • Sense of Direction – The sense of direction of a vector is specified by the order of two points on a line parallel to the vector. You can think of the sense as whether the vector is moving backward or forward, relative to a defined coordinate system.
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When there is more than one vector force and they are added together, it is crucial to keep track of direction and line of action of the force. Using the Cartesian Coordinate System, horizontal translation to the right along the x-axis and vertical translation upwards along the y-axis is defined as positive (+). On the other hand, horizontal translation to the left along the x-axis and vertical translation downward along the yaxis is defined as negative.
UNITS OF FORCE: The TOPIC OF UNITS OF FORCE can be referenced under the topic of UNITS on page 1 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing. The most commonly used unit for force is the NEWTON, which is an SI unit that is denoted by the symbol “𝑁”. The Newton is derived from Newton’s second law of motion where it is defined that a force of 1 𝑁 causes 1 𝑘𝑔 to accelerate 1 is more conventionally defined as 1
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& '(
. A Newton
Though, we are probably more familiar with and comfortable using SI units, we should be prepared to work problems that use US units as well, because we can expect to see these on the FE Exam. The standard US unit for force is the POUND with a symbol 𝑙𝑏& or 𝑙𝑏- . Similar to the Newton, a force of 1 𝑙𝑏- causes a mass of 1 𝑠𝑙𝑢𝑔 to accelerate at -1
1 (. '
US units are a confusing way of representing mass because universally the mass of an object is reported as a weight in 𝑙𝑏& or 𝑙𝑏- . However, the weight of an object in pounds is not a mass, but actually the force of gravity acting on the mass. Consequently, an extra step to determine an object’s mass in slugs must be completed using its weight in pounds using the following formula:
𝑚'34*' =
𝑊(𝑙𝑏) 𝑓𝑡 𝑔 ; 𝑠
Where,
𝑔 = 32.17
-1 '(
is the acceleration due to gravity
NEWTON’S 3 LAWS OF MOTION: The topic of NEWTON’S 3 LAWS OF MOTION is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook.
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Newton's laws of motion are three physical laws that form the basis for classical mechanics and can be summarized as such: 1. NEWTON’S FIRST LAW: a. NEWTON’S FIRST LAW OF MOTION, also commonly referred to as the LAW OF INERTIA, states that an object at rest tends to stay at rest until acted upon by an unbalanced force. b. If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion). 2. NEWTON’S SECOND LAW: a. NEWTON’S SECOND LAW OF MOTION states that when a force acts upon an object that has mas (𝑚), a corresponding acceleration is produced. b. If the result force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant in and the direction of this resultant force. c. A body of mass (𝑚), subject to a net force (𝐹), undergoes an acceleration (𝑎) that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., 𝐹 = 𝑚𝑎. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body. 3. NEWTON’S THIRD LAW: a. NEWTON’S THIRD LAW OF MOTION states that for every action, there is an equal and opposite reaction. The mutual forces of action and reaction between two bodies are equal, opposite, and collinear.
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b. The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. c. This means that whenever a first body exerts a force (𝐹) on a second body, the second body exerts a force (−𝐹) on the first body. “𝐹 and – 𝐹” are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with “𝐹” called the "action" and (−𝐹) the "reaction". The action and the reaction are simultaneous. TYPES OF FORCES: Forces can be classified in to categories based on how they are applied to another body. EXTERNAL FORCES are forces created by the interaction between the system of interest and its surroundings. Forces that you may be familiar with that are considered to be external forces are gravitational forces, drag or lift forces, and buoyancy forces, amongst others. Forces exerted by one part of a structure to another part are called CONSTRAINT FORCES, or SUPPORT REACTIONS. These forces occur in places such as joints and connections between components, and are crucial in the analysis of statics problems. INTERNAL FORCES are forces that occur inside a given structure or component as a response to applied external loads or external forces, such as support restraints. As an example, a rope stretched has a tension force acting on the inside. Most solid objects have a very complex distribution of internal forces. Due to the complex nature of internal force distributions, it is impossible to design a component that is guaranteed not to fail or deform, and this is why we design using a Factor of Safety defined off a very specific set of loading circumstances.
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CONCEPT EXAMPLE: The following problem introduces the concept reviewed within this module. Use this content as a primer for the subsequent material. Determine the mass of a chair (in lbs.) pushed with a net force of 20 𝑁 that causes it to accelerate at a rate of 4 𝑚/𝑠 ; . A. 0.44 𝑙𝑏𝑠 B. 176 𝑙𝑏𝑠 C. 5 𝑘𝑔 D. 11 𝑙𝑏𝑠
SOLUTION: As in most statics problem we can expect to see on the exam, you need to use the equations of equilibrium to solve for some unknown(s). We will identify the loads and external forces applied to the structure, and use the equations of equilibrium to solve for the desired unknown(s). The formula for NEWTON’S SECOND LAW is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook.
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The goal is to determine the mass of a chair pushed with a net force of 20 𝑁 that causes it to accelerate at a rate of 4 𝑚/𝑠 ; expressed in 𝑙𝑏𝑠. The formula of Newton’s Second Law of Motion for constant mass is ∑𝐹 = 𝑚𝑎 where: ∑𝐹 = 𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒 𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 (𝐹𝑛𝑒𝑡) 𝑚 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 In this problem, we are given: 𝑚 = 𝑡ℎ𝑒 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 𝑣𝑎𝑙𝑢𝑒 𝑤𝑒 𝑎𝑟𝑒 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 ∑𝐹 = 𝐹𝑛𝑒𝑡 = 20 𝑁 𝑜𝑟 20 𝑘𝑔 ∙ 𝑚S; 𝑠 S; 𝑎 = 4 𝑚 ∙ 𝑠 S; Plugging these values in to the formula of Newton’s Second Law of Motion for constant mass, we get:
F = ma
𝑘𝑔 ∙ 𝑚 𝐹 20 𝑁 20 𝑠 ; 𝑚= = 𝑚 = = 5 𝑘𝑔 𝑚 𝑎 4 ; 4 ; 𝑠 𝑠 Made with by Prepineer | Prepineer.com
𝑚 = 5 𝑘𝑔
2.2 𝑙𝑏𝑠 = 11 𝑙𝑏𝑠 1 𝑘𝑔
Therefore, the correct answer choice is D. 𝟏𝟏 𝒍𝒃𝒔, as the mass of the chair is 𝟏𝟏 𝒍𝒃𝒔.
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CONCEPT INTRO: A FORCE represents the action of one body on another. It can be exerted by actual contact or at a distance, as in the case of gravitational forces and magnetic forces. The TOPIC OF FORCES can be referenced under the topic of STATICS on page 67 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing.
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by Prepineer | Prepineer.com
A FORCE is a vector quantity that is characterized by its: • Magnitude – The magnitude of a vector is specified by a positive number and a unit having appropriate dimensions. No unit is stated if the dimensions are those of a pure number. • Line of Action – The line of action of a vector is hypothetical straight line that is collinear with the vector. The linear of actions helps to exaggerate or demonstrate the direction at which the force is acting. • Point of Action – The point of action of a vector is the exactly location or point about which the vector is acting on the define body of analysis. You can think of the point of action as the place or location that a forces acts, such that a point load would act directly on one point of action on a rigid body. • Direction – The direction of the vector is the orientation about which the force acts on the body at the point of action, relative to a define coordinate system and origin. • Sense of Direction – The sense of direction of a vector is specified by the order of two points on a line parallel to the vector. You can think of the sense as whether the vector is moving backward or forward, relative to a defined coordinate system.
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by Prepineer | Prepineer.com
When there is more than one vector force and they are added together, it is crucial to keep track of direction and line of action of the force. Using the Cartesian Coordinate System, horizontal translation to the right along the x-axis and vertical translation upwards along the y-axis is defined as positive (+). On the other hand, horizontal translation to the left along the x-axis and vertical translation downward along the yaxis is defined as negative.
UNITS OF FORCE: The TOPIC OF UNITS OF FORCE can be referenced under the topic of UNITS on page 1 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing. The most commonly used unit for force is the NEWTON, which is an SI unit that is denoted by the symbol “𝑁”. The Newton is derived from Newton’s second law of motion where it is defined that a force of 1 𝑁 causes 1 𝑘𝑔 to accelerate 1 is more conventionally defined as 1
Made with
)*& '(
.
by Prepineer | Prepineer.com
& '(
. A Newton
Though, we are probably more familiar with and comfortable using SI units, we should be prepared to work problems that use US units as well, because we can expect to see these on the FE Exam. The standard US unit for force is the POUND with a symbol 𝑙𝑏& or 𝑙𝑏- . Similar to the Newton, a force of 1 𝑙𝑏- causes a mass of 1 𝑠𝑙𝑢𝑔 to accelerate at -1
1 (. '
US units are a confusing way of representing mass because universally the mass of an object is reported as a weight in 𝑙𝑏& or 𝑙𝑏- . However, the weight of an object in pounds is not a mass, but actually the force of gravity acting on the mass. Consequently, an extra step to determine an object’s mass in slugs must be completed using its weight in pounds using the following formula:
𝑚'34*' =
𝑊(𝑙𝑏) 𝑓𝑡 𝑔 ; 𝑠
Where,
𝑔 = 32.17
-1 '(
is the acceleration due to gravity
NEWTON’S 3 LAWS OF MOTION: The topic of NEWTON’S 3 LAWS OF MOTION is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook.
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by Prepineer | Prepineer.com
Newton's laws of motion are three physical laws that form the basis for classical mechanics and can be summarized as such: 1. NEWTON’S FIRST LAW: a. NEWTON’S FIRST LAW OF MOTION, also commonly referred to as the LAW OF INERTIA, states that an object at rest tends to stay at rest until acted upon by an unbalanced force. b. If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion). 2. NEWTON’S SECOND LAW: a. NEWTON’S SECOND LAW OF MOTION states that when a force acts upon an object that has mas (𝑚), a corresponding acceleration is produced. b. If the result force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant in and the direction of this resultant force. c. A body of mass (𝑚), subject to a net force (𝐹), undergoes an acceleration (𝑎) that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., 𝐹 = 𝑚𝑎. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body. 3. NEWTON’S THIRD LAW: a. NEWTON’S THIRD LAW OF MOTION states that for every action, there is an equal and opposite reaction. The mutual forces of action and reaction between two bodies are equal, opposite, and collinear.
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b. The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. c. This means that whenever a first body exerts a force (𝐹) on a second body, the second body exerts a force (−𝐹) on the first body. “𝐹 and – 𝐹” are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with “𝐹” called the "action" and (−𝐹) the "reaction". The action and the reaction are simultaneous. TYPES OF FORCES: Forces can be classified in to categories based on how they are applied to another body. EXTERNAL FORCES are forces created by the interaction between the system of interest and its surroundings. Forces that you may be familiar with that are considered to be external forces are gravitational forces, drag or lift forces, and buoyancy forces, amongst others. Forces exerted by one part of a structure to another part are called CONSTRAINT FORCES, or SUPPORT REACTIONS. These forces occur in places such as joints and connections between components, and are crucial in the analysis of statics problems. INTERNAL FORCES are forces that occur inside a given structure or component as a response to applied external loads or external forces, such as support restraints. As an example, a rope stretched has a tension force acting on the inside. Most solid objects have a very complex distribution of internal forces. Due to the complex nature of internal force distributions, it is impossible to design a component that is guaranteed not to fail or deform, and this is why we design using a Factor of Safety defined off a very specific set of loading circumstances.
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by Prepineer | Prepineer.com
CONCEPT EXAMPLE: The following problem introduces the concept reviewed within this module. Use this content as a primer for the subsequent material. Determine the mass of a chair (in lbs.) pushed with a net force of 20 𝑁 that causes it to accelerate at a rate of 4 𝑚/𝑠 ; . A. 0.44 𝑙𝑏𝑠 B. 176 𝑙𝑏𝑠 C. 5 𝑘𝑔 D. 11 𝑙𝑏𝑠
SOLUTION: As in most statics problem we can expect to see on the exam, you need to use the equations of equilibrium to solve for some unknown(s). We will identify the loads and external forces applied to the structure, and use the equations of equilibrium to solve for the desired unknown(s). The formula for NEWTON’S SECOND LAW is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook.
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by Prepineer | Prepineer.com
The goal is to determine the mass of a chair pushed with a net force of 20 𝑁 that causes it to accelerate at a rate of 4 𝑚/𝑠 ; expressed in 𝑙𝑏𝑠. The formula of Newton’s Second Law of Motion for constant mass is ∑𝐹 = 𝑚𝑎 where: ∑𝐹 = 𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒 𝑎𝑐𝑡𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 (𝐹𝑛𝑒𝑡) 𝑚 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 In this problem, we are given: 𝑚 = 𝑡ℎ𝑒 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 𝑣𝑎𝑙𝑢𝑒 𝑤𝑒 𝑎𝑟𝑒 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 ∑𝐹 = 𝐹𝑛𝑒𝑡 = 20 𝑁 𝑜𝑟 20 𝑘𝑔 ∙ 𝑚S; 𝑠 S; 𝑎 = 4 𝑚 ∙ 𝑠 S; Plugging these values in to the formula of Newton’s Second Law of Motion for constant mass, we get:
F = ma
𝑘𝑔 ∙ 𝑚 𝐹 20 𝑁 20 𝑠 ; 𝑚= = 𝑚 = = 5 𝑘𝑔 𝑚 𝑎 4 ; 4 ; 𝑠 𝑠 Made with by Prepineer | Prepineer.com
𝑚 = 5 𝑘𝑔
2.2 𝑙𝑏𝑠 = 11 𝑙𝑏𝑠 1 𝑘𝑔
Therefore, the correct answer choice is D. 𝟏𝟏 𝒍𝒃𝒔, as the mass of the chair is 𝟏𝟏 𝒍𝒃𝒔.
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