Physics 101 learning object 1
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双麟 曹Two blocks of mass m1 and m2 are attached by a spring. A force F is exerted on m1, compressing the spring. For m1 to oscillate upwards after F is removed and lift m2, the minimum force F needed is (m1 + m2)g. The spring is compressed by an amount equal to the downward force of m1 divided by the spring constant. For the spring to lift m2 after oscillating due to F's removal, the additional compression must equal m2g divided by the spring constant. Adding these compressions equals the total downward force that must be balanced by F.
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Lo
1) Two blocks of mass m1 and m2 are attached by a spring. A force F is exerted on m1.
2) After F is removed, m1 undergoes simple harmonic motion, compressing and extending the spring.
3) For the spring to lift m2 using the motion of m1, the minimum force F must be (m1 + m2)g, the combined weight of both blocks.
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1) Two blocks of mass m1 and m2 are attached by a spring. A force F is exerted on m1.
2) After F is removed, m1 undergoes simple harmonic motion, compressing and extending the spring.
3) For the spring to lift m2 using the motion of m1, the minimum force F must be (m1 + m2)g, the combined weight of both blocks.
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The document discusses stresses in beams, including:
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The document discusses stresses in beams, including:
1. Pure bending causes zero shear force, resulting in a constant bending moment along the beam.
2. A positively curved beam under bending moment develops compression on top and tension on bottom, with the neutral axis in between with zero stress.
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An example calculates the width of a key preventing a pulley from rotating on a shaft under a given torque, by determining the shear force and dividing by the area of the key.
Bearing stress is calculated by dividing the bearing load by the bearing contact area, which can also be expressed by dividing the load by the product of the width and height of the bearing area.
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Shear stress is caused by forces acting parallel to the surface of an object. The shear stress τ can be calculated using the equation τ = V/A, where V is the shear load and A is the cross-sectional area resisting the force. Shear stress is illustrated in examples involving determining the width of a key connecting a pulley to a shaft and calculating the minimum diameter of a pin connecting structural members.
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Macaulay's method provides a continuous expression for the bending moment of a beam subjected to discontinuous loads like point loads, allowing the constants of integration to be valid for all sections of the beam. The key steps are:
1) Determine reaction forces.
2) Assume a section XX distance x from the left support and calculate the moment about it.
3) Insert the bending moment expression into the differential equation for the elastic curve and integrate twice to obtain expressions for slope and deflection with constants of integration.
4) Apply boundary conditions to determine the constants, resulting in final equations to calculate slope and deflection at any section. This avoids deriving separate equations for each beam section as with traditional methods
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1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis.
2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.
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This document discusses curved beams and unsymmetrical bending. It begins by introducing the Winkler-Bach theory for analyzing the bending of initially curved beams where bending occurs in the plane of curvature and the cross section is symmetrical about this plane. The theory obtains the stress-moment-deflection relationship assuming plane sections remain plane after bending, called the Winkler-Bach formula. It then examines bending of an infinitesimal portion of a curved beam, identifying the neutral axis and neutral surface where stress is zero. The linearized strain equation is presented and solved to derive the Winkler-Bach theory. Unsymmetrical bending is then briefly mentioned where loads can be applied in or out of the plane of symmetry for cross-
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This document discusses shear force diagrams, bending moment diagrams, and working stress in beams. It defines beams as structural members that are long compared to their lateral dimensions and induce bending when subjected to transverse loads. The document explains that shear forces balance external loads on beam cross sections and act parallel to the cross section. Bending moments are the resistance of a beam to bending and result from the summation of shear forces. The document also describes how to draw shear force and bending moment diagrams and defines working stress as the yield point divided by the factor of safety used in design.
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This document contains 9 questions related to mechanics of solids problems involving beams. The questions involve selecting beam sections based on allowable stresses, calculating maximum stresses in beams, and determining maximum loads beams can support. Beam cross sections include W, S, T, and inverted T shapes. Beams are subjected to uniformly distributed loads, concentrated loads, and combinations of loads. Calculations require determining maximum bending moments and stresses given beam properties, loads, and stress allowability criteria.
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The document summarizes key concepts about internal loadings and shear and moment diagrams in structural members. It discusses how to determine the normal force, shear force, and bending moment at a cross section using a method of sections. It also describes how to construct and plot shear and moment diagrams as functions of location along the member length using equilibrium equations. Graphical methods for establishing shear and moment diagrams using relationships between loadings, shear, and moment are also presented. Finally, techniques for analyzing cables subjected to concentrated and distributed forces are summarized.
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The document discusses calculating shear force, bending moment, and deflection distributions over the length of a beam subjected to various transverse loads. It summarizes that the beam material is linear-elastic and isotropic, with all loads acting laterally in the same plane as potential deflections. Deflections are assumed to be small compared to the beam length. Equilibrium equations are applied to relate the loading to shear force, bending moment, slope, and deflection. Examples of simply supported beams with single or multiple loads are provided, showing the relationships between the different mechanical properties.
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This document discusses deflection in simply supported beams. A simply supported beam is supported at both ends but not fixed, allowing it to move vertically but not horizontally. The theoretical deflection of a simply supported beam under a center load can be calculated using the Euler-Bernoulli beam equation, which takes into account the load, length, modulus of elasticity, and moment of inertia. The document compares theoretical deflection values calculated from the equation to practical deflection values measured in experiments.
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The document discusses stresses in beams, including:
1. Pure bending causes zero shear force, resulting in a constant bending moment along the beam.
2. A positively curved beam under bending moment develops compression on top and tension on bottom, with the neutral axis in between with zero stress.
3. Shear stresses in beams are highest at the center of rectangular beams and at the edge of circular beams.
4. Slope, deflection, and radius of curvature are related through beam equations involving the bending moment and moment of inertia.
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Work power-energy
With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
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1. Work done by a constant force depends on the magnitude of the force and the displacement along the direction of the force. Work done by opposing forces is negative. Centripetal forces do no work as they are always perpendicular to motion.
2. The work-kinetic energy theorem states that the work done on an object equals its change in kinetic energy. It can be used to calculate changes in speed.
3. Gravitational potential energy is defined as mgh. The principle of conservation of mechanical energy can be used to solve problems involving changes in kinetic and potential energy in an isolated system, such as an object moving under gravity.
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Elasticity is defined as an object's ability to return to its initial form after an external force is removed. Stress is calculated by dividing force by cross-sectional area, while strain is calculated by dividing change in length by initial length. Modulus of elasticity, also called Young's modulus, is calculated by dividing stress by strain and defines the relationship between stress and strain. Hooke's law states that stress is directly proportional to strain for an elastic material. Springs follow Hooke's law, with force proportional to displacement from equilibrium. Springs arranged in series have total displacement equal to the sum of individual displacements, while springs in parallel have the same displacement. Simple harmonic motion involves a restoring force proportional to displacement, like a spring or
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1. The lecture covered work, kinetic energy, and energy conservation.
2. Work is the transfer of energy via a force. It can be positive, negative, or zero depending on the angle between the force and displacement.
3. Kinetic energy is defined as 1/2 mv^2 and represents the energy of motion. The work done on an object causes a change in its kinetic energy.
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1. The lecture covered work, kinetic energy, and energy conservation.
2. Work is the transfer of energy using a force. Work can be positive, negative, or zero depending on the angle between the force and displacement.
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The document provides solutions to 4 physics problems from a final exam. Problem 1 involves calculating the tension in a rod connecting two boxes sliding down an inclined plane, given their masses and coefficients of friction. Problem 2 calculates the angular acceleration and velocity of a pulley with a hanging bucket. Problem 3 determines the work done by a spring and increase in thermal energy when a block compresses the spring. Problem 4 finds velocities after an elastic collision between a ball attached to a cord and a block.
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Work, energy, and power are defined. Work is force times distance. Kinetic energy is equal to one-half mass times velocity squared. Power is the rate of doing work, defined as work per unit time. Several examples of calculating work are provided for different scenarios like lifting an object, lowering an object, and work done by springs. The concept that work is based on the force component in the direction of motion is emphasized.
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Work, energy, and power are defined. Work is force times distance. Kinetic energy is equal to one-half mass times velocity squared. Power is the rate of doing work, defined as work per unit time. Several examples of calculating work are provided for different scenarios like lifting an object, springs, and overcoming friction. The key concepts of work, kinetic energy, and power are reviewed.
Work, power and energy
1. The document provides 11 physics problems related to work, power, and energy. The problems include calculations of velocity, force, acceleration, energy, and power for objects moving under the influence of forces or friction.
2. Sample questions calculate the velocity of blocks sliding down inclined planes, the heat generated when dragging an object, and the speed of a mass attached to a string passing over a pulley.
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A 0.2 kg block attached to a spring is stretched 20 cm and released. It travels through a 20 cm long, 0.3 friction area and up an incline. The block's initial potential energy is transferred to kinetic energy and work against friction until it stops. Calculations show the block will stop 1.7 times the length of the friction area, or 6 cm from the start.
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Trusses are structures composed of straight members connected at joints. They have three key characteristics: they only experience axial loads, loads are applied only at end points, and members are joined by pins. Trusses are used to support roofs and bridges. To analyze a truss, assumptions are made that loads act only at end points, member weight is ignored, and members experience only axial loads as either tension or compression. The method of joints and method of sections can be used to calculate the internal forces in each member and determine if each member experiences tension or compression.
Trusses
Trusses are structures composed of straight members connected at joints. They have three key characteristics: they only experience axial loads, loads are applied only at end points, and members are joined by pins. Trusses are used to support roofs and bridges. To analyze a truss, assumptions are made that loads act only at end points, member weight is ignored, and members experience only axial loads as either tension or compression. The method of joints and method of sections can be used to calculate the internal forces in each member and determine if each member is in tension or compression.
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The document discusses forces and equilibrium examples in physics. It covers textbook sections on Newton's laws of motion, free body diagrams, friction, gravity, springs, tension, and two-dimensional examples. Examples include calculating the force needed to keep a block from sliding down an incline and finding the tension in a string suspending a mass.
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The document discusses forces and equilibrium examples in physics. It covers textbook sections on Newton's laws of motion, friction, gravity, springs, tension, and two-dimensional examples. Key concepts include drawing free body diagrams, analyzing forces in different directions, and using equations like the force of a spring being proportional to its displacement.
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This document summarizes the work done by a horizontal mass spring system. It describes how the force exerted by a spring is proportional to its stretched or compressed length based on Hooke's law. It then shows the calculation for the work done by a spring as the product of the average force and distance. The document applies this to an example problem of a ball placed on a compressed spring on the floor that is released and may hit another identical spring on the ceiling. It shows the step-by-step work to calculate that the ball will reach a maximum height of 14.88 meters and compress the upper spring by 0.82 meters when it makes contact.
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This document discusses energy methods for structural analysis. It introduces key energy theorems like Betti's theorem, Maxwell's theorem, and Castigliano's theorem. It also discusses potential energy and stationary potential energy. Various energy terms are defined, such as external work, strain energy, and their relationships through the principle of conservation of energy. Examples are given of calculating energy for axial forces, shear forces, torsional moments, and different structural elements. Castigliano's first theorem is introduced for determining deflections and slopes using partial derivatives of internal strain energy.
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1. Newton's Laws of Motion describe the relationship between an object and the forces acting upon it. The three laws are: Law 1 explains inertia, Law 2 states that force equals mass times acceleration (F=ma), and Law 3 is the law of action-reaction.
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class 11 physics work energy and power study material free pdf download
class 11 physics work energy and power study material free pdf downloadVivekanand Anglo Vedic Academy
Welcome to the fascinating world of Work, Energy, and Power! In the realm of physics, these concepts form the cornerstone of understanding how objects interact with each other and how energy is transformed within systems. From the motion of everyday objects to the dynamics of celestial bodies, the principles of work, energy, and power are ubiquitous, shaping the very fabric of the universe.
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class 11 physics work energy and power study material free pdf download
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Physics 101 learning object 1
- 1. Physics 101 Learning Object 1: Vertical Oscillations Question Question: Two blocks with the mass of m1 and m2 respectively, is attached by a light spring (given its stiffness to be K) together (as shown in the graph below). Exert a pressure F on m1 block. In order to bring up m2 using m1 after the pressure F is removed, the minimum force F exerted on m2 should be ( ) A. m1g B. 2m1g C. (m1 +m2)g D. 2(m1 +m2)g
- 2. Solution: After the removal of pressure F, the block m1 undergoes the SHM. The balance position of m1 is its static position on the spring (that is, without the force exerted on its top). Assume the position to be a (as shown in the figure below), the difference of the length of the spring without m1 block on its top and the spring with m1 on its top (x0) is:
- 3. x0 =m1g/k The value of the amplitude during the SHM of m1 block is equal to the decrement of the spring with the pressure F exerted on m1 block on its top(x1). A= x1 = F/k Meanwhile the position of m1 block (b) is shown as follows, Assume the spring can just lift the m2 block with the increase of its length (x2) after the removal of the force F, thus, Kx2 = m2*g, x2 = m2*g/k
- 4. Since x1= x0+x2 F=(m1+m2)g The answer should be C