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The document describes a relativistic momentum paradox scenario involving two equal masses connected by a massless string and constrained to move parallel at a speed v. When the constraints are removed, the masses collide and stick together into a single blob with greater mass than the sum of the initial masses due to their collision speed. However, the document reasons that the x-direction momentum must remain constant, so the speed of the combined blob must be less than v, slowing down the overall apparatus.
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Using resolution of forces:
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2) Varignon's theorem states the algebraic summation of force components about any point equals the moment of the original force.
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Here are the key steps to solve this problem:
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The document discusses concepts related to equilibrium in physics including:
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- Conditions for translational and rotational equilibrium as the sum of forces and sum of torques being equal to zero respectively
- Examples of calculating tensions in ropes and finding the center of gravity to solve equilibrium problems
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The document discusses static equilibrium, where an object experiences no net forces or torques acting upon it. It defines static and dynamic equilibrium, and explores conditions for equilibrium through examples of masses attached to levers or hanging from rods. Key concepts covered include the definitions of force, torque, and their relationships. Torque is described as a twisting force that depends on the distance from the axis of rotation and the perpendicular component of the applied force.
81 einstein’s equivalence principle
81 - EINSTEIN’S EQUIVALENCE PRINCIPLE
https://drive.google.com/file/d/0B-yVvzgMrlRpenpGTHpSbEpra1E/view?usp=sharing
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Momento en estructuras
This document discusses basic principles of statics, which is the branch of mechanics dealing with stationary bodies under forces. It defines static equilibrium as when the sum of all forces and moments equals zero. It also discusses concepts such as static determinacy, types of forces including vectors and their addition, resolution of forces, concurrent forces, and free-body diagrams. Examples are provided to demonstrate how to determine reactions and tensions using these principles.
Mechanical Technology Grade 10 Chapter 8 forces
This chapter discusses forces and how to represent and analyze systems of forces. Key points include:
- A force is a push or pull that can change the motion of an object. Forces are measured in newtons.
- Systems of multiple forces can be analyzed using diagrams like the parallelogram, triangle, and polygon of forces to find the net force (resultant) and force needed to balance the system (equilibrant).
- Bow's notation uses letters to label spaces between force lines in a diagram, allowing multiple forces to be represented as vectors in equilibrium.
- Examples demonstrate using these force diagrams and techniques to solve for unknown forces in systems.
Statics ppt
The document discusses the shapes of chains and arches under gravity. It explains that a catenary is the curve formed by a chain hanging from two fixed points, with the tension in the chain causing it to form a smooth curve. It then explains two methods for analyzing these shapes: using mechanics and forces, and using the calculus of variations to find the curve that minimizes potential energy. The document notes that both methods produce the catenary curve as the solution. It then provides an example analysis of the forces in a tight horizontal string and in a freestanding arch.
How to Prepare Rotational Motion (Physics) for JEE Main
The document discusses the cross product, torque, rotational motion, and angular momentum. It defines the cross product of two vectors A and B as a vector C perpendicular to both A and B with magnitude ABsinθ. It describes properties of the cross product including being anti-commutative. It also defines torque as a measure of the tendency of a force to cause rotational motion, and discusses rotational dynamics and angular momentum.
Lecture5.pptx
1) Newton's law of viscosity was generalized to account for complex fluid flow patterns where velocity can vary in different directions and over time.
2) By analyzing forces on a small volume element sliced in different orientations, it was determined that stresses have both pressure and viscous components.
3) The viscous stresses were shown to be linear combinations of the velocity gradients, and for isotropic fluids can be expressed by two scalar coefficients multiplied by the symmetric parts of the velocity gradient tensor.
Unit 1 Notes
This document provides an overview of kinematics and mechanics concepts including:
- Kinematics deals with describing motion without considering forces. Key concepts include displacement, velocity, acceleration, and equations for uniformly accelerated motion.
- Dynamics considers how forces affect motion. Key concepts include forces, mass, acceleration, momentum, and equilibrium. Equilibrium occurs when net forces are balanced and there is no acceleration.
- Projectile motion refers to objects moving under the influence of gravity only. The horizontal and vertical components of motion can be analyzed separately using kinematics equations.
CONSERVATION OF MOMENTUM NameINTWO DIMENSIONS1. Two obje.docx
CONSERVATION OF MOMENTUM Name
INTWO DIMENSIONS
1. Two objects are arranged on a level, frictionless table as shown. Two experiments are conducted
in which object A is launched toward the stationary block B. The initial speed of object A is the
same in both experiments; the direction is not. The initid and final velocities of object A in each
experiment are shown.
The mass of block B is four times that of object A (m" = 4m^).
Top views Velocity Yectors
(drawn to scale)
Mech
HW-63
{
do,
Experiment 1 - before collision
ld",l= o ilur: ?
- after collision
Tn,
. uei
Direction of Lfio
Experiment2 - before collision 2 - after collision
a. In the space provided, draw separate arrows
represeiting the direction of the change in momentum
vector of object A in the two experiments.
Is the magnitude of the change in m.omcntum of
object A in experiment I greater than, less than, or
equal to that in experiment 2? Explain.
Experiment I Experiment 2
b. In the space provided, draw separate arrows
representing the direction of the change in momentum
vector of block B in the two experiments.
Afier the collisions, is the magnitude of the momentum
of block B in experiment I greater than, less than, or
equal to that in experiment 2? If the momentum of
block B is zero in either case, state that explicitly.
Explain.
Direction of Al^
Experiment I Experiment 2
Tutorials in Introductory Physics
McDermott, Shaffer, and the P,E.G., U. Wash.
I arson
Custom zod EA.,for U,CO, Boulder
Mech
HW-64
Conseroation of momentum in two dimensions
Two objects collide on a level, frictionless table. The mass of object A is 5.0 kg; the mass of
object n is f .O tg. The objects stick together after the collision. The initial velocity of object A
and the final velocity of both objects are shown.
2.
Before collision
dltAi
After collision
1do, = d"r)
(One side of a square represents 0.1 m/s)
In the space provided, draw separate arrows for
object A and for object B representing the direction of
the change in momentum vector of the object.
Is the magnitude of the change in m,omentum of
object A greater than, less than, or equal to that of
object B? Explain your reasoning.
Direction of Al
Object A Object B
b. System C is the system of both objects A and B combined. How does
the momentum of system C before the collision compare to the
momentum of system C after the collision? Discuss both magnitude
and direction.
Construct and label a vector showing the momentum 6f system C at an
instant before the collision. Show your work clearly.
c, Construct and label a vector showing the initial velocity of object B.
Show your work clearly.
(Each side of a square
represents 0.4 kg'm/s)
(Each side of a square
represents 0.1 m/s)
Tutorials in Introductory Physics
McDermott, Shaffer, and the P.E.G., U, Wash.
@ rson
Custom znd H., for U,CO, Boulder
Consentation of momentum in two dimensions Name
3. Object A collides on a horizontal frictionless surface with an Frictionles.
Engmech 01 (vectors)
Engineering mechanics is the science that studies how physical systems respond to external forces. It examines scalar and vector quantities like time, mass, force, and displacement. The document outlines fundamental concepts in engineering mechanics like particles, rigid bodies, and Newton's laws of motion, and methods for adding vectors including the Pythagorean theorem and head-to-tail graphical method.
Scrodinger Cat, Quantum theory, CP Violation and Anti-matter
This article presents my studies in Schrodinger's Equation, electron-positron CP Violation and anti-matter annihilation. Enjoy.
Engineering mechanics system of coplanar forces by
Engineering Mechanics covers various topics in mechanics including:
1. Relativistic mechanics deals with mechanics compatible with special and general relativity.
2. Quantum mechanics provides a mathematical description of energy, matter, and their interactions at nanoscopic scales.
3. Mechanics of deformable bodies deals with how forces are distributed in solid bodies and the resulting stresses and deformations.
Learning object 1 travelling waves
The document describes the movement of travelling waves through a medium. It defines key concepts such as pulses, displacement, and speed. It provides an analogy of a wave moving through a crowd at a sports game. The key equation given relates the displacement of a point on the medium to the distance and time: D(x,t) = D(x-vt). It then works through an example problem applying this equation to find the displacement of a marked point on a rope at a given time, as well as determining when the maximum displacement occurs for a different point. Finally, it discusses how the speed of a wave depends on the tension and linear mass density of the medium.
Similar to Prob77 (19)
How to Prepare Rotational Motion (Physics) for JEE Main
How to Prepare Rotational Motion (Physics) for JEE Main
CONSERVATION OF MOMENTUM NameINTWO DIMENSIONS1. Two obje.docx
CONSERVATION OF MOMENTUM NameINTWO DIMENSIONS1. Two obje.docx
Scrodinger Cat, Quantum theory, CP Violation and Anti-matter
Scrodinger Cat, Quantum theory, CP Violation and Anti-matter
Engineering mechanics system of coplanar forces by
Engineering mechanics system of coplanar forces by
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Prob77
- 1. Week 77 (3/1/04) Relativistic momentum paradox Two equal masses are connected by a massless string with tension T. (By “massless”, we mean that it has no mass in its unstretched, zero-length state.) The masses are constrained to move with speed v along parallel lines, as shown below. The constraints are then removed, and the masses are drawn together. They collide and make one blob which continues to move to the right. Is the following reasoning correct? If your answer is “no”, then state what is invalid about whichever of the four sentences is/are invalid. “The forces on the masses point in the y-direction. Therefore, there is no change in momentum in the x-direction. But the mass of the resulting blob is greater than the sum of the initial masses (because they collided with some relative speed). Therefore, the speed of the resulting blob must be less than v (to keep px constant), so the whole apparatus slows down in the x-direction.” v v T