"End of Chapter Optimization Summary" Interaction - Force PPT

"End of Chapter Optimization Summary" Interaction - Force PPT

Integration and improvement

Further analysis of the elasticity of rods and ropes

1. rod elasticity

Freely rotating rod: The elastic force must be along the direction of the rod, which can provide pulling force or pushing force.

Fixed rod: The elastic force is not necessarily along the direction of the rod, but is determined by the state of the object.

2. rope elasticity

(1) "Dead knot" rope: It can be understood as dividing the rope into two sections. The knot cannot slide along the rope. The two sides are regarded as two independent ropes, and the elastic forces are not necessarily equal.

(2) "Slipknot" rope: Generally, the rope crosses the pulley or a smooth hook is hung on the rope. It is actually the same rope. The knot can slide along the rope, and the elastic force on both sides of the rope is equal.

As shown in Figure A, the light rope AD crosses the fixed pulley on the right end of the fixed horizontal beam BC to hang an object with mass M1, ∠ACB=30°; in Figure B, one end of the light rod HG is fixed on the vertical wall with a hinge , the other end G is pulled by the string EG, and EG is also 30° with the horizontal direction. An object with mass M2 is pulled by the string GF at the G point of the light rod. Find:

(1) The ratio of the tension FTAC of the light rope AC section to the tension FTEG of the thin rope EG;

(2) The supporting force of light rod BC on end C;

(3) The supporting force of the light rod HG on the G end.

Summary and improvement

(1) In the problem of rope pole support, it is necessary to first determine whether the rope is a "dead knot" or a "slip knot", and whether the pole is a "free pole" or a "fixed pole". Generally, the node is selected as the research object for stress analysis.

(2) The elastic force of the rod is different from the elastic force of the rope. The elastic force of the rope always points along the rope in the direction of the rope contraction, but the elastic force of the rod does not necessarily follow the direction of the rod. The judgment of its size and direction must be determined according to the motion state of the object. , can be understood as "provided on demand", that is, in order to maintain the state of the object, the magnitude and direction of the required elastic force are obtained by solving the force balance.

The "sudden change" problem of friction

Common situations of sudden changes in friction

Category Description Case Illustration

Static - Static "sudden change" The object is in a state of equilibrium under the action of friction and other forces. When other forces acting on the object change suddenly, if the object can still remain stationary, the magnitude or direction of the static friction force on the object will change. A "sudden change" will occur. An object is stationary on an inclined plane under the action of a horizontal force F. If F suddenly increases and the object is still stationary, the magnitude or direction of the static friction force will "suddenly change."

Summary of methods

When the external force on an object changes, the friction force on the object may change suddenly. The key to solving this kind of problem is to correctly analyze the force and motion state of the object, so as to find the sudden "critical point" of the friction force of the object.

Critical and extreme value problems in object equilibrium

1. critical issue

(1) Critical state: a state in which the equilibrium state of an object is about to change.

(2) When a certain physical quantity changes, it will cause changes in other physical quantities, causing the equilibrium state of the object to "just happen" or "just not happen". "Just right" and "just right" often appear in the description of such problems and other words.

(3) The most effective way to deal with this type of problem is the hypothetical reasoning method, that is, first make assumptions, then formulate equilibrium equations based on equilibrium conditions and relevant knowledge, and finally solve them.

(4) Common critical states

2. Extreme value problem: It refers to the problem of the maximum value and minimum value of the force in the process of change in the balance problem. The following three methods are commonly used to solve this type of problem:

Analytical method: Formulate equations based on the equilibrium conditions of the object. When solving the equation, use mathematical knowledge to find the extreme value or find the extreme value based on physical critical conditions.

Graphical method: Make a force analysis diagram of the object based on its equilibrium conditions, draw a parallelogram or vector triangle for dynamic analysis, and determine the maximum or minimum value.

Limit method The limit method is an effective method for dealing with critical problems. It refers to pushing the problem to the extreme ("maximum", "minimum", "extreme right", "extreme left", etc.) by appropriately selecting a changing physical quantity. This exposes relatively hidden critical phenomena, makes the problem clear, and facilitates analysis and solution.

Summary and improvement

Issues that should be paid attention to when solving critical extreme value problems

(1) When solving critical problems and extreme value problems in equilibrium, we must first correctly conduct force analysis and change process analysis to find the critical points and extreme points of equilibrium.

(2) Critical conditions must be found in changes. We cannot stay in one state to study critical issues. Instead, we must push a certain physical quantity to the extreme, that is, the maximum and minimum, and make scientific reasoning and analysis accordingly, so as to Make judgments or draw general conclusions.

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