Problems of physical mechanics, problems of physical mechanics

Obviously, the key to this problem is the top ball.

The gravitational force of the top ball is g, so for the three balls holding it below it, the top ball has a downward pressure on them along the line.

The magnitude of this force divided vertically downward and horizontally is 3 to 1

Then for the ball below, the friction factor should be greater than 3 3 3

For example, I don't need to calculate the moment of the ball above to the ball below, because I directly use the whole method to see the four balls as a whole, and the internal force is considered an internal force, which has nothing to do with the plane.

For the top ball, because the sum of the moment vectors of the three bottom balls is 0, it will not rotate without consideration.

These four spheres are a regular tetrahedral structure, and the downward pressure direction is not 45°, which is the content of the solid geometry.

1. Study any ball below, because at the center of the sphere 0, the point A of the sphere touching the ground, and the three points of the contact point b between the ball and the above sphere, so the three forces are balanced, there are only two possibilities: parallel or intersecting at one point, this problem obviously three forces should be intersected at point B, then the direction of force at point B is the line between B and A, so as to know the direction of force at point B, and then consider the force on the top sphere, a gravity is set to g, and the force direction of the three contact points is known, and these three forces are equal, so these three forces can be calculated. Then according to the angle with the tangent to know the size of the friction, so as to calculate the lower limit of the friction coefficient here, and then calculate the next ball, the two forces are known, calculate the force at point A, you can know the friction force at point A, so as to know the lower limit of the friction coefficient at this point.

Based on the two cases, the maximum friction coefficient is taken, which is the final lower limit.

Let's help you analyze First of all, the fourth ball has an oblique downward force against the other three balls, and the combined force of these three forces is equal to the gravitational force of the ball. To make the four balls stationary, it is necessary to meet the net force on the horizontal plane is 0, and the formula of friction is f = mg, in fact, I can't remember very clearly, the friction force f should be equal to the component of the force of the fourth ball acting on the three balls obliquely downward. As a diagram, we can see that the horizontal angle of the downward force should be 45 degrees.

The magnitude of the diagonal downward force should be 1, so that it should be greater than or equal to 2 6I don't know if it's right! Please forgive me if you make a mistake!

u> = (root number 2) 6. The main difficulty of the problem is the determination of the direction of the force. The center of the four spheres can be connected, and it is found that it is a regular tetrahedron, referring to the relevant properties of the regular tetrahedron, the inclination angle b, cotb=(root number 2) 2, the following is easy to find:

UMG (1 3)mg is greater than or equal to COTB, so u> = (root number 2) 6

It is known that the velocity of the bullet is 500 m s, the firing point is 200 m from the active target, and the velocity of the active target is 3 m s

Seeking: The muzzle should be aimed at the distance l before the direction of the target's movement

Solution: t=s v is obtained from v=s t

There are 200m 500m s = l 3m s

l = A: When firing, the muzzle of the gun should be aimed in front of the direction of the target's movement.

There are two places in this problem where the wall bounces against the bar, point A and point B.

At point B, you can directly use the equilibrium condition in the vertical direction, nb=g at point A to balance with the torque, take point B as the center of rotation, so that the moment of nb and friction is 0, and take the counterclockwise direction as the positive direction

There is equation g*6*

na=3*sqr(7)*g/14

sqr() is the root number.

At the same time, from the balance of forces in the horizontal direction, it can be known that the frictional force is equal to the elastic force of point a.

Hope you're satisfied!

First of all, explain the uniform motion, the concept: 1, the mechanical motion with the same speed specified in junior high school physics is called uniform motion. In junior high school physics teaching, velocity is velocity, and the direction of velocity is not considered.

2. High school stipulates that the motion through the same displacement in the same time is called uniform motion, that is, the motion that does not change the magnitude and direction of velocity. or a motion with an acceleration of 0.

Therefore, there are the following judgments: when the object is in uniform motion, the acceleration is 0, and the resultant external force is 0;

Case study: the car does a uniform motion, the traction force of the car and the friction of the tire (ideal state) are equal, when hitting a person, the person will be affected by the thrust (the kinetic energy of the car does work), at the same time, the car is affected by the drag (action force and reaction force), because there is kinetic energy converted into work, the speed of the car will drop instantly. (Next, if you don't stop, go around the person, and the car will return to its original speed due to the traction of the car).