) 1) The trajectory of curve motion is a curve.

The speed direction of motion is always along the tangent direction of the trajectory, and the trajectory of curvilinear motion is a curve, so the speed direction of curvilinear motion is always changing.

Even if its speed is constant, its direction is constantly changing, and the curvilinear motion must be variable-speed motion.

3) Because the speed of curvilinear motion must change, at least its direction often changes, the medium speed of curvilinear motion object must not be zero, the force must not be zero, and there must be acceleration.

(Note) When the external force is zero, there are only two states: static and uniform linear motion.

) The speed direction of curvilinear motion has a certain change. Curved motion must be variable-speed motion, but variable-speed motion is not necessarily curvilinear motion.

2. Conditions for the motion of objects along curves

(1) From the dynamic point of view, the direction of external force on an object is not in a straight line with its velocity direction.

) 2) Kinematically, the acceleration direction and velocity direction of an object are not in a straight line.

3. Constant-speed and variable-speed movement: movement with constant acceleration (magnitude and direction).

It can also be said that even with external force, it will not change.

4 The relationship between resultant force, trajectory and velocity of curvilinear motion

(1) Trajectory characteristics: The trajectory is between the velocity direction and the resultant direction, and bends to the side of the resultant direction.

(2) Effect of resultant force: the tangential component F2 of resultant force changes the speed, and the radial component F 1 changes the direction of speed.

When the direction of resultant force forms an acute angle with the direction of velocity, the velocity of the object will increase.

When the direction of resultant force forms an obtuse angle with the direction of velocity, the velocity of the object decreases.

When the resultant force direction is perpendicular to the velocity direction, the velocity of the object remains unchanged.

(Example) Constant velocity circular motion)

Pull an object with a rope

Joint movement: actual movement.

Corresponding to the synthesis speed.

Methods: The combined speed was divided into the direction along the rope and the direction perpendicular to the rope.

Cross the river by boat

As we all know, the speed of a ship crossing a 200m wide river to the other side is 3m/s, and the speed of a ship in still water is 5 m/s.

(1) How should the ship cross the river to minimize the crossing time? What is the shortest time? What is the displacement of this ship?

2) How should a ship cross the river to minimize the navigation displacement? What is the shortest displacement? How long does it take to cross the river?

Crossing time: mainly depends on the speed of the ship perpendicular to the river bank. A ship must have a speed perpendicular to the river bank to cross the river.

(At this time =0, that is, the bow direction must be perpendicular to the river bank).

(1) Conclusion: It takes the shortest time for a ship to cross the river, and the bow direction must be perpendicular to the river bank.

The shortest time to cross the river is as follows

The qualified speed is as follows.

Alignment displacement:

or

) 2) Analysis:

How to cross the river: the bow and the river bank go upstream.

The shortest displacement is as follows.

The qualified speed is as follows.

The response time is as follows

As we all know, the speed of a ship crossing a 200-meter-wide river to the other side is 5m/s, and the speed in still water is 4 m/s.

(1) How should the ship cross the river to minimize the crossing time? What is the shortest time? What is the displacement of this ship?

2) How should a ship cross the river to minimize the navigation displacement? What is the shortest displacement? How long does it take to cross the river?

(1) Conclusion: It takes the shortest time for a ship to cross the river, and the bow direction must be perpendicular to the river bank.

The shortest time to cross the river is as follows

The qualified speed is as follows.

Alignment displacement:

or

(2) Method: Take the wave velocity endpoint as the center, the ship speed as the radius, and the first wave velocity endpoint as the tangent of the circle. Tangent is the direction of velocity.

As shown in the left figure, AC is the direction of the obtained synthesis speed.

Related conclusions:

4. Basic laws of uniform and slow motion

1. Speed:

Adjust the speed:

Direction:

2. Displacement

Adjust offset:

Direction:

3. The time is:

get

(determined by falling height y))

4) When the plate moves in a free fall in the vertical direction, all the laws of the plate's variable-speed linear motion are established in the vertical direction.

Five.

The tangent of the angle between velocity and horizontal direction is twice that between displacement and horizontal direction.

6. The distance from the intersection of the reverse extension line of the instantaneous velocity direction and the extension line of the initial velocity direction to the throwing point of the flat throwing object at any moment is equal to half of the horizontal displacement.

(a is the midpoint of OB).

5. Uniform circular motion 1. Linear speed: the ratio of the length of the arc through which particles pass to the service time.

Unit: m/s, m/s2. Angular velocity: the ratio of the rotation angle of particle radius to the service time.

Unit: radian/second, rad/s3. Period: the time required for an object to move around a uniform circle.

Unit: seconds, s4. Frequency: the number of times to complete circular motion per unit time.

Unit: Hertz, Hz5. Rotation speed: the rotation speed per unit time.

Unit: speed/second, r/s (speed n must be speed/second) 6. Centripetal acceleration:

7. centripetal force:

Three rotation modes

6. Circular motion of vertical plane

1. As shown in the photo on the rope model, when the ball moves in a circle in the vertical plane and crosses the highest point.

(Note: The rope only produces a pulling force on the ball).

(1) The critical condition for the ball to cross the highest point) The rope and the track just have no effect on the ball, and mg=m produces v=)2) The condition for the ball to cross the highest point v) v) When v, the rope exerts tension on the ball and the track exerts pressure on the ball) 3) The highest point.

2. "Rod model", when the ball moves circularly in the vertical plane and passes the highest point.

(Note) Glow sticks are different from thin lines. The fluorescent stick can produce both tension and thrust on the ball.

) )

(1) The critical condition for the ball to exceed the highest point) v=0, f=mg) f is the supporting force) 2) F0) F is the supporting force) 3) When v=, with the increase of f=0, 4) v, F increases, and f0(f is the pulling force) is 70. 000.

(The value of k is only related to the mass of the central celestial body) 2. Law of universal gravitation:

(1) gravity on the equator;

(g and a are two different physical quantities,) 2) the universal gravitation of the two poles:

Ignoring the rotation of the earth, gravity on the earth equals gravity.

(gold replacement)

4. Gravity acceleration at height h from the earth's surface:

5. The satellite moves around the earth in a uniform circle: gravity provides centripetal force.

(centripetal acceleration A in orbit is equal to the acceleration of gravity in orbit)

6. Calculating the mass of central celestial bodies: method 1;

(R and G are known) Method 2:

(V and R of known satellites) Method 3:

(W and R of known satellites) Method 4:

(The periods T and R of the satellite are known) Method 5) Known.

(Known satellites V and T) Method 6: Known

(V and W of a known satellite are equivalent to V and t )7. Calculation of earthwork density: earthwork volume formula:

A satellite near the earth.

(r=R).

8. Launch speed: When a satellite is launched by a multistage rocket, the speed at which the satellite leaves the last stage rocket.

Running speed refers to the linear speed of a satellite when it orbits the earth at a uniform speed. When the satellite "sticks" to the ground, the running speed is equal to the first cosmic speed.

The first cosmic speed (revolution speed) is 7.9 km/s.

The maximum speed of a satellite orbiting the earth.

The lowest launch speed of satellites on earth.

The second cosmic velocity (detachment velocity) is11.2km/s.

The minimum speed required for a satellite to get rid of the earth's gravity and stop orbiting the earth is launched from the earth's surface.

Third cosmic velocity (escape velocity)16.7km/s.

The minimum speed required for a satellite to get rid of the sun's gravity and fly to the outer space of the solar system and launch from the earth's surface.

8. Mechanical energy 1. Calculation of work.

2. Calculate the average power:

Instantaneous power calculation:

(the angle between the direction of force f and the direction of velocity v) 3. Gravity potential energy:

Gravity work calculation formula:

The change of gravity potential;

The relationship between gravity work and the change of gravity potential;

Characteristics of gravity doing work: gravity does positive work (A to B), and the gravity potential decreases.

Gravity is negative work (C to D), and the gravitational potential increases.

4. The elastic potential energy of the spring:

(Spring change)

Spring work is equal to the negative value of spring potential energy change:

Features: Elastic force has positive work on objects, and elastic potential energy decreases.

Elastic force does negative work on an object, and elastic potential energy increases.

5. Kinetic energy:

Changes in kinetic energy:

6. Kinetic energy theorem:

General deformation:

7. Conservation of mechanical energy (in a material system where only gravity or elasticity does work, kinetic energy and potential energy are transformed into each other, but the total amount of mechanical energy remains unchanged.

Formula:

(The sum of the potential energy and kinetic energy of the initial state is equal to the sum of the potential energy and kinetic energy of the final state)

(An increase in kinetic energy equals a decrease in potential energy)

(The increase of mechanical energy of object A is equal to the decrease of mechanical energy of object B).

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