As we already know, the force of gravity acts on all bodies that are on the surface of the Earth and near it. It does not matter whether they are at rest or in motion.
If a body falls freely to the Earth, then it will perform uniformly accelerated motion, and the speed will increase constantly, since the velocity vector and the free fall acceleration vector will be co-directed with each other.
The essence of vertical upward movement
If you throw some body vertically upward, and at the same time, assuming that there is no air resistance, then we can assume that it also performs uniformly accelerated motion, with the acceleration of free fall, which is caused by gravity. Only in this case, the speed that we gave to the body during the throw will be directed upward, and the acceleration of free fall will be directed downward, that is, they will be oppositely directed to each other. Therefore, the speed will gradually decrease.
After some time, a moment will come when the speed becomes zero. At this moment the body will reach its maximum height and will stop for a moment. Obviously, the greater the initial speed we give to the body, the greater the height it will rise by the time it stops.
- Next, the body will begin to fall down uniformly under the influence of gravity.
How to solve problems
When you are faced with tasks on the upward movement of a body, in which air resistance and other forces are not taken into account, but it is believed that only the force of gravity acts on the body, then since the movement is uniformly accelerated, you can apply the same formulas as for rectilinear uniformly accelerated motion with some initial speed V0.
Since in this case the acceleration ax is the acceleration of free fall of the body, then ax is replaced by gx.
- Vx=V0x+gx*t,
- Sx=V(0x)*t+(gx*t^2)/2.
It is also necessary to take into account that when moving upward, the free fall acceleration vector is directed downward, and the velocity vector is directed upward, that is, they are in different directions, and therefore, their projections will have different signs.
For example, if the Ox axis is directed upward, then the projection of the velocity vector when moving upward will be positive, and the projection of the free fall acceleration will be negative. This must be taken into account when substituting values into formulas, otherwise you will get a completely incorrect result.
1588. How to determine the acceleration of free fall, having at your disposal a stopwatch, a steel ball and a scale up to 3 m high?
1589. What is the depth of the shaft if a stone freely falling into it reaches the bottom 2 s after the start of the fall.
1590. The height of the Ostankino TV tower is 532 m. A brick was dropped from its highest point. How long will it take for it to fall to the ground? Ignore air resistance.
1591. Moscow building state university on Vorobyovy Gory has a height of 240 m. A piece of cladding has come off from the top of its spire and is freely falling down. How long will it take it to reach the ground? Ignore air resistance.
1592. A stone falls freely from a cliff. How far will it travel in the eighth second from the start of its fall?
1593. A brick falls freely from the roof of a building 122.5 m high. How far will the brick travel during the last second of its fall?
1594. Determine the depth of the well if a stone dropped into it touches the bottom of the well after 1 s.
1595. A pencil falls from a table 80 cm high to the floor. Determine the time of fall.
1596. A body falls from a height of 30 m. How far does it travel during the last second of its fall?
1597. Two bodies fall from different heights, but reach the ground at the same moment in time; in this case, the first body falls for 1 s, and the second for 2 s. How far from the ground was the second body when the first one began to fall?
1598. Prove that the time during which a body moving vertically upward reaches greatest height h is equal to the time during which the body falls from this height.
1599. A body moves vertically downward with an initial speed. What simple movements can this body movement be broken down into? Write formulas for the speed and distance traveled of this movement.
1600. A body is thrown vertically upward at a speed of 40 m/s. Calculate at what height the body will be after 2 s, 6 s, 8 s and 9 s, counting from the beginning of the movement. Explain your answers. To simplify calculations, take g equal to 10 m/s2.
1601. At what speed must a body be thrown vertically upward so that it returns back after 10 s?
1602. An arrow is shot vertically upward with an initial speed of 40 m/s. In how many seconds will it fall back to the ground? To simplify calculations, take g equal to 10 m/s2.
1603. A balloon rises uniformly vertically upward at a speed of 4 m/s. A load is suspended from it on a rope. At an altitude of 217 m the rope breaks. In how many seconds will the weight fall to the ground? Take g equal to 10 m/s2.
1604. A stone was thrown vertically upward with an initial speed of 30 m/s. 3 s after the first stone began to move, a second stone was also thrown upward with an initial speed of 45 m/s. At what height will the stones meet? Take g = 10 m/s2. Neglect air resistance.
1605. A cyclist climbs up a slope 100 m long. The speed at the beginning of the climb is 18 km/h, and at the end is 3 m/s. Assuming the movement is uniformly slow, determine how long the rise lasted.
1606. A sled moves down the mountain uniformly with an acceleration of 0.8 m/s2. The length of the mountain is 40 m. Having rolled down the mountain, the sled continues to move equally slow and stops after 8 s….
Movement of a body thrown vertically upward
Level I. Read the text
If a body falls freely to the Earth, then it will perform uniformly accelerated motion, and the speed will increase constantly, since the velocity vector and the acceleration vector of free fall will be co-directed with each other.
If we throw a certain body vertically upward, and at the same time assume that there is no air resistance, then we can assume that it also undergoes uniformly accelerated motion, with the acceleration of free fall, which is caused by gravity. Only in this case, the speed that we gave to the body during the throw will be directed upward, and the acceleration of free fall will be directed downward, that is, they will be oppositely directed to each other. Therefore, the speed will gradually decrease.
After some time, a moment will come when the speed becomes zero. At this moment the body will reach its maximum height and stop for a moment. Obviously, the greater the initial speed we give to the body, the greater the height it will rise by the time it stops.
All formulas for uniformly accelerated motion are applicable to the motion of a body thrown upward. V0 always > 0
The motion of a body thrown vertically upward is rectilinear movement with constant acceleration. If you direct the coordinate axis OY vertically upward, aligning the origin of coordinates with the Earth’s surface, then to analyze free fall without initial speed you can use the formula https://pandia.ru/text/78/086/images/image002_13.gif" width="151" height="57 src=">
Near the surface of the Earth, provided that there is no noticeable influence of the atmosphere, the speed of a body thrown vertically upward changes in time according to a linear law: https://pandia.ru/text/78/086/images/image004_7.gif" width="55" height ="28">.
The speed of the body at a certain height h can be found using the formula:
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The height of the body's rise over some time, knowing the final speed
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IIIlevel. Solve problems. For 9 b. 9a solves from a problem book!
1. A ball was thrown vertically upward at a speed of 18 m/s. How much movement will he make in 3 s?
2. An arrow fired vertically upward from a bow at a speed of 25 m/s hits the target in 2 s. What was the speed of the arrow when it reached the target?
3. A ball was shot vertically upward from a spring gun and rose to a height of 4.9 m. At what speed did the ball fly out of the gun?
4. The boy threw the ball vertically upward and caught it after 2 s. How high did the ball rise and what was its initial speed?
5. With what initial speed must a body be thrown vertically upward so that after 10 s it moves downward at a speed of 20 m/s?
6. “Humpty Dumpty sat on the wall (20 m high),
Humpty Dumpty fell in his sleep.
Do we need all the royal cavalry, all the royal army,
to Humpty, to Dumpty, Humpty Dumpty,
Collect Dumpty-Humpty"
(if it only crashes at 23 m/s?)
So is all the royal cavalry necessary?
7. Now the thunder of sabers, spurs, sultan,
And a chamber cadet caftan
Patterned - beauties are seduced,
Wasn't it a temptation?
When from the guard, others from the court
We came here for a while!
The women shouted: hurray!
And they threw caps into the air.
"Woe from Wit".
The girl Catherine threw her cap upward at a speed of 10 m/s. At the same time, she stood on the balcony of the 2nd floor (at a height of 5 meters). How long will the cap remain in flight if it falls at the feet of the brave hussar Nikita Petrovich (naturally standing under the balcony on the street).
This video tutorial is intended for self-study topic “Motion of a body thrown vertically upward.” In this lesson, students will gain an understanding of the motion of a body in free fall. The teacher will talk about the movement of a body thrown vertically upward.
In the previous lesson, we looked at the issue of the movement of a body that was in free fall. Let us remind you that free fall(Fig. 1) we call this movement that occurs under the influence of gravity. The force of gravity is directed vertically downwards along the radius towards the center of the Earth, acceleration of gravity at the same time equal to .
Rice. 1. Free fall
How will the movement of a body thrown vertically up differ? It will differ in that the initial speed will be directed vertically upward, i.e., it can also be counted along the radius, but not towards the center of the Earth, but, on the contrary, from the center of the Earth upward (Fig. 2). But the acceleration of free fall, as you know, is directed vertically downward. This means that we can say the following: the upward movement of a body in the first part of the path will be a slow motion, and this slow motion will also occur with the acceleration of free fall and also under the influence of gravity.
Rice. 2 Movement of a body thrown vertically upward
Let's look at the picture and see how the vectors are directed and how this fits into the reference frame.
Rice. 3. Movement of a body thrown vertically upward
In this case, the reference frame is connected to the ground. Axis Oy is directed vertically upward, just like the initial velocity vector. The body is acted upon by a force of gravity directed downward, which imparts to the body the acceleration of free fall, which will also be directed downward.
The following thing can be noted: the body will move slowly, will rise to a certain height, and then will start quickly fall down.
We have indicated the maximum height.
The motion of a body thrown vertically upward occurs near the Earth's surface, when the acceleration of free fall can be considered constant (Fig. 4).
Rice. 4. Near the Earth's surface
Let us turn to the equations that make it possible to determine the speed, instantaneous speed and distance traveled during the movement in question. The first equation is the velocity equation: . The second equation is the equation of motion for uniformly accelerated motion: .
Rice. 5. Axis Oy upward
Let's consider the first frame of reference - the frame of reference associated with the Earth, the axis Oy directed vertically upward (Fig. 5). The initial speed is also directed vertically upward. In the previous lesson, we already said that the acceleration of gravity is directed downwards along the radius towards the center of the Earth. So, if we now bring the velocity equation to this reference frame, we get the following: .
This is a projection of speed at a certain point in time. The equation of motion in this case has the form: 
.
Rice. 6. Axle Oy pointing down
Let's consider another frame of reference, when the axis Oy directed vertically downwards (Fig. 6). What will change from this?
. The projection of the initial velocity will have a minus sign, since its vector is directed upward, and the axis of the selected reference system is directed downward. In this case, the acceleration of gravity will have a plus sign, because it is directed downward. Equation of motion: 
.
Another very important concept, which needs to be considered is the concept of weightlessness.
Definition.Weightlessness- a state in which a body moves only under the influence of gravity.
Definition. Weight- the force with which a body acts on a support or suspension due to attraction to the Earth.
Rice. 7 Illustration for determining weight
If a body near the Earth or at a short distance from the Earth’s surface moves only under the influence of gravity, then it will not affect the support or suspension. This state is called weightlessness. Very often, weightlessness is confused with the concept of the absence of gravity. In this case, it is necessary to remember that weight is the action on the support, and weightlessness- this is when there is no effect on the support. Gravity is a force that always acts near the surface of the Earth. This force is the result of gravitational interaction with the Earth.
Let's pay attention to one more important point, associated with the free fall of bodies and movement vertically upward. When a body moves upward and moves with acceleration (Fig. 8), an action occurs that leads to the fact that the force with which the body acts on the support exceeds the force of gravity. When this happens, the state of the body is called overload, or the body itself is said to be under overload.
Rice. 8. Overload
Conclusion
The state of weightlessness, the state of overload are extreme cases. Basically, when a body moves on a horizontal surface, the weight of the body and the force of gravity most often remain equal to each other.
Bibliography
- Kikoin I.K., Kikoin A.K. Physics: Textbook. for 9th grade. avg. school - M.: Education, 1992. - 191 p.
- Sivukhin D.V. General course physics. - M.: State Publishing House of Technology
- theoretical literature, 2005. - T. 1. Mechanics. - P. 372.
- Sokolovich Yu.A., Bogdanova G.S. Physics: A reference book with examples of problem solving. - 2nd edition, revision. - X.: Vesta: Ranok Publishing House, 2005. - 464 p.
- Internet portal “eduspb.com” ()
- Internet portal “physbook.ru” ()
- Internet portal “phscs.ru” ()
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