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First of all, I'm just a freshman in high school, and I can only study it here, thank you.
1) When the air resistance is not taken into account, since the ball is only affected by gravity in the process of rising and descending, g is combined by m*a=f, then its acceleration a is equal, and the displacement and acceleration of the rise and fall are the same by s=1 2 *a*t*t, so the time is the same.
2) When considering the air resistance, the ball is subject to resistance in addition to gravity during the ascent and descent f
When rising, the direction of f is down, and when it falls, it is upward, but the direction of g is always downward, which leads to the difference in acceleration during the ascent and descent by m*a=f(combined), because the mass of the ball is not marginal, so the acceleration of the combined external force f is large, and it is s=1 2*a*t*t*t to get a large t is small, so when ascending, f is in the same direction as g, so it is larger than the external force, so a is large, so t is small.
Energy: Suppose the ball is thrown at the origin with 30j of energy (assuming it is all mechanical kinetic energy).
He loses 5 j of energy (internal energy) when he rises to the highest point, then he has 25 j of energy (both mechanical energy, gravitational potential energy) at the highest point
He descended to the bottom point and lost 5j (I assume 5j, but it could also be 4j 3j) of energy (internal energy), and at the bottom of the energy there is 20j (both mechanical energy, kinetic energy).
Then in the total mechanical energy during the ascent the total mechanical energy during the descent.
Compare any two points of the same height during the ascent and descent process.
The gravitational potential energy of these two points is the same but the mechanical energy is different (large during ascent) so the kinetic energy is different (large during ascent).
Thus comparing the kinetic energy at each corresponding point of the rise and fall, the former is the latter.
So the average kinetic energy is also the former and the latter, so the average velocity is the former and the latter.
So time is just a little bit of an ascent.
Actually, what I'm saying above is nothing more than explaining why the resistance work is less in the ascending process than in the descending process, that is, the energy lost is less than in the descending process.
Thank you, landlord, it should be understandable to take a closer look.
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I see, you should be able to understand:
Kinetic energy is related to velocity, mass.
Potential energy (gravitational potential energy) is related to height and mass.
The quality does not change in this question and can be left unconsidered.
Mechanical energy is the sum of gravitational potential energy and kinetic energy.
And because of the frictional force, the total mechanical energy is constantly decreasing.
Then at the same height point, the mechanical energy is smaller when descending than when ascending, because the gravitational potential energy is the same, the kinetic energy when ascending is relatively large, the mass is certain, then the speed is larger, and it is faster.
So the ascent time is shorter.
I'm also in the third year of junior high school, so that's how much I know, and I don't think this topic will use any knowledge other than energy.
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If the air resistance is not taken into account, the time is of course equal, because the velocity of the ball returning to its original position is equal to the original (conservation of mechanical energy), and the acceleration is equal, and the velocity is divided by the acceleration to get the time, so the time is equal;
If the air resistance is considered, there is an energy loss, the return to the origin velocity is smaller than the initial one, and the descending acceleration is smaller than the rising acceleration, so it is not possible to judge which one time is shorter: it is possible to be equal; It is possible to rise short; When you go to college and learn calculus, you can get accurate numerical solutions with differential equations, and work hard to get into college!
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If there is no air resistance, it is equal.
The ball moves upwards to make a uniform deceleration motion, reaches the highest point, and then falls down to make a free fall.
The mechanical energy of the whole process is conserved, so it can be known that the velocity at the throwing point and the velocity at the throwing point again are equal, and since the acceleration is also equal in the whole process, the initial velocity and the end velocity are also equal, so that the ejection time can be completely equal.
This situation is carried out in a completely ideal situation where there is no air resistance.
That's the answer, but I forgot if I learned so much in junior 3, hehe.
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Regardless of air resistance, the situation is very simple, and it is to take advantage of the symmetry of the process.
If we consider the air resistance, it can be imagined that the air resistance actually reduces the total energy of the ball, so the kinetic energy at each position of the fall, is less compared to the kinetic energy of that position when it is rising, that is, the velocity of the corresponding position when falling will be less than when it is rising. Obviously, the fall will be slower.
The above is a simple idea that can be calculated. The method is very simple, that is, consider an acceleration that is opposite to the direction of motion, and the magnitude of this acceleration is a function of velocity, but if you only consider fast and slow, it can be considered as a constant a. The orientation is in the positive direction, and the acceleration is -(a g) when ascending and a g when descending.
The rest of the steps are slightly ......
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Considering the air resistance, the time to rise is not equal in many cases, and many people have already replied to it above!
Second, air can be used as a fluid, and when the density of the ball is small, the speed at which the ball rises and falls may not be equal!
Third, consider whether the rising point is very high, and if so, consider the gravitational attraction of other particles!
Fourth, you have to consider whether the ball will still fall, if not, naturally the time of rise and the time of fall cannot be compared, because it will be infinite!
Think about it as much as you want, too much!
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Not necessarily. When the force generated by the upward throw minus the gravity force is greater than the specific gravity force, the ascent time is short.
When the force generated by the up-toss minus gravity is equal to gravity, the rise time is equal to the fall time.
When the force generated by the upper throw minus the gravity force is smaller than the specific gravity force, the ascent time is longer.
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1.Air resistance --- equal without consideration.
2.Air resistance is constant ā equal, the same as if air resistance were not taken into account.
3.If the speed is greater, the greater the resistance: then the total time of rising and falling is also equal, this place can not be thought of in sections, to think macroscopically, you can think of the rise as a fall, you will find that it is two completely waiting processes!
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Acceleration: Time is equal to 2s ratio a under the root number, the force is gravity plus resistance when rising, and gravity minus resistance when descending, so the acceleration when rising is large, and because s is equal, therefore, the time when rising is longer. From the perspective of energy, generally only the result is not the process, and I can't ask for time, so I think about it again, and then add it when I think of it.
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If air resistance is not taken into account, it is equal.
Consider that the upward throw time is short because the resistance upwards is opposite to the direction of gravity when it is downward.
The acceleration becomes smaller and the time becomes longer.
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If air resistance is not taken into account, it is equal.
If the air resistance is constant, it is also equal (the impulse is equal).
If the air resistance is proportional to the speed of the ball, it needs to be analyzed according to the equation.
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When the point is changed, the velocity of the object is 6=vt+1, and 16=v(t+t)+1 2a(t+t) 2 gets a=1m s 2
And because the ground is smooth, we get (10+6) 4=vb
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(1) The initial velocity is vo=5m s, and the termination velocity vt=0m svt=vo+at
0=5+4a
Acceleration a = i.e., the average ball rolling speed per second decreases.
2) Roll distance s=5
According to the formula, s=vo*t+1 2*a*t 2(t-4) 2=8
t=4-2ā2 sā
It took the ball to roll forward 5m.