circular motion 2

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2010-05-31 8:07 pm

When object is performing circular motion, a centripetal force is required. This centripetal force acts on the object radially. For example, if a satellite is moving round the earth surface from a fixed distance, the weight mg of the satellite then provides the requied centripetal force. But why object do not fall to the centre of the circle by the centripetal force since the centripetal force points toward the centre? Is a force which acts on the object tangentially needed?

Refer to the answer given by Wai Hung.

When satellite moves around the Earth, it will experience a centripetal force but the satellite will not fall to the Earth. You can try to explain this with two approaches.
First, you should realize that the centripetal force is perpendicular to the displacement of the satellite. By the defintion of work, the force does no work on the satellite. Yet when satellite moves towards the Earth, the weight mg does work on the satellite as the angle between force and displacement is 0 degree. Hence, with centripetal force, it will not cause the satellite to crash the Earth.
On the other way, you should note that the satellite is moving with tangential velocity. When the weight mg 'pulls' the satellite towards the Earth, the satellite moves with tangential velocity accordingly, keeping the distance between the satellite and the Earth unchanged.
In fact, you can think of the satellite as a ball being thrown on the Earth. If the ball is thrown with small velocity, it will fall onto the ground due to the presence of mg. However, if the ball the thrown faster and faster, the ball will travel with longer horizontal distance before it falls onto the ground, and eventually rotates in orbit around the Earth, which is the model of satellite motion.
My question:
Is it true that the satellite actually moves towards the earth but just it is unnoticeable?

更新1:

If I throw a ball horizontally with a very high speed, and a small constant force is acted on the ball downwards, it should eventually fall to the ground. But why the satellite do not fall to the ground by its weight? What is the difference between two cases?

回答 (2)

天同

2010-05-31 10:25 pm

✔ 最佳答案

As I have pointed out in my reply to your question that the motion of an objects depends on two factors: (i) the initial condition (i.e. mostly initial velocity) of the object, and (ii) the force that acts on the object, and which subsequently gives an acceleration and velocity to the object.

When the weight of the satellite acts on the satellite, because the direction of force and the initial velocity of the satellite are at right angle to each other, the force does not give any change of velocity in the direction of the "initial velocity". Instead, there is an acceleration and change of velocity in the direction which the force (i.e. the weight) acts. As a result, you could visualize that the resultant velocity of the satellite would be "deflected" from the direction of the "initial velocity" towards the direction which the force acts.

However, once the path traversed by the satellite is "deflected", the force that acted on the satelite also changes in direction, in such a way that it (the force) is always perpendicular to the velocity of the satellite. Thus, the process described in the preceding parapgraph repeats. The final scenario is that the satellite traverses a circular path around the earth.

You could compare the situation of just throwing a stone horizontally on earth surface with that of a satellite. In the former case, the force (i.e. the weight) always acts in one direction, which is vertically downward irrespect to the direction of velocity of the stone on its path. Thus a parabolic path is resulted. In the satellite case, the force keep changing in direction along with the change of velocity direction, which results to a circular path.

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AAA

2010-06-02 3:25 am

Is it true that the satellite actually moves towards the earth but just it is unnoticeable?
Answer: It is actually not the case. In fact, the satellite does not move to the Earth. Consider the case when satellite is not pulled towards the Earth by its weight, the satellite will not move in orbits. It will only move in a straight line unless other forces act on it. Hence, the weight is actually causing the orbit motion by antagonizing the straight movement of the satellite, rather than moving it towards the Earth.

If I throw a ball horizontally with a very high speed, and a small constant force is acted on the ball downwards, it should eventually fall to the ground. But why the satellite do not fall to the ground by its weight? What is the difference between two cases?

Answer: Refer to the previous answer, the satellite does fall. But it is actaully 'balanced' by the straight line motion of the satellite, causing it to move in orbits. And in fact, the cases of satellite and throwing ball is more or less the same. If the velocity of the thrown ball is high enough, the ball move travel in a certain horizontal distance before it falls vertically. In this case, the ball moves in orbits, like satellite.

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