Please help with a physics 11 question? (Thanks in advance!!!)?
2018-07-04 11:48 am
Two rocks are thrown off a cliff with the same initial speed Vo. The first rock is launched with an angle below the horizontal as shown below as 1. The second rock is launched above at the same angle. Using a conservation of energy argument, explain which rock would strike the water with larger final velocity if air resistance is included.
回答 (3)
2018-07-04 2:39 pm
✔ 最佳答案
Conservation of energy :Lost in P.E. = (Gain in K.E.) + (Work done to overcome air resistance)
Gain in K.E. = (Lost in P.E) - (Work done to overcome air resistance)
(1/2)mv² (1/2)mvₒ² = mgh - (Work done to overcome air resistance)
(1/2)mv² = (1/2)mvₒ² + mgh - (Work done to overcome air resistance)
For both paths, (1/2)mvₒ² and mgh are the same. Obviously, the path of rock 2 is longer than that of rock 1, and thus the work done to overcome air resistance by rock 2 is greater than that of rock 1. Therefore, rock 1 strikes the water with greater kinetic energy and thus larger final velocity.
2018-07-04 7:54 pm
Notwithstanding the first answer it isn't quite as simple as it seems.
Consider two items approaching terminal velocity ( which happens with air resistance because it is dependent on speed).
In this case the two speeds will both be very close to the same. Terminal velocity.
Now let us imagine objects which do not approach terminal velocity.
at the point P SOME of the energy of the second object has been lost. So it starts its descent with less velocity than the first object.
It has less friction because it is moving more slowly. So it can gradually APPROACH the speed of the first object during its subsequent descent.
( less friction gives more acceleration. But only while the speed is less than that of the first object )
So if the cliff is high or the object is light then they will both fall vertically into the water at terminal velocity.
If the cliff is low and the object is heavy then the first object will hit with a higher speed.
Consider two items approaching terminal velocity ( which happens with air resistance because it is dependent on speed).
In this case the two speeds will both be very close to the same. Terminal velocity.
Now let us imagine objects which do not approach terminal velocity.
at the point P SOME of the energy of the second object has been lost. So it starts its descent with less velocity than the first object.
It has less friction because it is moving more slowly. So it can gradually APPROACH the speed of the first object during its subsequent descent.
( less friction gives more acceleration. But only while the speed is less than that of the first object )
So if the cliff is high or the object is light then they will both fall vertically into the water at terminal velocity.
If the cliff is low and the object is heavy then the first object will hit with a higher speed.
2018-07-04 7:49 pm
There is a problem with the question.
if air resistance is included, the speed (v₀) and direction (θ) of the 2nd stone at point P can *not* be same as for stone 1 at its start point.
The description and the diagram are incompatible and lead to different answers. Which do you use? The question can't be answered.
if air resistance is included, the speed (v₀) and direction (θ) of the 2nd stone at point P can *not* be same as for stone 1 at its start point.
The description and the diagram are incompatible and lead to different answers. Which do you use? The question can't be answered.
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