Sunday, 7 October 2007 - 7:00 PM EDT

Name: "Special Relativity"

Hey,

 If there is no friction, the angle of the hill does not matter because gravity is a conservative force.  If there is friction, then the angle of the hill matters because it will affect the frictional force and the distance traveled.  Both of these factors will determine how much kinetic energy is lost to friction, thus reducing the final velocity.

Since the equation for kinetic energy is .5mv^2, if an arrow has twice the speed it has 4 times the kinetic energy, and thus it will travel 4 times as far as the slower arrow until friction with the hay (which cant be that much) will absorb all the energy.

It is easier to zig zag up a mountain then climb straight up because the angle of inclanation decreases.  This means that with each step, the altitude changes only a fraction of what it would had one climbed straight up.  Thus less energy is exerted by the climber each step and it seems easier to continue climbing.  However, zigzagging will require the same, if not more, energy than would climbing straight up the mountain, it is just that the power that must be generated is less.  Power is work over time.  If you increase the time (zigzagging) then you decrease the power output.

Thank you all

Sunday, 7 October 2007 - 7:18 PM EDT

Name: "Bob"

If the hill is icy and there is no friction, then the velocity does not depend on the angle because there are no non-conservative forces, so the potential energy at the top of the hill will equal the kinetic energy at the bottom. If there is friction, then the angle will matter because the frictional force (which is non-conservative) will be influenced by the angle of the incline.

 Since the formula for kinetic energy is .5mv^2 then doubling the velocity of the second arrow will quadrouple the kinetic energy, thus it will penetrate 4 times as far.

 It is easier to climb a mountain via a zig zag because in both cases, the work is the same, but since it takes longer to go up via a zig zag, the zig zag path requires much less power. (since power = Work/time)

Monday, 8 October 2007 - 1:35 AM EDT

Name: "Addis"

If it is icy and there is no friction then the angle of this hill will not matter at all. This is because the only force that will be acting on the sled to make it move will be the gravity, which is a conservative force.  However if there is friction and since friction is a non-conservative force then the angle of the hill will matter. Unlike in part a where the potential energy at the top will equal the bottom. In part b the friction which is a non-conservative force will cause it to lose some of it’s energy as it goes down the hill which will cause it to have a smaller velocity then in part a.

 

The equation for kinetic energy is 1/2mv^2 and since both arrow are identical. The only thing that changes is the velocity and this means that the one going faster will go four times farther then the one that is going slower. This is because the velocity is double which means it will go four times farther.

 

It would be easier to zigzag up the mountain. Although it might take the same amount of work to climb straight up the mountain as it takes to zigzag. When you zigzag it will take longer to climb the mountain this means that the power you needed to climb the mountain would be less.  We know this because power equal work over time.

Thursday, 11 October 2007 - 2:13 PM EDT

Name: "Dave"

a) no, conservation of energy proves that only the height of the hill would matter, no matter what angle there is, PE at the top will equal KE at the bottom, so the speed is always √2gh

 

b) yes, because friction is a non-conservative force and it depends on normal force, which depends on the angle of the incline

 

 

The faster arrow will go 4 times farther, this is because ½ mv2 = Wnc, so ½ mv2 = Ff x d, so d = ( ½ mv2)/Ff, and if v were doubled, it would be 4v2 in the numerator, meaning an increased distance of 4x the original distance

 

The zig zag path allows the same amount of work to be done over a shorter period of time, meaning less power, therefore requiring less stamina for the climber

Thursday, 11 October 2007 - 2:26 PM EDT

Name: "MaryBeth"

In any situation Wnc + PEi + KEi = PEf  + KEf. On a frictionless hill, there are no nonconservative forces so PEi will equal KEf. The angle will not matter. If there is friction involved, PEi – the work done by friction will equal KEf. Therefore, the angle will play a part in the frictional force and consequently decrease the final velocity.

 If one arrow has twice the velocity of another identical arrow, it will consequently have 4 times the kinetic energy of the slower arrow. This is because KE = .5mv^2. As a result of having 4 times the KE, it will penetrate 4 times as far.

 More complicated paths make it easier to climb up a mountain because the time to achieve the same vertical displacement is increased. Though the work is the same, the power exerted is less because it takes more time. P = w/t and in such an expression, if t gets bigger, p gets smaller.

Thursday, 8 November 2007 - 5:58 AM EST

Name: "Jonathan Hellmer"

Well, if there were to be no friction the angle or slope of the hill would not matter knowing that gravity is a conservative force.  On the other hand, if you do have friction,  then the anlge or slope of the hill would matter because it affects distance traveld and the frictional force.  So, because these two factors are being affected you can figure out he KE lost due to the friction which will conclude in reducing the final lvelocity. 

For the scenario with the arrows the one arrow will have 4 times the kinetic enery if the has twice the speed this is because of the equation for KE which is 1/2mv^2.  So, in conclusion this arrow will travel four times the distance/penetration in the hay while friction is stopping them.

It is easier to zig zag up a mountain because the that angle at which you are climbing at decreases (the inclanation), rather than when you climb straight up.  Therefore, this means that while you are climbing the altitude is changing a fraction of what it would be if you were to climb straight up.  This allows the climber to exert less energy making the climb easier.  Still, if you zig zag, you will still need the same or more energy as if you were climbing straight up.  This is because what is changing is the power that you need to climb up while zigzagging which is less.  This is all due to the fact that power equals work over the time.  So if you zig zag faster then the power will clearly decrease.