A brick is lifted to a given height and then dropped to the ground. Next, a second brick, which weighs twiceas much as the first, is lifted just as high as the first and then it too is dropped to the ground. When the second brick strikes the ground it has:
a) half as much kinectic energy
b) as much kinectic energy as the first
c) twice as much kinectic energy as the first
d) four times as much kinectic energy as the first
As always, decide on only one answer. A correct answer accompanied by a correct explanation beats a correct answer by itself.
I believe that I already know the answer (please don't let me be wrong!) to the question. I offer this question for the challenge of solving it as well as for the educational value.
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2007-07-09 05:02:53 · 9 answers · asked by ? 6 in Science & Mathematics ➔ Physics
You are all correct (those who didn't answer and then delete later that is...)!
El Jefe - Good job Boss!
Adam S - You are correct!
llcold - Correct and you touched upon the concept. Good work!
Norrie - Correct! And handy with equations!
FTL - Starting over with a new account? It's good to have self-confidence but it doesn't hurt to also practice being polite, particularly in case you turn out to be wrong. There are a lot of very smart people here. Give them some credit.
EyeOntheScreen - What can I say? You obviously know your stuff. Correct equation. Correct reasoning. Nice summary of the concept behind the math. With some added thoughts that allow for additinal consideration. And well written! Congratualtions!!!
Kiran the Man - You are the Man (O.K., but El Jefe is the Boss)! You got the answer right. Just be careful about guessing. If you understnad the concept behind the math you well gain confidence. Thank you!
2007-07-09 16:37:24 · update #1
Aaron - You found the answer mathematically and also provided a great explanantion of the concept. I'm sorry there can be only one! (But I did add a thumbs up for you).
PiGuy - Correct! I realize you understand the concept. Too bad you didn't find the question sooner. Thank you.
The answer is C. Lifting the brick of double weight is like lifting the first brick twice and so takes twice as much work, which all goes into kinetic energy as it falls.
2007-07-09 16:41:22 · update #2
By conservation of energy, the potential energy at the given height h PE = KE the kinetic energy when either brick hits the ground from dropping h. Thus, we have...
PE = mgh = 1/2 mv^2 = KE; where g is the acceleration due to gravity (9.81 m/sec^2 at Earth's surface).
Let w = mg, the weight of the first brick dropped and W = 2mg the weight of the second. So mgh = wh = ke for the small brick and 2mgh = Wh = KE for the large one.
Then W/w = 2mgh/h//mgh/h = 2 = KE/h//ke/h; so that 2 = KE/ke and KE = 2 ke. The kinetic energy of the big brick is twice the ke of the small brick; so c) is the answer.
Lesson learned, KE = 2 ke because of the conservation of energy and because W = 2mg and w = mg; so there is twice as much mass (2m) in the big brick than in the small brick (m). But this holds only if V = v, the velocities of the two bricks are the same. Why would they be the same?
Because both accelerate at g = 9.81 m/sec^2 when dropped. And from the SUVAT equation v = sqrt(2gh), which means V for the big one = v for the small one as they both started at h height above the ground when they were dropped.
2007-07-09 05:42:38 · answer #1 · answered by oldprof 7 · 1⤊ 1⤋
the answer is c.
again all the potential energy is converted to kinetic energy.
the force required to lift the second load to its height is twice that of the force to lift the first.
let the mass of the first brick be x.
hence the second brick has a mass of 2x.
taking acceleration due to gravity as 10m/s^2
mathematically the forces are
F1=m*a(here acceleration is done against that of gravity).
=10x
F2=m*a
=2x*10
=20x
since displacement of the loads are the same,work done in moving the 2nd brick is twice the work done in moving the 1st.so the second brick will have 2ce the potential energy and hence on dropping will have 2ce the kinetic energy.
therefore the answer is c.
different approach.
so the mass of the first brick is x.
K.E.1=mgh
=xgh
mass of the second brick is 2x.
hence
K.E.2=mgh
=2xgh
so taking the ratio of 2nd kinetic energy to first kinetic Energy we get
K.E.2:K.E.1=2xgh:xgh
=2:1
hence the second brick has twice the energy as the first.
2007-07-09 05:49:09 · answer #2 · answered by Anonymous · 1⤊ 0⤋
C) twice as much KE as first one
By the conservation of energy, the potential energy of blocks at highest point is totally converted to KE at bottom,neglecting air resistance.Thus, the PE of the 2nd block at the top(2 x mgh) is twice the PE of 1st block(mgh),hence the KE of the 2nd block will be twice that of 1st
2007-07-09 05:20:48 · answer #3 · answered by llcold 2 · 1⤊ 0⤋
It will have c..Twice the KE.
Assume brick 1 = 1 kg. at a height of 1m
KE = 1kg x 9.81(gravity) x 1m = 9.81 N
Brick 2 = 2kg at the same height..
KE = 2kg x 9.81 x 1m = 19.62 N (Twice brick 1)
(PE = mgh, when the brick is released the PE converts to KE we want KE..not velocity).
2007-07-09 05:21:36 · answer #4 · answered by Norrie 7 · 1⤊ 0⤋
Twice as much. If it's dropped from the same height, it will be falling at the same velocity.
KE = 1/2 * mv^2
The v is the same, the m is doubled, so KE is doubled.
2007-07-09 05:09:53 · answer #5 · answered by El Jefe 7 · 1⤊ 0⤋
F = mass * Acc.=mass *grav in case of fallin bods where g=9.8m/sec sq. ~ 10m/sec sq.
F1---> 1st brick = mg = 10m
F2 = 2mg = 20m
If its falling with twice as much force then the correct op. is 'c'
even if my reasoning is incorrect, i have a 99% hunch that c is de answer
2007-07-09 05:43:41 · answer #6 · answered by Kiran The Man 2 · 1⤊ 0⤋
Answer C) because it has twice the weight.
2007-07-09 13:23:13 · answer #7 · answered by Piguy 4 · 0⤊ 0⤋
according to the formula KE=1/2 * mv^2 .... it has double
C is correct
2007-07-09 05:20:00 · answer #8 · answered by Anonymous · 1⤊ 0⤋
You people just don't get it! The brick that weighs twice as much will fall faster, so it's (d), 4 times as much!
Don't you guys know anything!!!
2007-07-09 05:22:46 · answer #9 · answered by Anonymous · 2⤊ 3⤋