Potential Energy of the boxes

Classical Mechanics Level 2

Box A and B lie on differently curved surfaces as above. The masses of box A and B are m m and 2 m 2m , respectively, and the heights and lengths of the curved surfaces are the same. Which of the following statements is correct? (The frictions on the curved surfaces and the air resistance are negligible. And suppose the boxes are particles.)

a) The average velocity of A until the box arrives at the bottom is greater than that of B.

b) The works done by gravity on the boxes A and B are the same.

c) The mechanical energies at the moment both A and B arrive at the bottom are the same.

a) only b) and c) a) and b) c) only

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Lakshan Dumpa by Lakshan Dumpa , 24, India

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7 solutions

Milly Choochoo
Mar 10, 2014

a) True : box A will experience a greater net acceleration for a longer time, so it will complete the track/slope in a faster time, meaning that it will have a greater average velocity.

b) False : the potential energy of box B relative to the bottom/end of the slopes is greater than box A's, so gravity will do more work on it on its path down the slope.

c) False : same as b) - just notice that the total mechanical energy is conserved, and that box B's initial energy is greater than box A's

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The net downward Force is Higher In case of box a hence accelaration will be max on reaching the ground Of Box A. Those who thing That it will be same for both the bodies are wrong Since it is only true if the path is Linear or same Irrespective of The mass.

Yogesh Bist - 7 years, 3 months ago

since friction is ignored so as far as my knowledge is concerned only option A is correct.

Farooq Aslam - 7 years, 3 months ago

exact explanation

vijay sahu - 7 years, 3 months ago

average velocity hasno dependency on masss'

Prayas Trivedi - 7 years, 3 months ago

but gravity is a conservative force . so work done is path independent must be b and c

ishika saxena - 6 years, 5 months ago

good .....

Aditya Raj - 7 years, 3 months ago

how come box B's intial energy is greater than A's....?

Ganesh Maurya - 7 years, 3 months ago

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Although they are at the same initial height, box B has twice the mass of box A.

Milly Choochoo - 7 years, 3 months ago
Muzammil Kayani
Mar 14, 2014

greater the mass less the velocity,,,so B body with greater mass have less velocity,,A correct .. ..ME=K.e + Pe so potiential energies of both bodies are not same, C False ;; change in potential energy is equal to work done,,as potiential energies are diff so work done could never be same B false

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Qamar Raj
Mar 13, 2014

simple acclaration on A is greater so A come fast instead of B

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consider slope A-the rate of change of slope of A is greater than that of B i.e dm/dx (where m is the slope of curve) is greater for A than B

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Owesh Ali
Mar 12, 2014

answer is (a) because curve A is minimum angle than curve B because of that object A first come then object B hence proved

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the vertical component of m is more than 2m so it will more attracted by gravity pull and hence its velocity will be higher..

Yawar Khan - 7 years, 3 months ago

kindly sent dail such question

Faisal Hayat - 7 years, 3 months ago
Krishna Das
Mar 12, 2014

Av.velocity =displacement/time

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i did not understand the ans what you say

Partho Bikash - 7 years, 3 months ago

Good. Gud experience.......... Include more questions like this.......

Shravan Mv - 7 years, 3 months ago
Aditya Raj
Mar 11, 2014

a) True : box A will experience a greater net acceleration for a longer time, so it'll be faster at the end.

b) False : the potential energy of box B relative to the bottom/end of the slopes is greater than box A's, so gravity will do more work on it on its path down the slope.

c) False : same as b) - just notice that the total mechanical energy is conserved, and that box B's initial energy is greater than box A's

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lol you just copied and pasted my solution

Milly Choochoo - 7 years, 3 months ago

no i have not done it i have braians and 1 can thing like someone else also. its not a big deal.

Aditya Raj - 7 years, 3 months ago

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I was not saying that you couldn't do the problem. Obviously you got it right (as you were able to post this). Also, you are at a higher level than me in most areas, so my guess is that you are much smarter than I am.

I just thought this was funny.

Milly Choochoo - 7 years, 3 months ago

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