aye

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This question is #359 from EK 1001 Physics 2003 edition:

A block is on a frictionless ramp and has a mass of 50g and h is 20cm. The block has an initial velocity of 2 m/s, and slides down. If the coefficient of kinetic friction between the block and the flat portion of the ramp is .2, how far does the block travel along the flat portion of the ramp?

i know that the potential energy and the kinetic energy equal each other given the values of m, h, v. but could there be an instance where they would give an initial velocity of say, 3m/s, and therefore would not equal the potential energy?? if so, which value (p energy or k energy) would you use to get the answer?

also, now that i look at this question more, it doesn't make sense. how can the kinetic energy at the top of the ramp (due to its initial velocity) equal the potential energy? i thought the k energy would equal the p energy only the block reaches the bottom... sorry if i lost you... but any input would be appreciated!
 

cure4cancer

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can't use energy for this question unless you take into acccount the energy that was lost due to friction.
Best way to approach this problem is to realize that there is friction and that it would affect the acceleration of the object.

I'll let you think about how ;)
 

Medikit

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That frictionless ramp doesn't seem so frictionless to me
 

Daichi Katase

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DetectiveChubby said:
Ok...but seriously. You take the initial initial kinetic energy (.5*m*2^2) and at it to the potential energy. Since the ramp is frictionless, there will be no loss of energy and the energy at the bottom would be (mg*original height + initial kinetic energy) and it would all be in form of kinetuc energy.

Now....friction does work. Calculate the frictional force (Normal Force*k) and use it to find work (F*d)

use the equation:

F*d = (kinetic energy at the bottom of the ramp)
and solve for d. that is your distance travelled.
 

Daichi Katase

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what is the answer....i did it all in my head...so it is probably wrong. I get 2m?
 

anavistas

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u are right detective !but the answer is 20 cm rather than 2m you are missing one zero i don't know where !i used paper and pen!! :luck:
 

Shrike

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Initial energy = initial potential energy + initial potential energy
= 1/2 mv^2 + mgh (in Joules)
= (0.5 * 0.05kg * (2m/sec)^2) + (0.05kg * 10m/sec^2 * 0.2m)
= 0.1J + 0.1J
= 0.2J

(addressing one question: they are equal, but this is a coincidence)

Final potential + kinetic energy = 0 (at rest, at the bottom)

Final energy - initial energy = work done (by friction in this case)

(change in energy and work done are each negative in this case, incidentally, but it would be fine to ignore that)

work done by friction = -(mu)*normal force * d
-0.2J= -(mu)*mgd = -0.2*0.05kg * 10m/sec^2 *d = 0.1d
d=2m

Chubby is right. EK is wrong.

An alternative would be to work out speed at the bottom of the ramp = 2*sqrt(2), and then use v^2 = 2ad. Same answer, unsurprisingly.