Question

a small particle slides along a track with elevated ends and a flat Central part as shown in figure the flat part has a length 3 metre the curve portions of the track a friction less but for the flat part the coefficient of kinetic friction is musicals 20.2 the particle is released at point a which is at a height h is equals to 1.5 metre above the flat part of the track the position where the particle finally come to rest is
A) left to the midpoint of the flat part
B) right to the midpoint of the flat part
C) midpoint of the flat part
D) none of these​

Answer 1

Answer:

The answer will be option C

Explanation:

According to the problem the particle slides on  a track having the central part as flat .

It is also given that the particle released from the height let h

Now we will find the gain of kinetic energy by the particle while coming from point A to B

here a gravitational force will work

Therefore, wg = mgh

Now at the initial and the final position the kinetic energy of the particle will be zero

Therefore from work energy theorem we can say that

wg +wf = delta k

=> mgh +wf = 0

Now wf = - μ mg  x

=> mgh - μ mg x = 0

=> x = h/μ

by putting the values,

=> x = 1.5/0.2 = 7.5 m

Now when the particle is moving from B to C it has some kinetic energy

Now the length of the flat part is , l= 3 m

And we have x = 7.5 m

it says that the particle will traverse the flat part twice and third time it will stop

therefore x' = 7.5 -3 x 2 = 1.5 m

The particle will stop from B  to 1.5 m right which is position of E