Question

A 10-kg block on a rough horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position?

Answer 1

The spring must be tied with some wall on the left end.
Spring energy = 1/2 times force constant times displacement
max. spring energy =448 * 10^-2 joule
Energy loss due to friction = 30 * 8 * 10^-2 = 240*10^-2 joule
Energy convertible to kinetic energy = max. spring energy - energy loss due to friction
Kinetic energy = 208 * 10^-2 joule
Kinetic energy of the block = 1/2 times mass times velocity^2
velocity = 0.645 m/s

Answer 2

"Spring energy = 1/2 times force constant times displacement"

Haven't checked you numbers - maybe this is a typo - but it's actually

Spring energy = 1/2 times force constant times displacement squared

E - 0.5kx^2

@ShailKumar - I also note that you tend to give the complete answer - which is contrary to the terms and conditions of this site.

It would be a better learning opportunity if you gave guidance to the OP rather than the answer.

Answer 3

Yes! That's a typo. Thanks for the T&C.

Answer 4

I really did not know about T&C.

Answer 5

NP - it is good to show the method - but if you work it right through to the answer then it is unlikely that the OP will work it for themselves.

Answer 6

Hmm. kk...

Answer 7

i got the answer 4.48

Answer 8

It should be 2.08 J

Answer 9

can you solve it please

Answer 10

I have solved it above.

Answer 11

http://openstudy.com/study#/updates/53973a73e4b03871bbf06d69

Answer 12

whats the mistake here

Answer 13

Maximum KE = max. PE - energy loss due to friction. The mistake is that you did not consider frictional losses.

Answer 14

can you please once again tell me the solution

Answer 15

When the block is at extreme right, it has potential energy and zero kinetic energy.Energy is conserved. So, some of potential energy is converted into kinetic energy as the block moves towards equilibrium and some of it is lost against the friction in some other form e.g heat or sound.
Finally at the equilibrium, only kinetic energy lives in the block which you want to calculate.
So, KE = PE - energy loss due to friction.