A massless spring of constant k = 88.9 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance of d. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is µk = 0.34, and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. [Hint: The force of the track on the block will be zero if the block barely makes it through the-loop-the-loop.]

Question

so i did,
(.5)*(88.9)*X^2=(0.34)*(.5)*(9.81)*(2.5)+(2)*(1.5)*(.5)*(9.81)

44.45^2=18.88425
X=.6517994474m
What seems to be my mistakes because hw site doesn't accept my answer.

Answer 1

Potential energy stored in spring = (1/2)k d^2= 44.5 d^2
That will be the kinetic energy the block has departing the spring
KE =(1/2)mv^2 = 44.5 d^2

I assume that A to B is this next stretch between the spring and the bottom of the ferris wheelie.

normal force on track = m g
friction force = .34 m g
work done by friction = .34 m g (2.5)
= .85 m g

so kinetic energy at bottom of loop = 44.5 d^2 - .85 m g

Now

Loss of energy going up loop = m g h = 3 m g

Now at the top of the loop for zero force on track:
m v^2/r = m g

(1/2) m v^2 = m g r = (1/2)1.5 m g

Ke at top is therefore .75 m g

So the total kinetic energy at the bottom of the track must be 3.75 m g
so

3.75 m g = 44.5 d^2 - .85 m g
44.5 d^2 = 2.90 m g
d^2 = (2.90/44.5)(.5)(9.81)
d = .565

Answer 2

again, I appreciate your work but site doesn't accept this answer. I don't know why this is occurring for all the problems that I'm working on.

Answer 3

Beats me, but check my arithmetic carefully.

Answer 4

i tried to insert .6447721757 and the site says round-off error.

Answer 5

Damon, I think you made an arithmetic error here: 3.75 m g = 44.5 d^2 - .85 m g
44.5 d^2 = 2.90 m g

It should be 44.5d^2 = 4.6 m g

Then solve from there, I made that change and got the right answer.

Answer 6

44.5 d^2=4.6mg
d^2=(4.6*.5*9.81)/(44.5)=0.507033708
d=0.712062994m
Is this right? I have only one chance to insert the answer so i want to make sure.