A block of mass M = 3.5 kg is at rest on an incline (θ = 25.0°) that has friction between the incline’s surface and the base of the block. The block sits a distance L from the bottom of the incline. Attached to the block is a stretched spring (i.e., L Xo ) that has a spring constant k = 24.0 N/m and a natural length of Xo = 3.0 meters. Suppose the magnitude of the frictional force acting on the block is Ffr = 20.5 Newtons. Use g = 9.81 m/s2.

Question

A block of mass M = 3.5 kg is at rest on an incline (θ = 25.0°) that has friction between the incline’s surface and the base of the block. The block sits a distance L from the bottom of the incline. Attached to the block is a stretched spring (i.e., L > Xo ) that has a spring constant k = 24.0 N/m and a natural length of Xo = 3.0 meters. Suppose the magnitude of the frictional force acting on the block is Ffr = 20.5 Newtons. Use g = 9.81 m/s2.

anonymous · Answer

1) What is Fs , the magnitude of the spring force acting on the block?

2) What is L , the total length of the spring?

3) Given that the coefficient of static friction between the incline and the block is μs = 0.85, what is the maximum distance, Lmax , from the bottom of the incline the block can be so that it is still at rest?

anonymous · Answer

For #1, I feel that it should be F=ma

anonymous · Answer

@hartnn @ash2326

anonymous · Answer

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anonymous · Answer

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anonymous · Answer

spring force = Ff - mgsin(theta)

anonymous · Answer

find that, then for 2)  spring force = 24(L-3)

anonymous · Answer

what does Ff mean?

anonymous · Answer

Ffr

anonymous · Answer

the friction force given

anonymous · Answer

Thank you for the help. Im still puzzled by part 3 though.

anonymous · Answer

use mu static to calculate the max frictional force..

anonymous · Answer

then  spring force +mgsin25 = max frictional force
          24(L-3)  +mgsin25 = max frictional force...

solve for L

anonymous · Answer

Max frictional force is F>Us(N) correct?

anonymous · Answer

Us*N   yes.

anonymous · Answer

I would divide N by 20.5 because Us is not given

anonymous · Answer

Us is given

anonymous · Answer

Given that the coefficient of static friction between the incline and the block is μs = 0.85,

anonymous · Answer

any questions about the problem?  or you got it now? :)

anonymous · Answer

I get L to be 3.61. It is not the correct answer.

anonymous · Answer

your calculator work is off

anonymous · Answer

or something.

anonymous · Answer

maybe you didn't use  N = mgcos25 ?

anonymous · Answer

who knows.

anonymous · Answer

Shouldn't it be sin?

anonymous · Answer

why?

anonymous · Answer

mgsin25=N ? The answer should also be lower then the total legnth of the spring also right?

anonymous · Answer

is there a reason you're picking N= mgsin25?

anonymous · Answer

Thats what you respond I should do.

anonymous · Answer

you like sines better than cosines?

anonymous · Answer

then  spring force +mgsin25 = max frictional force
          24(L-3)  +mgsin25 = max frictional force...

anonymous · Answer

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