Solving for Distance: Spring Collision [SOLVED]

[grouchy]

[SOLVED] Spring Collision

Homework Statement

A 8 kg block is pushed by an external force against a spring with spring constant 173 N/m until the spring is compressed by 2.1 m from its uncompressed length (x = 0). The block rests on a horizontal plane that has a coefficient of kinetic friction of 0.56. The acceleration of gravity is 9.8 m/s^2. Remember: The block is not attached to the spring.

After all the external forces are removed (so the compressed spring releases the mass) how far D along the plane will the block move before coming to a stop? Answer in units of m.



The attempt at a solution...

Ui - Wf = 1/2mv^2

(0.56)mgd = 1/2kx^2 - 1/2mv^2 then I just moved everything over to get d but I used 1/2kx^2 to get the v by setting it equal to 1/2mv^2 so it just cancels out...

 

[PhanthomJay]

Homework Statement

A 8 kg block is pushed by an external force against a spring with spring constant 173 N/m until the spring is compressed by 2.1 m from its uncompressed length (x = 0). The block rests on a horizontal plane that has a coefficient of kinetic friction of 0.56. The acceleration of gravity is 9.8 m/s^2. Remember: The block is not attached to the spring.

After all the external forces are removed (so the compressed spring releases the mass) how far D along the plane will the block move before coming to a stop? Answer in units of m.



The attempt at a solution...

Ui - Wf = 1/2mv^2

(0.56)mgd = 1/2kx^2 - 1/2mv^2 then I just moved everything over to get d but I used 1/2kx^2 to get the v by setting it equal to 1/2mv^2 so it just cancels out...

But it is given that the block comes to a stop, so v_f =?

 

[grouchy]

attempt 2...

u = coefficient of friction)

1/2kx^2 = umg*d

d = 1/2kx^2/umg
d = 8.668616071m (wrong again)

 

[PhanthomJay]

attempt 2...

u = coefficient of friction)

1/2kx^2 = umg*d

d = 1/2kx^2/umg
d = 8.668616071m (wrong again)

Too many significant figures! Try 8.7 meters from its released position.

 

[grouchy]

that doesn't matter thought, the site even says "do not use" sig figs...

 

[PhanthomJay]

that doesn't matter thought, the site even says "do not use" sig figs...

Well maybe the darn site is looking for the distance it travels from its original position before the spring was compressed, from x =0, in which case maybe it's looking for d = (8.7 -2.1) = 6.6m?

 

[Doc Al]

attempt 2...

u = coefficient of friction)

1/2kx^2 = umg*d

d = 1/2kx^2/umg
d = 8.668616071m (wrong again)

Your method is fine. I would check your calculation again (I get a different 3rd digit). It shouldn't matter, but that depends on how fussy the online system is.

More important than that is where are you supposed to measure Distance from? From the compressed position (x = -2.1 m)? Or the unstretched position (x = 0)? (Based on how you described it, I'd say from the compressed position, just like you found.)

 

[grouchy]

yup. it was -2.1 so 6.6m. thanks guys