Question

A mass m = 13.0 kg rests on a frictionless table and accelerated by a spring with spring constant k = 5038.0 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.44. The mass leaves the spring at a speed v = 3.7 m/s.

How much work is done by the spring as it accelerates the mass?

How far was the spring stretched from its unstretched length?

The mass is measured to leave the rough spot with a final speed vf = 1.5 m/s.
How much work is done by friction as the mass crosses the rough spot?

Answer 1

Well we know that W=K right? Solve for K using \[\frac{ 1 }{ 2 }mv^2\]

Answer 2

88.98

Answer 3

got that in the past hour :)

Answer 4

ok. I gave you the wrong equation to use btw

Answer 5

did you use k(Xfinal-Xinitial)/2

Answer 6

Im trying to find the equation to find the stretched length.

Answer 7

The equation I just replied with is for that part. Xinitial should be 0 since the spring is at the equilibrium length

Answer 8

and that value will equal 88.98?

Answer 9

Yes because the spring does all the work since there is no friction

Answer 10

ok so just checking my math here 5038(xf)/2 = 88.98 ; 2519x = 88.98; 88.98/2519 = .035 which is not the right answer.

Answer 11

do you see fail anywhere?

Answer 12

Yes. But it was my fault. The equation was missing that Xfinal is raised to the 2nd power
\[Xfinal^2-Xinitial^2\]

Answer 13

So you should square root .035

Answer 14

squared makes the answer .18 which is still wrong... can you try it out and see if you get a different number?

Answer 15

make sure you add alot of sig figs. id say enter 5 decimal places

Answer 16

:D! yeaah good call, that worked.

Answer 17

The mass is measured to leave the rough spot with a final speed vf = 1.5 m/s.
How much work is done by friction as the mass crosses the rough spot? Any ideas how to do this one?

Answer 18

I actually have no idea on this one. I have the same types of problems as you have right know assuming you are usuing smart physics?

Answer 19

exactly right haha

Answer 20

Good luck on solving that problem. If I manage to solve it, I will come post a solution to it.

Answer 21

For sure, I appreciate it. Godspeed

Answer 22

@SilenTempest Hey man its 1/2 *mass*(velocity w/o friction^2 - velocity w/ friction^2) and that value negative.

Answer 23

So is it (1/2)Mv^2 (non friction) - (1/2)mv^2(w/ friction)?

Answer 24

Nevermind I got it.