Work Problem: Spring and Friction, find final Speed

[JoeyBob]

Homework Statement

See attached

Relevant Equations

Ek=1/2mv^2 Ep=1/2 k (x)^2

First calculated non conservative work from friction using Ff=umg. Non conservative work was -8.82.

Initial kinetic energy, 1/2mv^2, was 136.89.

Change in potential energy, 1/2k(x)^2, was 8.1216.

Ekf-Eki+Change Ep=Work NC

Ekf=W NC+Eki-change Ep

=-8.82+136.89-8.1216=119.9484

Ekf=1/2mv^2, v=7.3014 but answer should be 7.44. I've confirmed there were no rounding errors by trying the same calculation all at once in the calculator (I still get 7.3).

 

[TSny]

Check your calculation for W_NC.

 

[JoeyBob]

Check your calculation for W_NC.

Wouldnt it just be the friction force here, umg? This is 0.2*9.8*4.5=8.82. Friction force would be against it so it would also be negative.

 

[TSny]

Wouldnt it just be the friction force here, umg? This is 0.2*9.8*4.5=8.82. Friction force would be against it so it would also be negative.

Force and work do not have the same dimensions. So, the work cannot equal the force.

 

[JoeyBob]

Force and work do not have the same dimensions. So, the work cannot equal the force.

So I use the distance its been compressed to find the work. Thanks.

 

[TSny]

So I use the distance its been compressed to find the work. Thanks.

OK. Good. Note that you would have probably caught your error if you had included units in your calculations.

 

[JoeyBob]

OK. Good. Note that you would have probably caught your error if you had included units in your calculations.

Its more that I wasnt open minded enough to use that variable for two things - I only saw it as part of the potential energy of the spring (the compression).