A box slides down a plank, Find its velocity

[Girn261]

Homework Statement

A box sits on an inclined plank of 1.2m length by 0.6m vertical. The coefficient of friction is 0.40. If it is held at the top and released, what will be the velocity at the end of the plank?

Homework Equations

a=Fnet/m , C^2=a^2+b^2, v^2=u^2+2as

The Attempt at a Solution

Please see attached picture for my attempt the solution. I still get a slightly wrong answer.

 

[haruspex]

1.2 m length of plank.

 

[Girn261]

1.2 m length of plank.

hmm, still get wrong answer.. With 1.2m being the length of the incline, I get 1.039 for the "x" length. and with V being 1.3544

 

[CWatters]

Please show your working. I solved it two different ways (one of which was your method using plank length = 1.2) and both give same answer (which wasn't 1.3544). So most likely an arithmetic error somewhere.

 

[Girn261]

Please show your working. I solved it two different ways (one of which was your method using plank length = 1.2) and both give same answer (which wasn't 1.3544). So most likely an arithmetic error somewhere.

1.2^2=a^2+0.6m^2
a=1.039

v^2=u^2+2(a)(s)
0+(2)(.8829)(1.039)
sqrt 1.834 = 1.3544

 

[CWatters]

1.2^2=a^2+0.6m^2
a=1.039
v^2=u^2+2(a)(s)
0+(2)(.8829)(1.039)
sqrt 1.834 = 1.3544

It's confusing using "a" for two things.

The acceleration isn't 0.8829 m/s/s. Show how you got that.

The distance the object moves isn't 1.039m it's 1.2m.

Sorry got to go to bed now. It's nearly midnight here.

 

[Girn261]

It's confusing using "a" for two things.

The acceleration isn't 0.8829 m/s/s. Show how you got that.

The distance the object moves isn't 1.039m it's 1.2m.

Sorry got to go to bed now. It's nearly midnight here.

Please see picture for how I got acceleration

 

[haruspex]

Please see picture for how I got acceleration

This seems to be your first picture again, with the wrong plank length.

 

[Girn261]

This seems to be your first picture again, with the wrong plank length.

I know, just quoting to show how I got acceleration. With plank as A or B in pythagorean theorem, I still get wrong answer

 

[haruspex]

I know, just quoting to show how I got acceleration. With plank as A or B in pythagorean theorem, I still get wrong answer

Please post your working for how you get the wrong acceleration eventhough using the right plank length.
And, please, not as an image. Take the trouble to type your algebra so that people can read it much more easily and quote parts to point out errors.

 

[CWatters]

I know, just quoting to show how I got acceleration.

The equation for the acceleration contains terms Sin and Cos, you need to redo these calculations because they are also affected by the error with the plank length.

 

[Girn261]

I figured out my mistakes. Thank you for everyones help, I really appreciate this forum.

 

[CWatters]

What answer did you get?

Just for info, the alternative method I used was to apply conservation of energy.

The final KE = Initial PE - W_f

where
W_f = the work done against friction = L * μmgCosθ
L = length of plank

so..

0.5mv² = mgh - μmgLCosθ

mass cancels.
Rearrange to give

v = SQRT(2g(h - uLCosθ))