Forces Grade 12 Physics Question

[David John]

Homework Statement

At a construction site, a small crane is raising two boxes of nails on a plank to the roof. One box has already been opened and is half full, while the other box is new. The boxes, including the nails, weigh 10 kg and 20 kg, respectively, and are both the same size.

c) If the coefficient of kinetic friction is 0.3, how fast will the boxes accelerate along the plank, once they start to slide?

Homework Equations

a = mgsinΘ - mgcosΘ(μk)

The Attempt at a Solution

a = mgsinΘ - mgcosΘ(μk)
= g(sinΘ-cosΘ(μk))
= 9.8sin(21.8) - 0.3cos(21.8)
=0.91m/s^2

Note that in the previous part of the question, I found that the angle at which both boxes slide are at 21.8 degrees. I went on yahoo answers and saw 2 people solve this question using the equation above. I'm really confused as to how that equation was formed. In the previous part to this question, to find the angle at which the boxes slide, I used Fnetx = mgsinΘ - mgcosΘμs. The mass and gravity canceled out so I just solved for the angle that way. Not sure why that equation was used once again for this question. Is this the right formula and if so why?

 

[Let'sthink]

Homework Statement

At a construction site, a small crane is raising two boxes of nails on a plank to the roof. One box has already been opened and is half full, while the other box is new. The boxes, including the nails, weigh 10 kg and 20 kg, respectively, and are both the same size.

c) If the coefficient of kinetic friction is 0.3, how fast will the boxes accelerate along the plank, once they start to slide?

Homework Equations

a = mgsinΘ - mgcosΘ(μk)

The Attempt at a Solution

a = mgsinΘ - mgcosΘ(μk)
= g(sinΘ-cosΘ(μk))
= 9.8sin(21.8) - 0.3cos(21.8)
=0.91m/s^2

Note that in the previous part of the question, I found that the angle at which both boxes slide are at 21.8 degrees. I went on yahoo answers and saw 2 people solve this question using the equation above. I'm really confused as to how that equation was formed. In the previous part to this question, to find the angle at which the boxes slide, I used Fnetx = mgsinΘ - mgcosΘμs. The mass and gravity canceled out so I just solved for the angle that way. Not sure why that equation was used once again for this question. Is this the right formula and if so why?

Something is wrong in what you write at 2. and 3.; do you notice that?

 

[David John]

Something is wrong in what you write at 2. and 3.; do you notice that?

I'm not sure I understand what you mean? I know for some reason mass cancels out if that's what you mean. However I'm confused why only mass is canceled out and why gravity isn't

 

[Let'sthink]

I'm not sure I understand what you mean? I know for some reason mass cancels out if that's what you mean. However I'm confused why only mass is canceled out and why gravity isn't

Equations that you have written - are they dimensionally correct?

 

[David John]

I really don't know. I got that formula from yahoo answers. I really don't know if it's even the right formula to use

 

[Let'sthink]

I really don't know. I got that formula from yahoo answers. I really don't know if it's even the right formula to use

You can at least think what is wrong with these formula once you note that leave that wrong thread. Regarding your question why mass cancels is because mass that appears in Newton's law and Newton's gravitational law are same regarding why gravity does not cancel, I would say - what is on left hand side is not 'g' the property of gravity but a the observed acceleration. Just think for a while before starting asking question. Just try to think on what factors 'g' depend?