Mathematics Mechanics Help

Ricochet J · 5 Jun 2006 at 12:05

Right. Tomarrow i've got a Mathematics Mechanics 1 exam so I thought it would be a wise idea to go over the things I am weak on before the exam to reinforce my knowledge. So, the topic is Dynamics of a particle moving in a straight line

Mechanics 1 for Edexcel Book said:
Two particles P and Q, of mass 10kg and 15kg respectively, are connected by a light, inextensible string which passes over a light smooth pulley. Particle P rests on a smooth plane inclined at θ° to the horizontal, where sin θ° = 3/5. Particle Q hangs vertically on the edge of the plane, 2 m above a horizontal plane. Find:

a) The acceleration of the system
b) The tension in the string
c) The total distance that P travels up the plae, given that the string breaks after Q has travelled up 1 m.

That question may sound like quite a lot to take it but it is quite easy. All I need to do is resolve forces.
Now, the thing is, in question a) i'm always going wrong in a step and I don't really know why. I've compared my work to the answer in the book and i've found out where the error in my working occurs. Here is what the book gives (i'll highlight where I go wrong)

Mechanics 1 for Edexcel Book said:
Particle P:
Parallel to plane:
F = ma
T - 10g sin θ = 10a
T - 6g = 10a - (1)

Particle Q:
Vertical motion:
F = ma
15g - T = 15a - (2)

9g = 25a
a = (9*9.8)/25 = 3.528 ms^-2

Now I understand everything else fine. But one question, how the hell did they get from T - 10g sin θ = 10a to T - 6g = 10a

Thanks

Visage · 5 Jun 2006 at 12:11

Because sin theta = 3/5?

Flanders · 5 Jun 2006 at 12:12

EDIT:

Didnt read the question, you were given sin(theta)

KaHn · 5 Jun 2006 at 12:12

Visage said:
Because sin theta = 3/5?

What I was thinking

10g * 3/5 = 6g

KaHn

KaHn · 5 Jun 2006 at 12:13

Flanders said:
They didnt, its a seperate equation of motion. You have to form 2 equations as you have 2 "unknowns". Forming 2 equations envolving both (ie. T and a) enables you to solve simaltaneously therefore getting answers for both your "unkowns".

rofl?

KaHn

/also quoted so you cant get rid of it.

Flanders · 5 Jun 2006 at 12:14

KaHn said:
rofl?

KaHn

/also quoted so you cant get rid of it.

See edit

Ricochet J · 5 Jun 2006 at 12:15

OMG! Thank you guys!
Off course Sin Theta does indeed equal 3/5

Thank you guys so so much! If I could give you guys a kiss I wouldn't!
But thank you!

Unconditional · 5 Jun 2006 at 12:20

Do you need my paypal address?

Ricochet J · 5 Jun 2006 at 12:22

Unconditional said:
Do you need my paypal address?

WTF