Mathematics: Post your doubts here!

[Pixie Twinkles]

A book of mass 0.8 kg is placed on a rough plane inclined at an angle of 60 degrees to the horizontal. The book is just prevented from sliding down the plane by a force of magnitude 5N acting parallel to the line of greatest slope to the plane. Find the coefficient of friction between the book and the plane.

 

[Anum96]

A book of mass 0.8 kg is placed on a rough plane inclined at an angle of 60 degrees to the horizontal. The book is just prevented from sliding down the plane by a force of magnitude 5N acting parallel to the line of greatest slope to the plane. Find the coefficient of friction between the book and the plane.

Component of weight of book is F=mgsin60
normal to plane; R=mgcos60
Use abolute values;
F =0.8*9.8*sqrt(3)/2 = 6.79 N
R = 0.8*9.8*1/2 = 3.92 N.

Ff(Force of friction) = uR = 3.92u, where u is the coefficient of friction, and the applied force of 5N. ie
F = R + 5
6.79 = 3.92u + 5
1.79 = 3.92u
u = 0.456

 

[i_try9621]

the common difference, r = 2cosθ / √3

-1 < 2cosθ / √3 < 1
multiply with √3, you'll get:

-√3 < 2 cosθ < √3

divide by 2, you 'll get:

-√3/2 < cosθ < √3/2

now taking cosine inverse,

π/6 < θ < 5π/6 (Ans.)

Shouldn't it be only π/6, because of the range given in the question ( 0 < θ < π) ?
Or am I missing something ?

 

[i_try9621]

Component of weight of book is F=mgsin60
normal to plane; R=mgcos60
Use abolute values;
F =0.8*9.8*sqrt(3)/2 = 6.79 N
R = 0.8*9.8*1/2 = 3.92 N.

Ff(Force of friction) = uR = 3.92u, where u is the coefficient of friction, and the applied force of 5N. ie
F = R + 5
6.79 = 3.92u + 5
1.79 = 3.92u
u = 2.19.

Ans. is 0.457 or 0.46 ( 2.d.p)
there is a mistake while dividing.

 

[Anum96]

Ans. is 0.457 or 0.46 ( 2.d.p)
there is a mistake while dividing.

Corrected. Thanks

 

[Rizwan Javed]

Shouldn't it be only π/6, because of the range given in the question ( 0 < θ < π) ?
Or am I missing something ?

The values of theta calculated are already in that range. 5π/6 is smaller than π.

 

[Pixie Twinkles]

Component of weight of book is F=mgsin60
normal to plane; R=mgcos60
Use abolute values;
F =0.8*9.8*sqrt(3)/2 = 6.79 N
R = 0.8*9.8*1/2 = 3.92 N.

Ff(Force of friction) = uR = 3.92u, where u is the coefficient of friction, and the applied force of 5N. ie
F = R + 5
6.79 = 3.92u + 5
1.79 = 3.92u
u = 0.456

Thank you so much!!

 

[Anum96]

Thank you so much!!

You're welcome!!

 

[i_try9621]

Corrected. Thanks

Anytime

 

[i_try9621]

The values of theta calculated are already in that range. 5π/6 is smaller than π.

yeah right, my bad.

 

[The Sarcastic Retard]

6(ii)

 

[The Sarcastic Retard]

Any idea where can I get S2 topical past papers?

 

[The Sarcastic Retard]

9(ii)

 

[i_try9621]

Ques. 7 and Ques. 14 please?

 

[farhan141]

9(ii)

Please tag me when someone solves it. I want to know abt this too.

 

[Anum96]

9(ii)

Please tag me when someone solves it. I want to know abt this too.

 

[Maayee]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_32.pdf
can someone help me with q7b
and
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s14_qp_33.pdf ....Q7bi

 

[Eugene99]

the last part (v), how do I solve this?

 

[The Sarcastic Retard]

Thanks.

 

[Mr.Physics]

The weight, X grams, of soup put in a tin by machine A is normally distributed with a mean of 160 g and a standard deviation of 5 g. A tin is selected at random.
(a) Find the probability that this tin contains more than 168 g

Help plz