Inclined string on an incline plane

In the figure above, a 10 kg sphere is supported on a frictionless plane inclined at angle θ \theta = 45° from the horizontal. The angle ϕ \phi is 25°. Calculate the tension in the cable (in N).


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The answer is 76.4602.

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3 solutions

Satvik Pandey
Oct 7, 2014

Abhishek, is this a problem of book Resnic Halliday (Principles of Physics).?

If we resolve mg parallel to the plane.It will come out to be

m g s i n θ mgsin\theta (in downward direction)

and if we resolve Tension in the string(T) parallel to the plane. It will come out to be

T c o s ϕ Tcos\phi (in upward direction)

As sphere is at rest so

m g s i n θ = T c o s ϕ mgsin\theta =Tcos\phi

So

T = 98 c o s ( 25 ) 2 T=\frac { 98 }{ cos(25)\sqrt { 2 } }

On putting value of cos(25) we will get T=76.46N

It will be nice to explain with diagram.Could anyone tell me how to add diagrams in solutions?

I was trying with g=10 SI units. You must mention g properly.

Pranjal Jain - 6 years, 7 months ago

Yes indeed it is !

Abhishek Singh - 6 years, 8 months ago

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Could you please tell me how to add diagrams in solutions? :D

satvik pandey - 6 years, 8 months ago

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Yes, you can use markdown links. Go to an image sharing site (say imgur.com), and upload your image there; then type ![Image](link) \text{![Image](link)} , and you're done!

Satvik Golechha - 6 years, 6 months ago

Hey but what if we resolve the forces perpendicular to the plane ???? Then we don't get the same result??

Kislay Raj - 6 years, 3 months ago

i took g=10.you had to mentioned that😞

safa m - 6 years, 2 months ago

Good solution. Up voted.

Niranjan Khanderia - 6 years, 1 month ago

Wtf you didnt say g = 9.8

Benyamin Krisna - 5 years, 3 months ago
Paola Ramírez
Feb 21, 2015

By a free boddy diagram

x = m g sin 45 ° T c o s 25 ° = 0 \sum_x=mg\sin45°-Tcos25°=0

m g sin 45 ° = T cos 25 ° mg \sin45°=T \cos25°

T = m g sin 45 ° cos 25 T=\frac{mg \sin45°}{\cos25}

T = 98 × sin 45 ° cos 25 ° 76.46 T=\frac{98\times \sin 45°}{\cos25°} \approx \boxed{76.46}

I did by resolving forces along vertical and horizontal. But resolving along the inclined is definitely the best solution.

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