Question 8) A block of mass 25 kg rests on a frictionless...

Question 8) A block of mass 25 kg rests on a frictionless incline plane that makes an angle of 40 degrees with the horizontal. If the block is being held at rest by a rope on the incline, what is the tension in the rope? Assume that the acceleration due to gravity is $g = 9.8 \text{ m/s}^2$. A) 157.48 Newtons B) 187.68 Newtons C) 245.00 Newtons D) 195.94 Newtons $F_{net} =$ $9.8 \frac{m}{s^2} = \frac{F \cos \theta - mg \sin \theta}{m}$

Transcript

00:01 Hello everyone we are going to understand this question here given in the question given mass of box mass of box that is represented by m which is 50 kilogram angle of inclination of inclined plane angle of inclination of inclined plane that is represented by theta which is 45 degree and coefficient of static friction coefficient of static friction that is represented by mu which is 0 .2 let the minimum requirement let the minimum required tension be t let the minimum required tension minimum required tension be t now using free body diagram so first of all let's represent let's the let's draw the free body body diagram.

01:40 So weight of the block is working vertically downward that is m into g now taking the component of weight along to the plane and perpendicular to the plane so if this angle is theta which is given 45 then perpendicular component of weight perpendicular to the plane that is m g cost theta and component of weight that is along to the inclined plane that is m g plus theta and component of weight that is mg, sine theta and normal reaction is n.

02:20 As here it is given that block is moving with constant speed, so tension in the string be t.

02:32 So here we can write t is equal to mg sine theta and here block is moving moving in upward direction.

02:47 So the block is means we have to find the minimum tension in the string.

02:50 It means friction force is in upward direction then only tension will be minimum so here we can write t is equal to m g sine theta minus f s or again we can write t is equal to m g sine theta minus mu mg cof theta now substituting the value in this here minimum tension in the string here here tension in the string is minimum tension in the string is minimum it means block is tending to slide toward the downward it means block tends to slide in downward direction tends to slide in downward direction.

04:32 Downward direction.

04:37 So we can write t is equal to m g sine theta t is equal to mg sin theta minus mu m g into 4theta...

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