- #1
brotherbobby
- 579
- 147
- Homework Statement
- A block of mass 25 kg is held in place on an inclined plane of angle ##30^{\circ}## as shown in the diagram below. The coefficient of static friction is 0.6. (a) What is the tension in the string? (b) If the string is cut, what is the acceleration of the block? ##\mathbf{Textbook\;\;answers : (a) T = 122.5\; \text{N}\; (b) Zero.}##
- Relevant Equations
- Newton's law : ##\Sigma F_x = ma_x## and maximum static frictional force ##f_S^{max} = \mu R##, where ##R## is the reaction normal to the surface.
(a) Ridiculously simple though it looks, I can't see how the string will be tight. One of the two has to be true.
(1) The static friction ##f_S = mg \sin\theta = 25\times 10\times \sin 30^{\circ} = 122.5\; \text{N} ##. The maximum static friction ##f_S = \mu mg \cos \theta = 0.6\times 25\times 10\times \cos 30^{\circ} \approx 130\;\text{N}##. Hence if friction is holding the block in place, the rope is slack and the tension in the rope ##\boxed{T=0}##. (This is what I believe will happen).
(2) The string was tied to the block (somehow) and the string-block system placed on the incline. In that case there is no tendency of relative motion between the block and the incline so static friction is zero. The rope is tight and it balances the component of gravity along the incline : ##\boxed{T = 122.5\;\text{N}}##. (This is the answer in the book as I mentioned earlier).(b) If the string is cut, friction will keep the block in place and therefore its acceleration ##\boxed{a=0}##. (Agrees with the book).
Any help?