**Problem 1:**A rope with a constant and known tension \( T \) is pulling a block by way of a massless pulley a height \( h \) above the block. The block has a mass \( M \) and is moving over a floor with a known coefficient of friction \( \mu \) but with a nonzero acceleration.**a)** Draw a Free Body Diagram for the block, along with your choice of coordinate system.**b)** Write Newton’s 2nd Law for the box as a vector and decomposed in both of your directions.**c)** List any constraints on the motion on the block to continue sliding on the floor.**d)** Write \(\cos(\theta)\) and \(\sin(\theta)\) as functions of \( x \) and \( h \).**e)** Find the acceleration as a function of the distance \( x \). Your answer will look like \(\vec{a}(x) = \) Take \( T, m, h, \) and \(\mu \) to be known. \(\theta \) should be replaced by what you found in (d).---**Diagram Explanation:**The diagram shows:- A block of mass \( M \) on a horizontal surface with a coefficient of friction \( \mu \).- A pulley system where the rope applies tension \( T \).- The height of the pulley above the block is \( h \).- The block is moving along the horizontal \( x \)-axis.- The gravitational force \( g \) acts downward on the system.- The angle \(\theta\) formed by the tension and the horizontal is implied for calculation purposes.

Name: **Problem 1:**A rope with a constant and known tension \( T \) is pul
Uploaded: 2024-03-20T06:57:57.000Z
Channel: Bartleby
Description: **Problem 1:**A rope with a constant and known tension \( T \) is pulling a block by way of a massless pulley a height \( h \) above the block. The block has a mass \( M \) and is moving over a floor with a known coefficient of friction \( \mu \) bu