(Solved): 1. A box of mass \( m \) is releaved from rea at Point \( A \), the top of a long. frictionless sli ...

1. A box of mass \( m \) is releaved from rea at Point \( A \), the top of a long. frictionless slide. Point \( A \) is at height \( H \) above the level of Points \( B \) and \( C \). Although the slide is frictionless, the horizontal surface from Point \( B \) to \( C \) is not. The coefficient of kinetic frietion between the box and this surface is \( \mu_{c} \) and the horizontal distance between Point \( \mathrm{B} \) and \( \mathrm{C} \) is \( x \). (a) Find the speed of the box when its height above Point \( B \) is \( \frac{1}{2} H \). (b) Find the speed of the box when it reaches Point B; (c) Determine the value of \( \mu_{1} \) so that the box comes to res at Point \( \mathrm{C} \). (d) Now assume that Points B and \( \mathrm{C} \) were not on the same horizontal level, In particular, assume that the surface from B to \( \mathrm{C} \) had a uniform upward slope so that Point C were still at a horizontal distance of \( x \) from B but now at a vertical height of \( y \) above B. Answer the quevtion posed in part (c). (c) If the slide were not frictionless, determine the work done by friction as the box moved from Point A to Point B if the spoed of the box as it reached Point B were half the speed calculated in part (b).