(Solved): 1) Please draw the free-body diagram of mass \( M \) in Figure \( 1(a) \). The diagram should incl ...

1) Please draw the free-body diagram of mass \( M \) in Figure \( 1(a) \). The diagram should include the pulling force \( F \), gravitational force \( M g \), normal force \( N \), and friction force \( f_{k} \). 2) Consider the graph in Figure 1(b). Please explain why the average of pulling force \( F \) in Region (ii) can be regarded as the kinetic friction force \( f_{k} \). (You may refer to the free body diagram in Question 1.) 3) Consider an object on an inclined plane with angle \( \phi \), as in the right figure. If it is driven by gravity and is sliding down at a constant speed, please show that the coefficient of kinetic friction \( \mu_{k}=\tan \phi \). (Hint: use the relation in Eq. (1).) \( f_{k}=\mu_{k} N \)