A bin is given a push across a horizontal surface. The bin has a mass m, the push gives it an initial speed of v., and the coefficient of kinetic friction between the bin and the surface is ". (a) Use energy considerations to find an expression for the distance the bin moves before it stops. (Use any variable or symbol stated above along with the following as necessary: g.) d = X From conservation of energy we have Asystem = ) T. The change in energy of the system is the change in kinetic energy of the bin, and the only energy transfer is the work done by friction. Remember to express the work done by friction as a scalar product. (b) What If? If the initial speed of the bin is increased by a factor of 2, determine an expression for the new distance d , the box slides in terms of the old distance d. 4 d