Your firm needs to haul granite blocks up a 15° slope out of a quarry and to lower dirt into the quarry to fill the holes. You design a system in which a granite block on a cart with steel wheels (weight w1, including both block and cart) is pulled uphill on steel rails by a dirt-filled bucket (weight w2, including both dirt and bucket) that descends vertically into the quarry. How must the weights w1 and w2 be related in order for the system to move with constant speed? Ignore friction in the pulley and wheels, and ignore the weight of the cable.

Your firm needs to haul granite blocks up a 15° slope out of a quarry and to lower dirt into the quarry to fill the holes. You design a system in which a granite block on a cart with steel wheels (weight w1, including both block and cart) is pulled uphill on steel rails by a dirt-filled bucket (weight w2, including both dirt and bucket) that descends vertically into the quarry. How must the weights w1 and w2 be related in order for the system to move with constant speed? Ignore friction in the pulley and wheels, and ignore the weight of the cable.