A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 100 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.

a) How much work W is done in pulling the rope to the top of the building?

Since the rope weighs 0.4 lb/ft, the portion of the rope below the top of the building from x ft to (x + ?x) ft weighs ........... ?x lb.

b)

Step 1

We will think of the work in two pieces: the work needed to lift the top half of the rope and the work needed to lift the bottom half of the rope.

Step 2. The bottom half of the rope is lifted15ft, and this requires a constant force of ........... lb.

Since the rope weighs 0.4 lb/ft, the portion of the rope below the top of the building from X ft to (x + Ax) ft weighs 0437,- Ax lb. Submit ]; (you cannot come back) Step 2 The bottom half of the rope is lifted 15 ft, and this requires a constant force of 90 X lb. Submit Skip (you cannot come back)7. [2\" Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentiallyt If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A heavy rope, 30 ft long, weighs 0.4 lb/: and hangs over the edge of a building 100 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it. How much work W is done in pulling the rope to the top of the building? Ax lb. cnlw >4 Since the rope weighs 0.4 lb/ft, the portion of the rope below the top of the building from x ft to (x + AX) ft weighs Submit xmyou cannot come back) How much work W is done in pulling half the rope to the top of the building? Step 1 We will think of the work in two pieces: the work needed to lift the top half of the rope and the work needed to lift the bottom half of the rope. The work done to lift the top half of the rope follows the same thinking as in part (a). Since the top half is only 15 ft long, this portion of the work equals the following. 15 /15 2 / ?x dx 0 i 5 W1 15 _/15 all a\" = 45 .y /45 ft-lb The bottom half of the rope is lifted 15 , and this requires a constant force of x lb