A uniform chain of length 8 feet is held vertically so that the lower end just touches the floor. The chain weighs 2 Ib/ft. The upper end that is held is released from rest at t= 0 and the chain falls straight down. If x(t) denotes the length of the chain on the floor at time t (in seconds), air resistance is ignored, and the positive direction is taken to be downward, then we have the following. (Take the acceleration of gravity to be 32 ft/s?.) (8 - x)dx - (dx = 256 (a) Let v be the chain's velocity in ft/s. Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t. V(x) = ft/s x(t) = ft v(t) = ft/s (b) Determine how long it takes for the chain to fall completely to the ground. (c) What velocity (in ft/s) does the model in part (a) predict for the upper end of the chain as it hits the ground? O o O v9 O Lg
A uniform chain of length 8 feet is held vertically so that the lower end just touches the floor. The chain weighs 2 Ib/ft. The upper end that is held is released from rest at t= 0 and the chain falls straight down. If x(t) denotes the length of the chain on the floor at time t (in seconds), air resistance is ignored, and the positive direction is taken to be downward, then we have the following. (Take the acceleration of gravity to be 32 ft/s?.) (8 - x)dx - (dx = 256 (a) Let v be the chain's velocity in ft/s. Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t. V(x) = ft/s x(t) = ft v(t) = ft/s (b) Determine how long it takes for the chain to fall completely to the ground. (c) What velocity (in ft/s) does the model in part (a) predict for the upper end of the chain as it hits the ground? O o O v9 O Lg
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:A uniform chain of length 8 feet is held vertically so that the lower end just touches the floor. The chain weighs 2 lb/ft. The upper end that is held is released from rest at t= 0 and the chain falls
straight down. If x(t) denotes the length of the chain on the floor at time t (in seconds), air resistance is ignored, and the positive direction is taken to be downward, then we have the following.
(Take the acceleration of gravity to be 32 ft/s.)
(8 - x) dex
dr2
= 256
- -
(a) Let v be the chain's velocity
ft/s. Solve for v in terms of x. Solve for x in terms of t. Express v in terms of t.
v(x) =
ft/s
x(t) =
ft
v(t) =
ft/s
(b) Determine how long it takes for the chain to fall completely to the ground.
(c) What velocity (in ft/s) does the model in part (a) predict for the upper end of the chain as it hits the ground?
O o
O va
O Lg
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