Shown at right are two boxes (mass m and 2m) attached to identical springs, and attached to each other by a string running over a pulley. The springs are initially neither stretched nor compressed and the masses are initially at rest. The blocks then speed up and eventually slow down again until each block has moved a distance s, at which point both blocks are momentarily at rest. Determine a symbolic expression in terms of given variables for the spring constant of each identical spring. No explanation necessary. We'll use the work-energy theorem with a system consisting of both blocks, the string, both springs, and the Earth. The net external work on this system is zero (the various normal forces all act on points of contact that are not moving). The initial and final kinetic energy for both blocks is zero because they are not moving 2m m ΔΕ = 0 ks² · − 0 + ¼½ks² − 0 + mgs − 0 + (−2mgs) − 0 = 0 k = mg S
Shown at right are two boxes (mass m and 2m) attached to identical springs, and attached to each other by a string running over a pulley. The springs are initially neither stretched nor compressed and the masses are initially at rest. The blocks then speed up and eventually slow down again until each block has moved a distance s, at which point both blocks are momentarily at rest. Determine a symbolic expression in terms of given variables for the spring constant of each identical spring. No explanation necessary. We'll use the work-energy theorem with a system consisting of both blocks, the string, both springs, and the Earth. The net external work on this system is zero (the various normal forces all act on points of contact that are not moving). The initial and final kinetic energy for both blocks is zero because they are not moving 2m m ΔΕ = 0 ks² · − 0 + ¼½ks² − 0 + mgs − 0 + (−2mgs) − 0 = 0 k = mg S
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Transcribed Image Text:Shown at right are two boxes (mass m and 2m) attached to identical springs, and
attached to each other by a string running over a pulley. The springs are initially
neither stretched nor compressed and the masses are initially at rest. The blocks then
speed up and eventually slow down again until each block has moved a distance s, at
which point both blocks are momentarily at rest.
Determine a symbolic expression in terms of given variables for the spring constant of
each identical spring. No explanation necessary.
We'll use the work-energy theorem with a system consisting of both blocks, the string, both
springs, and the Earth. The net external work on this system is zero (the various normal forces
all act on points of contact that are not moving). The initial and final kinetic energy for both
blocks is zero because they are not moving
2m m
ΔΕ = 0
ks² · − 0 + ¼½ks² − 0 + mgs − 0 + (−2mgs) − 0 = 0
k =
mg
S
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