A 3.08 m long rope hangs from the ceiling subject only to its own weight. The ma
ID: 1543351 • Letter: A
Question
A 3.08 m long rope hangs from the ceiling subject only to its own weight. The mass per unit length is not constant and is given by =6.38(kg/m)(m)-4y4, where y is the distance from the bottom of the rope. A pulse is sent up the rope from the bottom. How fast (in m/s) is the pulse going when it is halfway up the rope? (If necessary, use g=9.88m/s2.)
Hint: Using calculus or a spreadsheet, break the rope up into infinitesimal or small elements and find the tension at each point on way up the rope.
The equation given for is unclear to me, does anyone have any idea what it could mean? Is the (m)-4 possibly mass? The units kind of make sense but seem to be inverted? Not sure.
EDIT: I have attached my work so far, does this look right?
(4): G+38 6.38 6383 Ele .38 m TUy)- 6-383(+54 5) 5m" my ! 117H31139- -in-15 GCIT T-T -y -Explanation / Answer
units of are [MASS]/[METER]
= 6.38(kg/m)(m)-4y4 implies-> = (6.38)x(y4)
where unit of first term is kg/m and unit of second term is m4/m4 Since the units of "y" are any way in metres
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