Tension of String/ Mass question

[neoking77]

Homework Statement

The figure shows two masses hanging from a steel wire. The mass of the wire is 60.0 g. A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms.

What is mass m?

Homework Equations

v = sqrt(Ts/mu)

The Attempt at a Solution

T=mu*v^2

t = 0.024s
d = 4m
v = d/t = 166.666m/s

mu = m/L = 60g/8m = 7.5

T = 208331Nsin40 = mg
m = 208331Nsin40/g
m = 13.66

but the answer is 17.8kg. where did i go wrong?

 

[andrevdh]

the tension that you get from

T=mu*v^2

(I get 209 N - it is 60 grams) is the x-component of the tension in the inclined part of the wire.

 

[rl.bhat]

Convert 60 g to kg and try again.

 

[rl.bhat]

By using Lami's theorem You can find tension across point 1 and 2.
T/cos40 = mg/sin40. Hence T = mg*cot40.
m = (7.5^-3*166.67^2)/9.8*cot40
= 17.8kg.