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Gold3nlily
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Homework Statement
In Fig. 8-44, a spring with k = 170 N/m is at the top of a frictionless incline of angle θ = 37.0°. The lower end of the incline is distance D = 1.00 m from the end of the spring, which is at its relaxed length. A 2.00 kg canister is pushed against the spring until the spring is compressed 0.200 m and released from rest. (a) What is the speed of the canister at the instant the spring returns to its relaxed length (which is when the canister loses contact with the spring)? (b) What is the speed of the canister when it reaches the lower end of the incline?
Image:
http://edugen.wiley.com/edugen/courses/crs4957/halliday9118/halliday9118c08/image_n/nt0051-y.gif
The answer from the book is:
(a) 2.40 m/s; (b) 4.19 m/s
Homework Equations
Emec1 = Emec2
Us = 1/2 k x^2
kE =1/2 m v^2
Ug = mgh
h = sin@*D
@=37
k=170 N/m
D=1m
m=2kg
d=0.2m
The Attempt at a Solution
(a) What is the speed of the canister at the instant the spring
returns to its relaxed length ?
My answer is close to the correct answer at 2.9m/s but I
think it should be closer...
Emec1 = Emec2
Ke + U = KE + U
0 + 1/2 kd^2 = 1/2mv^2 +mgh
h = sin@*D
1/2 kd^2 = 1/2mv^2 +mg sin (40)*D
mv^2= 1/2 k(0.2)^2 - (2)(9.8)sin (40)*1
v= sq(-16.79/2)
I also think I did something wrong b/c had to eliminate negative sign...
v= 2.9m/s
What could I have done differently?
(b) What is the speed of the canister when it reaches the lower end of the incline?
u bottom = 0; b/c h = 0
Emec1 = Emec2
Ke + U = KEb + Ub
1/2mv^2 +mg sin (40)*D = 1/2mv^2 + 0
cancel "m" and multiply by 2
v^2 + 2g sin (40)*1 = v^2
2.4^2 + 12.5986 = v^2
v = sq(18.358)
v = 4.28 m/s
This is still very close to the right answer but slightly different. (I Used
the books value for velocity to calculate part B) Sigh, I wish I was good
at this...