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PirateFan308
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Homework Statement
A 0.150 kg frame, when suspended from a coil spring, stretches the spring 0.070m. A 0.200kg lump of putty is dropped from rest onto the frame from a height of 30.0cm
Find the maximum distance the frame moves downward from its initial position
Homework Equations
SEp+GEp+Ek = SEp+GEp+Ek
mgh+(0.5)(m)(v)2 + (1.5)(k)(x)2 = mgh+(0.5)(m)(v)2 + (1.5)(k)(x)2
initial momentum = final momentum
The Attempt at a Solution
To find velocity of the putty just before it hits the frame:
Ep = Ek
mgh = (0.5)mv2
(0.150)(9.81)(0.30) = (0.5)(0.150)(v)(v)
(v)(v) = 5.886
v = 2.426 m/s
To find the velocity of the putty and the frame after the putty hits:
initial momentum = final momentum
mv + mv = mv + mv
(0.200)(2.426) + 0 = (0.200+0.150)v
v = 1.386 m/s
To find k of the spring:
GEp = SEp
mgh = (0.5)kx2
(0.15)(9.81)(0.07) = (0.5)(k)(0.07)2
k = 42 N/m
To find the distance the frame moves downward:
mgh+(0.5)(m)(v)2 + (1.5)(k)(x)2 = mgh+(0.5)(m)(v)2 + (1.5)(k)(x)2
(0.35)(9.81)(h-0.07) + (0.5)(0.35)(1.386)2 + (0.5)(42)(0.070)2 = (0) + (0) + (1.5)(42)(h)2
(3.4335h - 0.240345) + (0.439) = 21h2
0 = 21h2 - 3.4335h - 0.199
h = 0.20887 or -0.04537
h - 0.07 = 0.1389 or -0.1153
I figure the height (because of my reference) must be negative, so it must be -0.1153m
Is this correct? I got a bit confused about h on the last equation ...