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danyork
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1. First let me start by saying that there are similar posts about this, but I wasn't able to figure out what I need through those.
A 3.45 kg mass vertically compresses a spring 67.0 cm before it starts to rebound. How high will the Mass move above the uncompressed if the mass is left to “bounce” back up?
2. Homework Equations
mg=-kx
k=-mg/x
U=1/2kx^2
E(top) = E(bottom)
3. The Attempt at a Solution :
To figure this out (or at least try to) I set the spring's neutral position as 0m and the distance from the spring's neutral up to the top of the rebound as 'd'. I also set 0.670m as 'a' to help work my way through the problem.
Here's how I tried to work my way through:
Energy at the bottom:
K=0
U(spring)=1/2k(a^2)
U(g)=mg(-a)
Energy at the top:
K=0
U(spring)=1/2k(d^2)
U(g)=mgd
Then I set the energy at the bottom equal to the energy at the top:
1/2k(d^2)+mgd=1/2k(a^2)-mg(-a)
Here is how I broke that equation down:
Get rid of the 1/2:
k(d^2)+2mgd=k(a^2)-2mg(-a)
Get rid of the k by using k=-mg/a:
d^2-2ad=a^2-2a^2
Get everything on one side:
d^2-2ad+a^2=0
(d-a)(d-a)=0
d=0.67
The spring has to work against gravity on the way up, does it make sense that it goes the same distance up as it was compressed?
A 3.45 kg mass vertically compresses a spring 67.0 cm before it starts to rebound. How high will the Mass move above the uncompressed if the mass is left to “bounce” back up?
2. Homework Equations
mg=-kx
k=-mg/x
U=1/2kx^2
E(top) = E(bottom)
3. The Attempt at a Solution :
To figure this out (or at least try to) I set the spring's neutral position as 0m and the distance from the spring's neutral up to the top of the rebound as 'd'. I also set 0.670m as 'a' to help work my way through the problem.
Here's how I tried to work my way through:
Energy at the bottom:
K=0
U(spring)=1/2k(a^2)
U(g)=mg(-a)
Energy at the top:
K=0
U(spring)=1/2k(d^2)
U(g)=mgd
Then I set the energy at the bottom equal to the energy at the top:
1/2k(d^2)+mgd=1/2k(a^2)-mg(-a)
Here is how I broke that equation down:
Get rid of the 1/2:
k(d^2)+2mgd=k(a^2)-2mg(-a)
Get rid of the k by using k=-mg/a:
d^2-2ad=a^2-2a^2
Get everything on one side:
d^2-2ad+a^2=0
(d-a)(d-a)=0
d=0.67
The spring has to work against gravity on the way up, does it make sense that it goes the same distance up as it was compressed?
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