A spring has a length of 0.2 m (its unloaded length plus the extension X0+x1) when a 0.3 kg mass hangs from it, and a length of 0.75 m (X0+x2) when a 1.95 kg mass hangs from it. Χο x=0 X₁ X2 W₁ W₂ Think & Prepare 1. Draw free body diagrams of the two masses. At equilibrium, what the relationship between the spring force and the the weight in the two cases? 2. Set up two equations, one for each mass, based on the relationship in 1. 3. How many unknowns are there? How many equations? How do you solve for the unknowns? (a) What is the force constant of the spring? k= N m (b) What is the unloaded length of the spring? x= = m

University Physics Volume 1
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Author:William Moebs, Samuel J. Ling, Jeff Sanny
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Chapter15: Oscillations
Section: Chapter Questions
Problem 32P: Fish are hung on a spring scale to determine their mass. (a) What is the force constant of the...
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A spring has a length of 0.2 m (its unloaded length plus the extension X0+x1) when a 0.3 kg mass
hangs from it, and a length of 0.75 m (X0+x2) when a 1.95 kg mass hangs from it.
Χο
x=0
X₁
X2
W₁
W₂
Think & Prepare
1. Draw free body diagrams of the two masses. At equilibrium, what the relationship between the
spring force and the the weight in the two cases?
2. Set up two equations, one for each mass, based on the relationship in 1.
3. How many unknowns are there? How many equations? How do you solve for the unknowns?
(a) What is the force constant of the spring?
k=
N
m
(b) What is the unloaded length of the spring?
x=
=
m
Transcribed Image Text:A spring has a length of 0.2 m (its unloaded length plus the extension X0+x1) when a 0.3 kg mass hangs from it, and a length of 0.75 m (X0+x2) when a 1.95 kg mass hangs from it. Χο x=0 X₁ X2 W₁ W₂ Think & Prepare 1. Draw free body diagrams of the two masses. At equilibrium, what the relationship between the spring force and the the weight in the two cases? 2. Set up two equations, one for each mass, based on the relationship in 1. 3. How many unknowns are there? How many equations? How do you solve for the unknowns? (a) What is the force constant of the spring? k= N m (b) What is the unloaded length of the spring? x= = m
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