AP Physics 1 : Spring Force
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Example Questions
Example Question #51 : Spring Force
Two springs with unknown constants are hung in parallel from a ceiling. However, we do know that one spring has a constant 
Since the springs are held in constant, we can determine a total equivalent constant by simply adding the two individual constants together:
From the problem statement, we know:
Substituting this in, we get:
The problem statement tells us that a mass is attached and the springs stretch an unknown distance. At this point, the system has reached a new equilibrium. The problem statement tells us that another mass is attached and the springs stretch more. Since spring forces are linear, the new mass and distance stretched is the only information we need to solve the problem. Using Hooke's Law:
Rearranging for the spring constant:
Plugging in our values:
Example Question #52 : Spring Force
Two springs with unknown constants are hung from a ceiling. However, we do know that the constant of one is four times that of the other. A block of mass 
Since the springs are added in parallel, we can simply add their constants together to get an equivalent constant.
From the statement, we know:
Substituting this in, we get:
Now we can use Hooke's Law along with the information of how far the block causes the springs to stretch:
Rearranging for the equivalent constant:
Plugging in our values:
Now we can use the expression for the potential energy stored in a spring:
The problem statement is asking for the total potential energy stored, so we need to use the total distance stretched (which includes both from the mass and manually). Plugging in our values, we get:
Example Question #53 : Spring Force
A force of 
The force applied to a spring can be represented by
where F is force, k is spring constant, and x is the distance compressed.
Solving this equation for k
and plugging in our values
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