AP Physics 1 : Spring Force
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Example Questions
Example Question #21 : Spring Force
A narrow spring is placed inside a wider spring of the same length. The spring constant of the wider spring is twice that of the narrow spring. The two-spring-system is used to hold up a box of mass 
Determine the spring constant of the wider spring.
Use Hooke's law:
and
Wide spring:
Narrow spring:
From given information:
Substitute:
Summation of forces:
Where 
Solve for 
Plug back into the following formula and solve for the spring constant of the wider spring.
Example Question #22 : Spring Force
A narrow spring is placed inside a wider spring of the same length. The spring constant of the wider spring is twice that of the narrow spring. The two-spring-system is used to hold up a box of mass 
Determine the spring constant of the narrower spring.
Use Hooke's law:
and
Wide spring:
Narrow spring:
From given information:
Substitute:
Summation of forces:
Where
Solve for
Example Question #23 : Spring Force
A certain spring is held stretched 
How much work was done in stretching the spring from 
The spring is held outside of equilibrium at rest by a certain force. That means that this force is equal in magnitude to the restoring force of the spring. By Hooke's law, the magnitude of the restoring force is given by
Where 
Now we need to find the work required to stretch the spring further from 
Therefore the work done is just the negative of the above, or
Example Question #21 : Spring Force
One spring is placed inside of another. They both have the same spring constant. Together, they are used to suspend a mass of 
Example Question #21 : Spring Force
One spring is placed inside of another. They both have the same spring constant. Together, they are used to suspend a mass of 
Use Hooke's law and plug in known values:
Each spring will stretch the same amount,
Example Question #26 : Spring Force
Two springs are attached end to end. They have the same spring constant. They stretch a total of 
Use Hooke's law:
Each spring stretched the same amount, 
Plug in values:
Solve for 
Example Question #21 : Spring Force
Two springs are attached end to end. They have the same spring constant. They stretch a total of 
Use Hooke's law:
Each spring stretched the same amount,
Plug in values:
Solve for
Now find the stretch distance if the springs were used in parallel.
Plug in values:
Solve for 
Example Question #28 : Spring Force
A 
Since the mass in in equilibrium, this tells us the net force 
Example Question #29 : Spring Force
If a spring of constant 
From the definition of the spring potential,
Plugging in the given values lets us arrive at a calculated compression,
Example Question #30 : Spring Force
A vertical spring has a constant 
We can calculate the energy needed to be stored in the spring from the change in potential energy that the object experiences:
Where our change in height is going to be the distance between its high point and the point when the spring is compressed. Furthermore, this change in potential energy will be equal to the energy stored in the spring:
We can also develop an expression for the change in height:
Substituting this back into our expression:
Distributing and rearranging:
Plugging in our values, we get:
Using the quadratic formula, we get:
Where a positive distance represents compression of the spring, and a negative distance represents extension of the spring. Therefore, the positive distance is our answer.
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