AP Physics 1 : Spring Force
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Example Questions
Example Question #711 : Newtonian Mechanics
An object is attached to a spring, and is stretched 3m. If the restoring force is equal to 
Hooke's law states that the spring force is equal to the product of the spring constant and the displacement of the spring:
The force is negative because it acts in the direction opposite of the displacement from the equilibrium position (i.e. when we stretch we do so in the positive direction). We are given the force and the displacement, so we just solve for k:
Example Question #11 : Spring Force
What is the spring constant of a spring that requires an applied force of 
This question is giving us the amount of force needed to displace an object attached to a spring, and is asking us to calculate the spring constant. Thus, we will need to make use of Hooke's law.
The above equation, Hooke's law, tells us that the restoring force of the spring is related to the displacement of the attached object. It's important to note that in the question stem, we are told that an external force of 
Example Question #11 : Spring Force
An upright spring of rest length 
Where 
Solve for 
Plug in values:
Example Question #143 : Forces
Two springs are used in parallel to suspend a mass of 
None of these
Where 
Since
Substitute and plug in values:
Solving for 
Example Question #11 : Spring Force
A helicopter uses a 
Determine the net forces on the submarine:
Plug in values:
Determine what forces are acting on the submarine:
Plug in values
*Note: Acceleration due to gravity is going down so it is a negative
Solve for 
Example Question #14 : Spring Force
Two identical, massless, 
Each spring will be subject to the same force, and since they have the same spring constant, stretch the same amount. Thus:
Total stretch:
Stretch of one spring:
Use Hooke's law:
The force will be equal to the force of gravity on the mass:
Solve for 
Example Question #12 : 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 
How would much would these stretch if instead both springs were used to attach a box of mass 
The force of the spring in relationship to strain is independent of direction. Thus, the same force pulling on the spring would result in an equal amount of length change, albeit by stretching instead of compressing.
Example Question #12 : 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 
What would the compression be if the mass were instead 
In this problem the "spring within a spring" can be treated as a single spring.
Use Hooke's law:
Plug in values:
Solve for 
Again use Hooke's Law:
Plug in values:
Solve for
Example Question #14 : 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 
What is the spring constant of the combined system?
In this problem the "spring within a spring" can be treated as a single spring.
Use Hooke's law:
Plug in values and solve for the spring constant:
Example Question #16 : 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 potential energy being stored in the springs.
In this problem the "spring within a spring" can be treated as a single spring.
Use Hooke's law:
Convert to meters and plug in values:
Solve for
Use the equation for the potential energy stored in a spring:
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