AP Physics 1 : Forces
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Example Questions
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 #11 : 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:
Example Question #151 : Specific Forces
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 #152 : Specific Forces
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 #21 : 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 #154 : Specific Forces
One spring is placed inside of another. They both have the same spring constant. Together, they are used to suspend a mass of 
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