What is the value of the spring constant k?

In summary, a 20-kg mass attached to a vertically hanging spring was given an initial downward velocity of 2 m/s and observed to reach a maximum displacement of 0.2m from its equilibrium position. The spring constant k can be calculated by using the equation for potential energy stored in a spring, which involves the mass, acceleration due to gravity, and maximum displacement. By setting the kinetic energy of the mass equal to the potential energy stored in the spring, the value of k can be determined using the principle of conservation of energy.
  • #1
mathgirl2007
11
0
A 20-kg mass was initially at rest, attached to the end of a vertically hanging spring. When given an initial downward velocity of 2 m/s from its equilibrium rest position, the mass was observed to attain a maximum displacement of 0.2m from its equilibrium position. What is the value of the spring constant k?


Please help me. I cannot figure this one out. I think the equation is just mg-kdeltay=0 but I can't figure it out. I know 20 kg is the mass. w=mg=20(9.8)=196.

Thanks in advance for all of your help!
 
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  • #2
mathgirl2007 said:
A 20-kg mass was initially at rest, attached to the end of a vertically hanging spring. When given an initial downward velocity of 2 m/s from its equilibrium rest position, the mass was observed to attain a maximum displacement of 0.2m from its equilibrium position. What is the value of the spring constant k?


Please help me. I cannot figure this one out. I think the equation is just mg-kdeltay=0 but I can't figure it out. I know 20 kg is the mass. w=mg=20(9.8)=196.

Thanks in advance for all of your help!

If it has velocity, it has kinetic energy. The kinetic energy will get absorbed by the retarding force of the spring as the velocity slows. When the velocity goes to 0, the spring should be at maximum displacement.
 
  • #3
i really don't understand this one.
can someone please just explain how to find k for me
 
  • #4
mathgirl2007 said:
i really don't understand this one.
can someone please just explain how to find k for me

What is the kinetic energy of the mass when it is moving at 2 m/s?

When that kinetic energy is reduced to 0 by the spring, how much potential energy is then stored in the spring. (Hint: Conservation of Energy)

What is the formula for potential energy stored in a spring? (Hint: It involves the spring constant k.)
 

FAQ: What is the value of the spring constant k?

What is the definition of spring constant?

The spring constant, also known as the force constant or stiffness constant, is a measure of the stiffness of a spring. It is represented by the letter k and is defined as the force required to stretch or compress a spring by a unit distance.

How do you calculate the spring constant?

The spring constant can be calculated by dividing the applied force by the displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement of the spring.

What is the unit of measurement for spring constant?

The unit of measurement for spring constant depends on the unit of measurement used for force and displacement. In SI units, the unit for spring constant is Newtons per meter (N/m).

How does the spring constant affect the behavior of a spring?

The spring constant determines the strength of the force that the spring exerts in response to a displacement. A higher spring constant means a stiffer spring and a greater force for the same amount of displacement, while a lower spring constant means a less stiff spring and a smaller force for the same amount of displacement.

What are some real-life examples of spring constant?

The spring constant can be observed in various objects and systems in our daily lives. Some examples include a car's suspension system, a pogo stick, a diving board, a door hinge, and a mattress. The spring constant also applies to more complex systems such as bridges and buildings that use springs to absorb and distribute forces.

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