Calculating Spring Constant and Force for a Vertical Spring

In summary, the spring constant of a vertical spring that is stretched by 2.0 cm when a mass of 100g is placed on it is found to be k = ((.100kg)(9.81m/s^2))/(.02m-yo). To determine the force required to compress the spring by 0.5 cm, the equation mg = k(y-yo) can be used, where yo represents the y-value when the spring is not stretched or compressed.
  • #1
dg_5021
80
0
A mass of 100g causes a vertical spring to stretch by 2.0 cm (a) Find the spring constant of the spring in N/M. (b) How much force will cause the spring to compress by 0.5 cm?

Can some help me? How do u do this? What formula do I have to use?
 
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  • #2
If the mass is stationary, the net force acting on it is zero.
Gravity exerts a force on the mass downwards.
The spring exerts a force on the mass upwards.
Since the net force is zero, these must be equal.
The force of the spring is given by Hooke's law.
 
  • #3
Hooke's law is : mg = k(y-yo)

so that would be: k= (mg)/(y-yo)
k= ((.100kg)(9.81m/s^2))/(.02m-yo)

What is yo?
 
  • #4
Here y0 would be the y-value when the string is not streched or compressed.
So that y-y0 measures the displacement from equilibrium of the spring.
In your problem y-y0 is 2.0 cm.
 

Related to Calculating Spring Constant and Force for a Vertical Spring

What is the spring constant of a spring?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It is represented by the variable k and is measured in units of force per unit length, such as newtons per meter (N/m).

How is the spring constant of a spring calculated?

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

What factors affect the spring constant of a spring?

The spring constant of a spring is determined by its material, dimensions, and shape. It is also affected by the temperature, as the stiffness of a spring can change with temperature.

Why is the spring constant important?

The spring constant is important because it allows us to predict the behavior of a spring when a force is applied to it. It is also used in many practical applications, such as in the design of springs for mechanical systems.

Can the spring constant of a spring change?

Yes, the spring constant of a spring can change under certain conditions. For example, if a spring is stretched beyond its elastic limit, it may become permanently deformed and its spring constant may change. Additionally, the stiffness of a spring can change with temperature or if the material or dimensions of the spring are altered.

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