Finding Force Constant of a Spring

In summary, a 1.80 kg block with a speed of 1.95 m/s hits a spring and compresses it 14.0 cm before coming to rest. Given a coefficient of kinetic friction of 0.560, the problem asks to find the force constant of the spring. To solve this, we first find the frictional force, which is equal to μk*mg. Then, using the equation 1/2*m*v^2 = Fr*x + 1/2*k*x^2, we can solve for the force constant of the spring.
  • #1
court2011
14
0

Homework Statement


A 1.80 kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 1.95 m/s and compresses it a distance of 14.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is µk = 0.560, what is the force constant of the spring?


Homework Equations



k=2U/x^2

The Attempt at a Solution


k=2(0.560)/0.14^2
 
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  • #2
Hi court2011, welcome to PF.
The kinetic energy of the block is utilized to do the work to overcome the friction and compress the spring.
What is the frictional force?
 
  • #3
hi! the problem doesn't say so I am assuming i have to find it given the coefficient of kinetic friction?
 
  • #4
Kinetic energy of the block = Potential energy of the spring + work done against the frictional force.
 
  • #5
ok so potential energy is = mgy but if its going horizontal isn't y=0 so the potential energy is 0?
 
  • #6
Potential energy stored in the spring is 1/2*k*x^2.
 
  • #7
ok i need to find k so how do i get the potential energy without having k in the equation?
 
  • #8
First of all find the frictional force.
Then using 1/2*m*v^2 = Fr*x + 1/2*k*x^2 find k.
 
  • #9
is Fr where i am supposed to insert the frictional force? because i did and I still got the problem wrong but equation seems right how do i find the frictional force isn't it fk=ukN?
 
  • #10
I am refereeing Fr as fk which is equal to μk*N. Now what is the normal force?
 
  • #11
ma which is 1.8*1.95=3.51
 
  • #12
The normal force is mg.
Frictional force is μk*mg.
 

1. What is a force constant?

A force constant is a measure of the stiffness of a spring or any other elastic object. It is represented by the symbol k and is typically measured in units of newtons per meter (N/m).

2. Why is it important to determine the force constant of a spring?

Knowing the force constant of a spring allows us to understand its behavior and how much force is required to stretch or compress it. This information is essential for designing and engineering various mechanical systems that use springs.

3. What is the formula for calculating force constant?

The formula for calculating force constant is k = F/x, where k is the force constant, F is the applied force, and x is the displacement of the spring from its equilibrium position.

4. How do you experimentally determine the force constant of a spring?

To determine the force constant of a spring experimentally, you will need to measure the displacement of the spring for different applied forces. Then, you can plot a graph of force vs. displacement and calculate the slope of the line, which is equal to the force constant.

5. Can the force constant of a spring change?

Yes, the force constant of a spring can change depending on various factors such as the material of the spring, its dimensions, and temperature. It can also change if the spring is stretched or compressed beyond its elastic limit.

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