Finding the spring constant of a spring in a pulley system

In summary: In that case, the net force on the object would be zero. So if the object is at rest in the mathematical sense, then the force of the spring would be nullifiying the force of gravity.In summary, the book says the correct value is 588 Newton/meter while my attempt says 294.
  • #1
Prandals
2
0

Homework Statement


Ok so here is the prompt: a 3kg object is fastened to a light spring over a pulley. The pulley is frictionless and its inertia may be neglected. The object is released from rest when the spring is unstretched. If the object drops 0.1 meters before stopping, find the spring constant of the spring

Homework Equations


Spring force=kx
Gravity force=mg

3. The Attempt at a Solution
My attempt: Since the object is at rest i fgured that the force of the spring must be nullifiying the force of gravity. Therefore, forcespring=kx=weight=mg. plugging in the values and solving for K, i got K=294 Newton/meter. However the book says the correct value is 588 which is double mines. I have re-traced my steps and found that there is absolutely no mistake in getting the value 294. Is the book wrong or am i using the wrong method?
 
Physics news on Phys.org
  • #2
The easiest way to go about it is to use the conservation of energy. The ball falls downward, meaning its potential energy decreases. For energy to be conserved, to what form of energy was it converted to?
 
  • #3
RedDelicious said:
The easiest way to go about it is to use the conservation of energy. The ball falls downward, meaning its potential energy decreases. For energy to be conserved, to what form of energy was it converted to?
so I just use the formula for Work done by non conservative forces Wnon-conservative=0=changeinPE+changePEElastice+changeinKE right?
 
  • #4
I need one more information to make sure whether you were right. The object is fastened to only one spring over a pulley or there are something more that you didn't mention about. Because if there aren't anything more then your answer is right.
 
  • #5
And you have to use energy to solve this. Book is right. 588 is the correct answer
 
  • #6
Prandals said:
so I just use the formula for Work done by non conservative forces Wnon-conservative=0=changeinPE+changePEElastice+changeinKE right?

Looks good
 
  • Like
Likes Prandals
  • #7
Prandals said:
My attempt: Since the object is at rest i fgured that the force of the spring must be nullifiying the force of gravity.
It depends what you mean by at rest. The question says it stops, but that doesn't mean all motion has ceased. It only means that its velocity is instantaneously zero.
 
  • Like
Likes Prandals

What is a spring constant?

A spring constant, also known as a force constant, is a measure of the stiffness of a spring. It is defined as the force required to stretch or compress a spring by a certain distance.

How do you find the spring constant of a spring in a pulley system?

To find the spring constant of a spring in a pulley system, we can use the equation k = (mg - T)/x, where k is the spring constant, m is the mass attached to the spring, g is the acceleration due to gravity, T is the tension in the spring, and x is the distance the spring is stretched or compressed. This equation can be derived from Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement.

What is the difference between a spring constant and a spring rate?

A spring constant and a spring rate are two different ways of expressing the stiffness of a spring. The spring constant is measured in units of force per unit of distance, while the spring rate is measured in units of force per unit of length. Essentially, the spring rate is equal to the spring constant multiplied by the length of the spring.

Can the spring constant of a spring in a pulley system change?

The spring constant of a spring in a pulley system can change if the length or material of the spring is altered, or if the mass attached to the spring is changed. However, for a specific spring in a specific pulley system, the spring constant will remain constant as long as these variables do not change.

Why is it important to know the spring constant of a spring in a pulley system?

Knowing the spring constant of a spring in a pulley system is important for understanding the behavior of the system. It allows us to predict the amount of force required to stretch or compress the spring, and how the system will respond to external forces. This information is crucial in designing and analyzing various mechanical systems.

Similar threads

Time period of SHM & Energy conservation in pulley-spring-block system
    • Introductory Physics Homework Help
Replies
24
Views
1K
Calculating the spring force constant K
    • Introductory Physics Homework Help
Replies
14
Views
354
Spring constant formlula for Force and Work Done
    • Introductory Physics Homework Help
Replies
12
Views
746
Spring Problem Involving Variables and Constants Only
    • Introductory Physics Homework Help
Replies
3
Views
368
Finding spring constant k based on diagram -- Don't understand how to interpret force as drawn
    • Introductory Physics Homework Help
Replies
5
Views
178
What is the Relationship Between Force and Spring Constant?
    • Introductory Physics Homework Help
Replies
14
Views
2K
Find the velocity and acceleration of a pulley in a mass-spring system
    • Introductory Physics Homework Help
Replies
14
Views
1K
Find spring constant k using an electrical circuit
    • Introductory Physics Homework Help
Replies
10
Views
911
Trouble understanding the influence of a real spring in a system
    • Introductory Physics Homework Help
Replies
3
Views
863
Difficulty in deciding when to apply work energy theorem
    • Introductory Physics Homework Help
Replies
2
Views
473

Hot Threads

Recent Insights

Back
Top