How Does Mass Affect Spring Stretch in Hooke's Law?

In summary, on a horizontal frictionless surface, a 2.0 kg mass and a 3.0 kg mass are connected by a massless spring with a spring constant of 140N/m. A 15 N force is applied to the larger mass, causing the spring to stretch. The answer for the amount of stretch is 4.28 cm, but it can only be found using the force on the smaller mass (2 kg). The direction of force is the key factor in determining the correct answer.
  • #1
mateomy
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A 2.0 kg mass and a 3.0 kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k=140N/m. A 15 N force is applied to the larger mass, as a shown (see picture). How much does the spring stretch from its equilibrium length?


hookesExample.jpg




I've solved this problem -the answer is 4.28cm- but I had to do it using the force on the smaller of the masses (2 kg). My question is why I have to take it from that mass? Why couldn't you just find it from the 3 kg mass, by just taking the initial 15 N force as proportional to the Force of the spring? If you do this the book says that answer is wrong. The physical interpretation of WHY we have to to find it from the 2kg force is eluding me.
 
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  • #2
The direction of force makes all the difference.
 

What is Hooke's Law?

Hooke's Law is a physical law that states that the force required to extend or compress a spring is directly proportional to the distance the spring is extended or compressed.

What is a spring constant?

A spring constant, also known as a force constant or stiffness, is a measure of how stiff a spring is. It is the ratio of the force applied to the displacement of the spring.

How is Hooke's Law used in real-life applications?

Hooke's Law is used in various real-life applications such as in the design of shock absorbers, suspension systems, and weighing scales. It is also used in mechanical engineering, material testing, and in the study of elasticity.

What is the mathematical formula for Hooke's Law?

The mathematical formula for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring.

What are the limitations of Hooke's Law?

Hooke's Law is only applicable to materials that exhibit elastic behavior, meaning they return to their original shape after being stretched or compressed. It also assumes that the spring is being stretched or compressed within its elastic limit, and that the material is isotropic, meaning it has the same properties in all directions.

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