Hooke's Law - A spring between 2 masses accelerating to the right.

In summary: So what does this net force do? Does the 15N applied force and the tension from the spring only push the large mass? Does it contribute nothing to the stretch in length?The net force does push the large mass, but it also applies a force that is equal and opposite to the applied force. This causes the mass to stay stationary (unless the tension from the spring is too much).
  • #1
CaptainSFS
58
0

Homework Statement



http://pyrofool.googlepages.com/lab25.gif

A 2 kg mass and a 3 kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k = 140 N/m. A 15 N force is applied to the larger mass. How much does the spring stretch from its equilibrium length? The masses uniformly accelerate with no oscillations.

Homework Equations



Fspring = -kx (Hooke's law)

The Attempt at a Solution



I haven't the slightest clue how to figure the 2 kg mass in. I know I'm solving for x, but like I mentioned, I don't know what to do with the 2 kg mass. Thanks for any help.
 
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  • #2
Hint: What's the acceleration of the system?
 
  • #3
so i think the acceleration is 3m/s2. so the first mass has a force of 9N and the smaller mass has a force of 6N.

Would I find x for each mass then using Hooke's law and then find the difference between the two? If that's the case would the answer then be 2.14cm?
 
  • #4
CaptainSFS said:
so i think the acceleration is 3m/s2. so the first mass has a force of 9N and the smaller mass has a force of 6N.
Good. (Note that those are the net forces on each mass.)
Would I find x for each mass then using Hooke's law and then find the difference between the two? If that's the case would the answer then be 2.14cm?
No, it's easier than that. Consider the smaller mass. You know the force that must be exerted on it. So what must be the stretch in the spring to exert such a force?
 
  • #5
oh alright. That makes sense. So it's just 6 N / 140 N/m. = 4.29cm. Cool. thanks for your help. :)
 
  • #6
What happens to the 9N force exerted on the larger mass? How come that doesn't contribute to any extension in the spring?
 
  • #7
compwiz3000 said:
What happens to the 9N force exerted on the larger mass? How come that doesn't contribute to any extension in the spring?
The 9N is the net force on the larger mass, not an individual force. The individual forces acting on that mass are the 15N applied force and the tension from the spring.
 
  • #8
Doc Al said:
The 9N is the net force on the larger mass, not an individual force. The individual forces acting on that mass are the 15N applied force and the tension from the spring.

So what does this net force do? Does the 15N applied force and the tension from the spring only push the large mass? Does it contribute nothing to the stretch in length?
 

FAQ: Hooke's Law - A spring between 2 masses accelerating to the right.

What is Hooke's Law?

Hooke's Law is a principle in physics that describes the relationship between the force applied to a spring and the resulting displacement of the spring. It states that the force applied is directly proportional to the displacement, and the constant of proportionality is known as the spring constant.

How does Hooke's Law apply to a spring between two masses accelerating to the right?

In this scenario, Hooke's Law can be used to calculate the force exerted on the spring by the two masses, as well as the displacement of the spring. The force applied by the masses causes the spring to stretch or compress, and according to Hooke's Law, the displacement of the spring is directly proportional to the force applied.

What are the units of measurement for the spring constant in Hooke's Law?

The units of measurement for the spring constant in Hooke's Law are typically newtons per meter (N/m) in the SI system, or pounds per inch (lb/in) in the imperial system. However, the exact units may vary depending on the specific application.

Can Hooke's Law be applied to all types of springs?

Yes, Hooke's Law can be applied to all types of springs, as long as the material of the spring follows the linear elastic behavior. This means that the spring should return to its original shape and size when the force is removed. Non-linear materials, such as rubber, may not follow Hooke's Law.

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

Hooke's Law is used in many real-world applications, such as in building structures, measuring weight using a spring scale, and designing suspension systems in vehicles. It is also used in experiments to determine the properties of materials, such as the elasticity of a material.

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