Mass attached to spring on frictionless table

In summary, the problem involves an ideal spring with un-stretched length of 0.10 m, a block of mass 10 kg attached to one end of the spring, a string passing over a frictionless pulley and a block of mass 2 kg hanging from the other end of the string. The system is in equilibrium when the length of the spring is 0.20 m. The task is to calculate the tension in the string and the force constant of the spring.
  • #1
cflemer
2
0

Homework Statement


An ideal spring of an un-stretched length 0.10 m is placed horizontally on a frictionless table. One end of the spring is fixed and the other end is attached to block of mass M = 10 kg. The 10 kg block is also attached to a massless string that passes over a small frictionless pulley. A block of mass m = 2 kg hangs from the other end of the string. When this spring-and-blocks system is in equilibrium, the length of the spring is .20 m.

Calculate tension in the string.

Calculate the force constant of the spring.

(there is a diagram, but it is complicated and I don't know how i would get it on here)


Homework Equations


F=ma


The Attempt at a Solution

 
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  • #2
Welcome to PF!

cflemer said:
An ideal spring of an un-stretched length 0.10 m is placed horizontally on a frictionless table. One end of the spring is fixed and the other end is attached to block of mass M = 10 kg. The 10 kg block is also attached to a massless string that passes over a small frictionless pulley. A block of mass m = 2 kg hangs from the other end of the string. When this spring-and-blocks system is in equilibrium, the length of the spring is .20 m.

Calculate tension in the string.

Calculate the force constant of the spring.

Hi cflemer !Welcome to PF! :smile:

(there's no need for a diagram … your description is fine :smile:)

Show us what you've tried, and where you're stuck, and then we'll know how to help. :wink:
 

FAQ: Mass attached to spring on frictionless table

1. What is the purpose of studying a mass attached to a spring on a frictionless table?

The purpose of studying a mass attached to a spring on a frictionless table is to understand the principles of simple harmonic motion, which is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. This concept has many practical applications, such as in the design of oscillating systems like pendulums and springs.

2. How does the mass affect the motion of the spring on a frictionless table?

The mass attached to the spring affects the motion by determining the amplitude (maximum displacement) and period (time for one complete cycle) of the oscillation. Heavier masses will have larger amplitudes and longer periods, while lighter masses will have smaller amplitudes and shorter periods.

3. What happens to the motion of the spring if there is friction present on the table?

If there is friction present on the table, the motion of the spring will eventually dampen and come to a stop. This is because friction acts as a dissipative force, converting the kinetic energy of the system into heat energy, causing the oscillations to gradually decrease in amplitude until they stop completely.

4. How does the spring constant affect the motion of the mass on the frictionless table?

The spring constant, also known as the stiffness constant, determines the strength of the restoring force of the spring. A higher spring constant will result in a stronger restoring force and therefore a shorter period of oscillation. Conversely, a lower spring constant will result in a weaker restoring force and a longer period of oscillation.

5. Can the mass attached to the spring on a frictionless table ever reach equilibrium?

No, the mass attached to the spring will never reach equilibrium on a frictionless table. This is because the motion of the mass and spring is perpetuated by the constant exchange of potential and kinetic energy, causing the mass to continuously oscillate between two points without ever coming to rest at equilibrium.

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