Horizontal spring with friction

In summary, the problem involves a spring with a constant of 105 N/m that has been compressed horizontally by a 2 kg mass for a distance of 0.1m. The mass then moves a distance of 0.25m after it is released. The goal is to find the coefficient of kinetic friction between the mass and the horizontal surface. This can be solved using the conservation of energy, where the initial potential energy stored in the spring is equal to the work done by the friction force on the mass. The work done by the spring is calculated using the equation Work=force*distance, and the work done by friction is equal to the kinetic friction coefficient multiplied by the mass and gravitational force exerted by the surface, multiplied
  • #1
Ali 2
22
1

Homework Statement


A spring with negligible mass has a constant of 105 N/m. It has been compressed horizantally with a 2 kg mass for a distance of 0.1m. If the mass has moved after release for a distance of 0.25m, what is the coefficient of kinetic friction between mass and horizontal surface.



Homework Equations


F=-kx (spring force)
f= C N, f is friction, C is the kinetic friction coefficient, and N is the force exerted on the mass by the horizontal surface


The Attempt at a Solution


 
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  • #2
i would recommend using work to solve this problem.
Work=force*distance
also work done by a spring is .5*k*x^2
 
  • #3
Conservation of energy would be the easiest way to solve this.
What happens to the potential energy initially stored in the spring?
 
  • #4
hello
ok the work done by the spring is 0.5*k*x02 - 0.5*k*x12
we know that x0=-0.1m
but what is x1, since the 0.25m given in the question is the distance not the displacement??!?
 
  • #5
ok i see what you mean ap123
the energy stored initially = the work done by the friction force
0.5*k*x0^2= C * mg * distance
 
  • #6
Yes, you've got it :)
 

Related to Horizontal spring with friction

1. What is a horizontal spring with friction?

A horizontal spring with friction is a physical system that consists of a spring attached to a horizontal surface and a mass attached to the spring. The spring exerts a force on the mass, causing it to oscillate back and forth. However, the presence of friction between the mass and the surface causes the amplitude of the oscillations to decrease over time.

2. How does friction affect the behavior of a horizontal spring?

Friction reduces the amplitude of the oscillations of the mass attached to the spring. This means that the mass will gradually come to rest instead of oscillating indefinitely. Friction also causes the period of the oscillations to increase over time.

3. How is the motion of a horizontal spring with friction described mathematically?

The motion of a horizontal spring with friction can be described using the equation of motion for a damped harmonic oscillator. This equation takes into account the mass of the object, the spring constant, the damping coefficient (representing the effect of friction), and the initial conditions of the system.

4. Can the amplitude of the oscillations in a horizontal spring with friction be increased?

Yes, the amplitude of the oscillations can be increased by reducing the amount of friction present in the system. This can be achieved by using a smoother surface or lubricating the contact points between the mass and the surface.

5. How does the spring constant affect the behavior of a horizontal spring with friction?

The spring constant represents the stiffness of the spring. A higher spring constant means that the spring will exert a stronger force on the mass, resulting in larger amplitude oscillations. However, the presence of friction will still cause the amplitude to decrease over time, even with a high spring constant.

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