Horizontal spring problem with friction?

In summary, the problem involves a 4-kg object sliding at a speed of 5 m/s on a smooth surface before encountering a rough surface with a coefficient of kinetic friction of 0.20. After leaving the rough surface, the object continues on a smooth surface until it hits a horizontally-aligned spring with a spring constant of 200 N/m attached to a wall. Using the law of mechanical energy with non-conservative forces, the maximum compression of the spring can be calculated by setting the total energy before equal to the total energy after plus the work done by friction. The formula for work done by non-conservative forces is W_{NC} = F_fdcos\theta.
  • #1
peachy112girl
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Homework Statement


A 4-kg object sliding at speed 5 m/s along a smooth horizontal surface encounters a rough surface, 1.5 meters wide. The coefficient of kinetic friction over the rough surface is 0.20. After leaving the rough surface, the object continues over smooth surface until it strikes the ends of a horizontally-aligned spring, whose spring constant is 200 N/m, and whose opposite end is attached to a wall. What will be the maximum compression of the spring, in meters?

Homework Equations


The Attempt at a Solution


I know this must be a conservation of energy problem.

0.5 mv2 + 0.5 kx2 = 0.5 mv02 + 0.5 kx02

But since friction is involved, I'm not sure how to incorporate it.
 
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  • #2
*edit* Welcome TO PF! remember to post any additional questions, we help with homework not do it, that way it helps you get a grasp on things :)

Almost, this isn't a conservation of energy problem. This is the law of mechanical energy with Non-Conservative Forces.

Your formula should be something like:

[tex]\sum{E_{before}} = \sum{E_{after}} + W_{NC}[/tex]

so the total energy before is equal to the total energy after plus the work done by non conservative forces, in this case. Friction. remember its work not force. [tex]W_{NC} = F_fdcos\theta [/tex]
 
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  • #3
Senjai said:
*edit* Welcome TO PF! remember to post any additional questions, we help with homework not do it, that way it helps you get a grasp on things :)

Almost, this isn't a conservation of energy problem. This is the law of mechanical energy with Non-Conservative Forces.

Your formula should be something like:

[tex]\sum{E_{before}} = \sum{E_{after}} + W_{NC}[/tex]

so the total energy before is equal to the total energy after plus the work done by non conservative forces, in this case. Friction. remember its work not force. [tex]W_{NC} = F_fdcos\theta [/tex]

Thank you for the help! I was able to work it out!
 

FAQ: Horizontal spring problem with friction?

What is a horizontal spring problem with friction?

A horizontal spring problem with friction is a physics problem that involves a horizontal spring attached to a mass on a horizontal surface. The friction between the mass and the surface affects the motion of the mass, making it more complex than a simple spring problem.

What is the formula for calculating the force of friction in a horizontal spring problem?

The formula for calculating the force of friction in a horizontal spring problem is μN, where μ is the coefficient of friction and N is the normal force between the mass and the surface. It is important to note that the coefficient of friction can vary depending on the surface and materials involved.

How does friction affect the motion of the mass in a horizontal spring problem?

Friction acts in the opposite direction of motion, slowing down the mass and reducing its amplitude in a horizontal spring problem. It also causes the mass to experience a net force in the opposite direction of its motion, making the oscillations of the mass gradually decrease over time.

How can friction be reduced in a horizontal spring problem?

Friction can be reduced in a horizontal spring problem by using a surface with a lower coefficient of friction, or by using lubricants to decrease the friction between the mass and the surface. Additionally, increasing the mass of the object can also reduce the effects of friction.

What are some real-life applications of horizontal spring problems with friction?

Horizontal spring problems with friction can be seen in various real-life scenarios, such as in car suspensions, door hinges, and shock absorbers. Understanding the effects of friction in these systems is crucial in designing and optimizing their performance.

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