Spring constant with given mass, find Work

B) (1/2)*(2000)*(0.1m)^2In summary, the problem involves a block attached to a spring on a horizontal table, with the spring having a stiffness constant of 2000 N/m. The block moves from its equilibrium position to being stretched by 10.0 cm, and then from that position to being compressed by 3.00 cm. The work done by the spring force can be calculated using the equation Work = Integral from initial position to final position of the Force of the spring. The solutions for (a) and (b) are (1/2)*(2000)*(-.1m)^2 and (1/2)*(2000)*(0.1m)^2
  • #1
BC2210
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Homework Statement



A block of mass 1.50 kg is attached to one end of a horizontal spring, the other end of which is fixed to a vertical wall. The spring has a stifffness constant of 2000 N/m. The block slides without friction on a horizontal table, set close to the wall. Find the work done by the spring force if the block moves (a) from the equilibrium position till the spring is stretched by 10.0 cm, (b) from this last position till the sring is compressed by 3.00 cm.

Homework Equations



Work = Integral from initial position to final position of the Force of the spring?

The Attempt at a Solution



Im not really sure where to begin with this one, we just started the chapter on Work!
 
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  • #2
F of spring = -k[tex]\Delta[/tex]x?

So -2000 * 10cm?

And then integrate from 0 to 10cm of the product?
 
  • #3
A) (1/2)*(2000)*(-.1m)^2 ?
 

1. What is the formula for calculating work with a given spring constant and mass?

The formula for calculating work with a given spring constant (k) and mass (m) is: W = 0.5 * k * (x^2), where x is the displacement of the spring from its equilibrium position.

2. How do you determine the spring constant for a given mass and work?

To determine the spring constant (k) for a given mass (m) and work (W), you can rearrange the work formula to solve for k: k = 2W / m * (x^2).

3. Can the spring constant change with a given mass and work?

Yes, the spring constant can change with a given mass and work. It is dependent on the material and structure of the spring, and can be affected by factors such as temperature and wear and tear.

4. How does the work done by a spring change with an increase in mass?

As the mass increases, the work done by a spring also increases. This is because the force required to stretch or compress the spring also increases with a heavier mass, leading to a greater amount of work being done.

5. What are the units for spring constant, mass, and work in this equation?

The units for the spring constant are N/m (newtons per meter). The units for mass are kg (kilograms). The units for work are J (joules).

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