How much work is required to compress a spring, k = 33.3 N/m, from its equilibrium point at x = 0.0 m to x = 5.0 m?
I am not sure how to approach a problem like this - what equation do I use? I know work = Force * Distance, but these aren't exactly terms I would use to describe a spring...
the equation for work (energy) compressing a spring is similar to the kinetic energy equation
work = 1/2 k x^2
Ah, springs can be a bit bouncy when it comes to work, but fear not! I'll help you unravel this coil conundrum.
To calculate the work required to compress a spring, we'll use the equation:
Work = (1/2) * k * x^2
Where k is the spring constant (given as 33.3 N/m) and x is the distance the spring is compressed (given as 5.0 m).
Plugging in the values:
Work = (1/2) * 33.3 N/m * (5.0 m)^2
Work = (1/2) * 33.3 N/m * 25 m^2
Work = 416.25 N⋅m
Voila! The work required to compress the spring from x = 0.0 m to x = 5.0 m is 416.25 N⋅m, or as I like to call it, the spring's personal "workout" session.
To determine the work required to compress a spring, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium. Hooke's Law equation is given by F = -kx, where F is the force, k is the spring constant, and x is the displacement from equilibrium.
To find the work done, you can integrate the force over the distance. In this case, the distance over which the work is done is from x = 0.0 m to x = 5.0 m.
The work, W, can be calculated using the equation:
W = ∫(F dx)
Using Hooke's Law, the force can be expressed as F = -kx. Substituting this expression in the above equation, we get:
W = ∫(-kx dx)
Integrating this equation over the limits from x = 0.0 m to x = 5.0 m, we can find the work required.
W = -k ∫(x dx)
To evaluate the integral, we can use the power rule of integration: ∫(x dx) = (1/2)x^2.
W = -k * [(1/2)x^2]
Now, substitute the values: k = 33.3 N/m and distance, x = 5.0 m, into the equation to find the work.
W = -33.3 N/m * [(1/2)(5.0 m)^2]
Calculating this will give you the value of work in joules (J).
To determine the work required to compress a spring, you can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position.
The equation representing Hooke's Law is F = -kx, where F is the force exerted by the spring, k is the spring constant (in this case, 33.3 N/m), and x is the displacement from the equilibrium point.
In this case, the spring is compressed from x = 0.0 m to x = 5.0 m. The displacement, x, is equal to 5.0 m - 0.0 m = 5.0 m.
So, to calculate the work, you first need to calculate the force exerted by the spring at x = 5.0 m. Using Hooke's Law, you can substitute the values into the equation F = -kx:
F = -kx
F = -(33.3 N/m)(5.0 m)
F = -166.5 N
Now that you have the force, you can use the equation for work:
Work = Force * Distance
In this case, the distance is the displacement, x = 5.0 m. So, substituting the values:
Work = (-166.5 N) * (5.0 m)
Work = -832.5 N⋅m
The work required to compress the spring from x = 0.0 m to x = 5.0 m is -832.5 N⋅m.