A spring with a spring constant of 22N/m is initally compressed by 2.3cm. How much work is required to compress the spring an additional 1.7 cm?
I can't find information in my book about compression; only work and exertion. Please help and provide all steps for work. Thank you! Jackie
To find the work required to compress a spring, you need to use Hooke's Law, which relates the force exerted by a spring to its displacement.
1. Start by finding the force exerted by the spring when it is compressed by 2.3cm:
According to Hooke's Law, the force exerted by a spring can be calculated using the formula F = kx, where F is the force, k is the spring constant, and x is the displacement.
In this case, k = 22N/m (given), and x = 2.3cm = 0.023m (converted from centimeters to meters).
So, F = (22N/m) * (0.023m) = 0.506N.
2. Next, find the additional force required to compress the spring by an additional 1.7cm:
You can calculate this force using the same Hooke's Law formula, but now with the new displacement.
x = 1.7cm = 0.017m (converted from centimeters to meters).
So, F' = (22N/m) * (0.017m) = 0.374N.
3. Now, calculate the work required to compress the spring for the additional 1.7cm:
The work done on an object is given by the formula W = F * d, where W is the work, F is the force, and d is the distance moved in the direction of the force.
Here, the force F' (0.374N) was exerted over a distance d = 1.7cm = 0.017m.
So, W = (0.374N) * (0.017m) = 0.006358N∙m (or Joules).
Therefore, the work required to compress the spring an additional 1.7cm is approximately 0.0064 Joules.
x/0.017 = 22/1
X = 0.374 N.
Work=F*d = 0.374 * 0.017=0.0064 Joules.