SOS: Solving the Spring Constant of an Elastic Cord

[Sean1082]

Homework Statement

An elastic cord is 56 cm long when a weight of 73 N hangs from it but is 81cm long when a weight of 160 N hangs from it.

What is the spring constant "k" of this elastic cord?

Homework Equations

mg=kx

The Attempt at a Solution

No idea... my teacher doesn't know how to teach physics and the whole class is completely lost.

 

[Doc Al]

Express what Hooke's law says for each situation:
F₁ = kx₁
F₂ = kx₂

Combine those equations and see what you can deduce.

 

[Sean1082]

I have no idea what you mean by combine...

 

[Doc Al]

Another way to solve this is to call the unknown unstretched length of the spring L. Now write Hooke's law for each of the given conditions. You'll have two equations which you can solve simultaneously.

 

[rwisz]

As a scientist, it is important to approach problems like this with a systematic and analytical mindset. The first step would be to gather all the relevant information and data provided in the homework statement. In this case, we have the length of the cord (56 cm and 81 cm) and the weight hanging from it (73 N and 160 N).

Next, we can use the given equation, mg=kx, to solve for the spring constant. This equation relates the weight (m) hanging from the cord to the spring constant (k) and the change in length (x) of the cord. In this case, we have two sets of values for m and x, so we can set up two equations and solve for k.

Using the first set of data (73 N and 56 cm), we have:
73 N = k(56 cm)
Solving for k, we get k = 1.30 N/cm

Using the second set of data (160 N and 81 cm), we have:
160 N = k(81 cm)
Solving for k, we get k = 1.98 N/cm

Since we have two different values for k, we can take the average of the two to get a more accurate estimate.
(k1 + k2)/2 = (1.30 N/cm + 1.98 N/cm)/2 = 1.64 N/cm

Therefore, the spring constant (k) of this elastic cord is approximately 1.64 N/cm.

In conclusion, it is important to approach physics problems with a logical and analytical mindset, using the given equations and data to solve for the unknown variable. If you are still feeling lost or confused, it may be helpful to seek additional resources such as textbooks, online tutorials, or asking for help from a teacher or tutor.