You find that if you hang a 1.85 weight from a vertical spring, it stretches 5.50 .

What is the force constant of this spring in N/m?

How much mass should you hang from the spring so it will stretch by 8.45 from its original, unstretched length?

Indicate your subject in the "School Subject" box, so those with expertise in the area will respond to the question.

Use fsp=kx to find k; where fsp=w=mg(w=1.25)(9.81). B) Use that same formula to find the fsp, and then use fsp where w=mg to find m.

To find the force constant of the spring in N/m, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

The formula for Hooke's Law is: F = k * x

Where:
F is the force applied to the spring (in Newtons)
k is the force constant or spring constant (in N/m)
x is the displacement from the equilibrium position (in meters)

Given that the weight of 1.85 kg stretches the spring by 5.50 m, we can use this information to find the force constant.

Step 1: Convert the weight from kilograms to Newtons.
The weight of an object can be found by multiplying its mass (in kg) by the acceleration due to gravity (9.8 m/s^2). So, the weight is given by: Weight = mass * gravity.
In this case, the weight = 1.85 kg * 9.8 m/s^2 = 18.13 N (approximately).

Step 2: Use Hooke's Law to find the force constant.
We have the force (F) as 18.13 N and the displacement (x) as 5.50 m. Rearrange the formula to solve for the force constant:
k = F / x = 18.13 N / 5.50 m ≈ 3.30 N/m

Therefore, the force constant of this spring is approximately 3.30 N/m.

Moving on to the second question, we need to determine how much mass should be hung from the spring to stretch it by 8.45 m.

Step 1: Use Hooke's Law to find the force required.
Using the same formula, F = k * x, we have the force constant (k) as 3.30 N/m and the displacement (x) as 8.45 m. Substitute these values to find the force required:
F = 3.30 N/m * 8.45 m ≈ 27.8 N

Step 2: Convert the force into mass.
To convert the force into mass, we divide the force by the acceleration due to gravity:
Mass = Force / gravity = 27.8 N / 9.8 m/s^2 ≈ 2.83 kg

Therefore, you should hang approximately 2.83 kg of mass from the spring to stretch it by 8.45 m.