The force required to stretch a Hooke’s-law

spring varies from 0 N to 62.4 N as we stretch
the spring by moving one end 17.2 cm from
its unstressed position.
a) Find the force constant of the spring.
Answer in units of N/m

b) Find the work done in stretching the spring.
Answer in units of J

a) 62.4 N/0.172 m = 362.8 N/m

b) (1/2)*(max stretch)(max force)
= 0.5*0.172 m*62.4 N = ___ J

thank you for the help!!!

a) Well, the force required to stretch the spring is directly proportional to the displacement. So, we can write this relationship as F = kx, where F is the force, k is the force constant, and x is the displacement.

We know that the force varies from 0 N to 62.4 N, and the displacement is 17.2 cm (or 0.172 m). Plugging in these values, we can set up the equation:

62.4 N = k * 0.172 m

Now we can solve for k:

k = 62.4 N / 0.172 m

Calculating this, we find that the force constant of the spring is approximately 362.8 N/m.

b) Alright, now let's find the work done in stretching the spring. The work done is given by the equation W = (1/2)kx^2, where W is the work done, k is the force constant, and x is the displacement.

Plugging in the values, we have:

W = (1/2) * 362.8 N/m * (0.172 m)^2

Calculating this, we find that the work done in stretching the spring is approximately 5.69 J.

a) To find the force constant of the spring, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law: F = k * x

where F is the force applied, k is the force constant (also known as spring constant), and x is the displacement from the equilibrium position.

Given:
Maximum force, F = 62.4 N
Displacement, x = 17.2 cm = 0.172 m

Using Hooke's Law, we have:
F = k * x

Rearranging the equation to solve for k:
k = F / x

Plugging in the values:
k = 62.4 N / 0.172 m

Calculating the force constant:
k = 362.79 N/m

Therefore, the force constant of the spring is 362.79 N/m.

b) To find the work done in stretching the spring, we can use the equation:

Work (W) = (1/2) * k * x^2

Given:
Force constant, k = 362.79 N/m
Displacement, x = 0.172 m

Plugging in the values, we have:
W = (1/2) * 362.79 N/m * (0.172 m)^2

Calculating the work done:
W = 5.901 J

Therefore, the work done in stretching the spring is 5.901 J.

To find the force constant of the spring, we can use Hooke's Law equation:

F = k * x

where F is the force applied, k is the force constant (also known as spring constant), and x is the displacement from the unstressed position.

a) To find the force constant (k), we can rearrange the equation:

k = F / x

Given:
F = 62.4 N (maximum force)
x = 17.2 cm = 0.172 m (displacement)

Substituting these values into the equation, we find:

k = 62.4 N / 0.172 m ≈ 362.79 N/m

Therefore, the force constant of the spring is approximately 362.79 N/m.

b) To find the work done in stretching the spring, we can use the work-energy principle:

Work = (1/2) * k * x^2

Given the force constant (k) as 362.79 N/m and the displacement (x) as 0.172 m, we can substitute these values into the equation:

Work = (1/2) * 362.79 N/m * (0.172 m)^2 ≈ 5.97 J

Therefore, the work done in stretching the spring is approximately 5.97 Joules.