To stretch a certain spring by 2.00 cm from its equilibrium position requires 9.50 J of work.

a. What is the force constant of this spring?

b. What was the maximum force required to stretch it by that distance?

a. Solve the equation

E = 9.50 J
= (1/2) k X^2
for k, using X = 0.020 m
The answer will be in N/m/

b. Force = k X
I don't know why they call that the "maximum" force. You can't stretch it that far with less force.

a. Force constant, also known as spring constant, is a measure of how stiff a spring is. To find the force constant, you can use the formula:

Force constant (k) = (Work done) / (Distance stretched)

Plugging in the values, we have:

k = 9.50 J / 0.020 m

Now, let's do some math!

k = 475 N/m

So, the force constant of this spring is 475 N/m.

b. To find the maximum force required to stretch the spring, you can use Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the distance it is stretched (x), multiplied by the force constant (k):

F = k * x

Plugging in the values, we have:

F = 475 N/m * 0.020 m

Time to calculate the maximum force!

F = 9.5 N

Therefore, the maximum force required to stretch the spring by 2.00 cm is 9.5 N. Remember, don't stretch yourself too thin!

To find the force constant of the spring and the maximum force required, we 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 can be expressed as:

F = k * x

where F is the force applied to the spring, k is the force constant, and x is the displacement from equilibrium.

Given that the spring is stretched by 2.00 cm (which is 0.02 m) from its equilibrium position and requires 9.50 J of work, we can solve for the force constant.

a. To find the force constant (k):

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

Since only work is given, we can rearrange the equation and solve for k:

k = (2 * W) / x^2

k = (2 * 9.50 J) / (0.02 m)^2

k = 950 N/m

Therefore, the force constant of this spring is 950 N/m.

b. To find the maximum force required:

F = k * x

F = 950 N/m * 0.02 m

F = 19 N

Therefore, the maximum force required to stretch the spring by 2.00 cm is 19 N.

To find the force constant of a spring and the maximum force required to stretch it by a certain distance, 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.

a. To find the force constant, we can use the equation:

W = (1/2)kx^2

Where:
W = work done on the spring (in joules)
k = force constant of the spring (in N/m)
x = displacement of the spring (in meters)

Given:
W = 9.50 J
x = 2.00 cm = 0.02 m

Substituting the given values into the equation, we have:

9.50 = (1/2)k(0.02)^2

Simplifying the equation:

9.50 = (1/2)k(0.0004)

Divide both sides of the equation by 0.0004:

k = 9.50 / (0.0004 * (1/2))

k = 9.50 / 0.0002

k = 47500 N/m

Therefore, the force constant of this spring is 47500 N/m.

b. The maximum force required to stretch the spring can be found using Hooke's Law:

F = kx

Where:
F = force (in newtons)
k = force constant of the spring (in N/m)
x = displacement of the spring (in meters)

Substituting the given values into the equation, we have:

F = 47500 N/m * 0.02 m

F = 950 N

Therefore, the maximum force required to stretch the spring by 2.00 cm is 950 N.