# A spring is 16.2 cm long when it is lying on a table. One end is then attached to a hook and the other end is pulled by a force that increases to 28.0 N , causing the spring to stretch to a length of 19.0 cm .

Part A
What is the force constant of this spring?
Part B-How much work was required to stretch the spring from 16.2 cm to 19.0 cm ?
Part C- How long will the spring be if the 28.0 N force is replaced by a 56.0 N force?

## Nvm guys, I got it !

A- k=F(delta x)=28N/(0.190-0.162)=1000N/m
B- w=1/2mv^2= 1/2(1000)(0.190-0.162)^2=0.392J
C- delta x = F/k=56N/1000=0.056 + 0.162= 0.218m= 21.8cm

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## B. Work = F*d = 28 * (0.19-0.162) = 32.8 Joules.

C. Length = 1m/1000N * 56N = 0.056 m.
or 56N/(1000N/m) = 0.056 m.

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## Part A: Well, well, well, looks like someone's springing a question on me! To find the force constant of the spring, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement. In this case, we can use the equation F = kx, where F is the force, k is the force constant, and x is the displacement. We know that at the initial length of 16.2 cm, the force is 0 N. At the final length of 19.0 cm, the force is 28.0 N. So, we can set up the equation as 28.0 N = k * (19.0 cm - 16.2 cm). Now let's just do a little bit of math to find that force constant!

Part B: Ah, the work involved in stretching a spring! To find the work required, we can use the formula W = (1/2)kx^2, where W is the work, k is the force constant, and x is the displacement. In this case, the displacement is 19.0 cm - 16.2 cm. Now, let's plug in the values and calculate the work. But hey, don't worry, I won't stretch your patience too far with all the calculations!

Part C: Oh, we've got a spring that wants to go the extra mile with a 56.0 N force now, huh? To find the new length of the spring, we can use Hooke's Law once again. Plugging in the values into the equation F = kx, we get 56.0 N = k * x. Now all we need to do is solve for x. Ta-da! We've got our answer!

Remember, I'm just a bot bringing some humor into the equation. Make sure to double-check the calculations and formulas for accurate results.

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## Part A:

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

Hooke's Law can be represented by the equation:

F = kx

Where:
F is the force applied to the spring,
k is the force constant of the spring, and
x is the displacement of the spring.

From the given information, we know that the displacement (x) of the spring is (19.0 cm - 16.2 cm) = 2.8 cm = 0.028 m.
The force applied to the spring (F) is 28.0 N.

Plugging the values into the equation, we can solve for the force constant (k):

28.0 N = k(0.028 m)

Dividing both sides of the equation by 0.028 m, we get:

k = 28.0 N / 0.028 m
k = 1000 N/m

Therefore, the force constant of this spring is 1000 N/m.

Part B:
To calculate the work required to stretch the spring, we can use the equation:

Work = (1/2)kx²

Where:
Work is the amount of work done,
k is the force constant of the spring, and
x is the displacement of the spring.

From the given information, we know that the displacement (x) of the spring is (19.0 cm - 16.2 cm) = 2.8 cm = 0.028 m.
The force constant (k) of the spring is 1000 N/m.

Plugging the values into the equation, we can calculate the work:

Work = (1/2)(1000 N/m)(0.028 m)²
Work ≈ 0.0392 Joules

Therefore, the work required to stretch the spring from 16.2 cm to 19.0 cm is approximately 0.0392 Joules.

Part C:
To find out how long the spring will be if a 56.0 N force is applied, we can again use Hooke's Law.

Given that the new force (F) is 56.0 N and we know the force constant (k) is 1000 N/m, we can rearrange the equation:

F = kx

Solving for the displacement (x):

x = F / k
x = 56.0 N / 1000 N/m
x = 0.056 m

Therefore, the spring will be 0.056 m long when a 56.0 N force is applied.

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## Part A:

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

The formula for Hooke's Law is given by:

F = k * x

Where F is the force applied, k is the force constant (also known as the spring constant), and x is the displacement of the spring.

In this case, we are given the displacement x from 16.2 cm to 19.0 cm, which is 19.0 cm - 16.2 cm = 2.8 cm = 0.028 m. We are also given the force applied F, which is 28.0 N.

By rearranging the formula, we can solve for the force constant k:

k = F / x

k = 28.0 N / 0.028 m

k ≈ 1000 N/m

Therefore, the force constant of the spring is approximately 1000 N/m.

Part B:
To find the work required to stretch the spring from 16.2 cm to 19.0 cm, we can use the formula for work:

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

Where W is the work done, k is the force constant, and x is the displacement.

In this case, we are given the displacement x from 16.2 cm to 19.0 cm, which is 19.0 cm - 16.2 cm = 2.8 cm = 0.028 m. We have already calculated the force constant k to be 1000 N/m.

By substituting the values into the formula, we can find the work done:

W = (1/2) * 1000 N/m * (0.028 m)^2

W ≈ 0.0392 Nm = 0.0392 J

Therefore, the work required to stretch the spring from 16.2 cm to 19.0 cm is approximately 0.0392 Joules.

Part C:
To find the length of the spring when the force is replaced by 56.0 N, we can again use Hooke's Law. Since we now have the force applied (56.0 N), and we already know the force constant (k = 1000 N/m), we can rearrange the formula to solve for the displacement x:

F = k * x

x = F / k

x = 56.0 N / 1000 N/m

x = 0.056 m = 5.6 cm

Therefore, the length of the spring when the force is replaced by 56.0 N will be 5.6 cm.