2. A spring of spring constant 220 N/m is sitting on a table. You pick it up and stretch it so that it is 8.0 cm longer than it was on the table top. How much work did it take you to stretch the spring? (Hint: This work is just negative the work done by the spring on you!)

what is 1/2k x^2

To determine the amount of work required to stretch the spring, we need to calculate the work done by the person (you) against the force of the spring.

The work done by a force can be calculated using the formula:

Work = Force × Distance × cos(theta)

In this case, the force is the force exerted by the spring when it is stretched and the distance is the change in length of the spring. Since the force exerted by a spring is proportional to its displacement, we can use Hooke's Law to find the force.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, this relationship can be expressed as:

F = k × x

Where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement from the equilibrium position.

In this problem, the spring constant (k) is given as 220 N/m, and the displacement (x) is 8.0 cm (which we need to convert to meters by dividing by 100).

Let's calculate the force exerted by the spring first:

F = k × x
= 220 N/m × (8.0 cm / 100)
= 17.6 N

Now, we can calculate the work done by you against the spring:

Work = Force × Distance × cos(theta)

Since the force and displacement are in the same direction, the angle between them is 0 degrees, and cos(0) = 1.

Work = 17.6 N × 8.0 cm × cos(0)
= 17.6 N × 0.08 m × 1
= 1.408 J

Therefore, it took 1.408 Joules of work to stretch the spring.