To stretch a spring 7.00 cm from its unstretched length, 16.0 J of work must be done.

What is the force constant of this spring?

What magnitude force is needed to stretch the spring 7.00 cm from its unstretched length?

How much work must be done to compress this spring 4.00 {\rm cm} from its unstretched length?

What force is needed to stretch it this distance?
F =

The force constant is part 1 is just the spring constant so you would just rearrange the potential equation of

Ep = 1/2kx^2 to Ep/0.5x^2 = k
so 16 / 0.5 x 0.007^2
and that gives you k = 6530.6 N/m

part 2
you need to use hooke's law F=kx
so 6530.6 x 0.07
which means F = 457.1 N

part 3
you just use the potential equation again Ep=1/2kx^2
so Ep = 0.5 x 6530.6 x (-0.04)^2
Ep = 5.2 J

part 4
and finally use F = -kx
F = -(-0.04) x 6530.6
so F = 261.2 N

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

F = k * x

where F is the force applied to the spring, k is the force constant, and x is the displacement of the spring from its unstretched length.

Given that 16.0 J of work is done to stretch the spring 7.00 cm, we can calculate the force constant as follows:

Work = (1/2) * k * x²

16.0 J = (1/2) * k * (0.07 m)²

Solving for k:

k = (2 * Work) / x²

k = (2 * 16.0 J) / (0.07 m)²

k ≈ 3265.31 N/m

So, the force constant of this spring is approximately 3265.31 N/m.

To calculate the magnitude of force needed to stretch the spring 7.00 cm from its unstretched length, we can use Hooke's Law again:

F = k * x

F = 3265.31 N/m * 0.07 m

F ≈ 228.57 N

So, the magnitude of force needed to stretch the spring 7.00 cm is approximately 228.57 N.

To calculate the work done to compress the spring 4.00 cm from its unstretched length, we can use the same formula for work:

Work = (1/2) * k * x²

Work = (1/2) * 3265.31 N/m * (0.04 m)²

Work ≈ 2.08 J

So, the work done to compress the spring 4.00 cm from its unstretched length is approximately 2.08 J.

Lastly, to find the force needed to stretch the spring this distance, we can once again use Hooke's Law:

F = k * x

F = 3265.31 N/m * 0.04 m

F ≈ 130.61 N

So, the force needed to stretch the spring this distance is approximately 130.61 N.

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.

The formula for the force constant (k) of a spring is given by:

k = (F/x)

where:
k is the force constant,
F is the force applied, and
x is the displacement from the equilibrium position.

Given that to stretch the spring 7.00 cm (0.07 m) from its unstretched length, 16.0 J of work is done, we can use the following steps to find the force constant:

Step 1: Convert the displacement to meters.
x = 0.07 m

Step 2: Use the work done formula to find the force applied.
W = F * x
16.0 J = F * 0.07 m

Step 3: Solve for the force.
F = (16.0 J) / (0.07 m)
F ≈ 228.57 N

Therefore, the magnitude force needed to stretch the spring 7.00 cm from its unstretched length is approximately 228.57 N.

To answer the second question, we can use the same formula and steps as above. Given that the displacement is now compressing the spring by 4.00 cm (0.04 m), we can find the force needed as follows:

Step 1: Convert the displacement to meters.
x = -0.04 m (negative sign indicates compression)

Step 2: Use the work done formula to find the force applied.
16.0 J = F * (-0.04 m)

Step 3: Solve for the force.
F = (16.0 J) / (-0.04 m)
F ≈ -400 N

Therefore, the magnitude force needed to compress the spring 4.00 cm from its unstretched length is approximately 400 N.

To find the force needed to stretch the spring a given distance, we can use the formula for the force constant (k) and rearrange it to solve for F:

F = k * x

Given that the displacement is still 7.00 cm (0.07 m), we can use the same force constant as before to find the force needed.

F = (228.57 N/m) * 0.07 m
F ≈ 16 N

Therefore, the force needed to stretch the spring a distance of 7.00 cm from its unstretched length is approximately 16 N.