Spring has a upstretched length of 20cm. When a 6N weight is hung on, it stretched to 32 cm. If the 6N weight is replaced by a 10N weight. What will be the new length?

To find the new length when a 10N weight is hung on the spring, we can use Hooke's Law which states that the force applied to a spring is directly proportional to the extension of the spring.

Let x be the new length of the spring when a 10N weight is hung on it.

Using Hooke's Law:

F = kx

Where:
F = force applied to the spring
k = spring constant
x = extension of the spring

First, let's find the spring constant k using the initial conditions:

When a 6N weight is hung on the spring, it stretches to 32 cm:
6N = k(32 cm)
k = 6N / 32 cm
k = 0.1875 N/cm

Now, we can find the new length x when a 10N weight is hung on the spring:

10N = 0.1875 N/cm * x
x = 10N / 0.1875 N/cm
x = 53.33 cm

Therefore, when a 10N weight is hung on the spring, the new length will be 53.33 cm.

Step 1: Determine the spring constant (k)

Using the formula: k = F / Δx

Where:
- k is the spring constant
- F is the force applied (6N)
- Δx is the change in length (32cm - 20cm = 12cm)

k = 6N / 12cm
k = 0.5N/cm

Step 2: Calculate the new change in length (Δx')

Using the formula: F = k - Δx'

Where:
- F is the new force applied (10N)
- k is the spring constant (0.5N/cm)
- Δx' is the new change in length

10N = 0.5N/cm - Δx'
Δx' = 20cm

Step 3: Calculate the new length (L')

Using the formula: L' = L + Δx'

Where:
- L' is the new length
- L is the original length (20cm)
- Δx' is the new change in length (20cm)

L' = 20cm + 20cm
L' = 40cm

Therefore, the new length of the spring when a 10N weight is hung on will be 40cm.