A spiral spring of nature 20cm,has a scale pan hanging freely in its lower end. When an object of mass 40g is placed in the pan,its length becomes 21.8cm.when another object of mass 60g is placed in the pan,the length becomes 22.05cm. Calculate the mass of the scale pan

50kg

Solve please

To solve this problem, we will use Hooke's Law, which states that the extension of a spring is directly proportional to the force applied to it.

First, let's calculate the extension of the spring when the 40g object is added:

Initial length of the spring (L0) = 20cm
Extension of the spring (ΔL) = Final length (L) - Initial length (L0) = 21.8cm - 20cm = 1.8cm

Next, let's calculate the force exerted by the 40g object:

Force (F) = mass (m) × acceleration due to gravity (g)
F = 40g × 9.8 m/s² = 392 N (newtons)

Now, we can calculate the spring constant (k) using Hooke's Law:

F = k × ΔL
392N = k × 1.8cm

To make calculations easier, let's convert centimeters to meters:

1.8cm = 0.018m

Now, we can solve for the spring constant (k):

k = 392N / 0.018m ≈ 21,777.78 N/m

With the spring constant (k) calculated, we can determine the mass of the scale pan when the 60g object is added.

Extension of the spring (ΔL) = Final length (L) - Initial length (L0) = 22.05cm - 20cm = 2.05cm

Force (F) = mass (m) × acceleration due to gravity (g)
F = 60g × 9.8 m/s² = 588 N

Now, we can use Hooke's Law to find the displacement of the spring:

F = k × ΔL
588N = 21,777.78 N/m × ΔL

Again, let's convert centimeters to meters:

2.05cm = 0.0205m

Now, we solve for the displacement (ΔL):

ΔL = 588N / 21, 777.78 N/m ≈ 0.027m

Finally, we can determine the mass of the scale pan:

Force (F) = mass (m) × acceleration due to gravity (g)
588N = m × 9.8 m/s²

Solving for the mass (m):

m = 588N / 9.8 m/s² ≈ 60g

Therefore, the mass of the scale pan is approximately 60g.