A spiral spring of natural length 20.00cm has a scalepan hanging freely at a lower rate.When an object of mass 40g is placed in the ground,it lengths become 21.8cm.When another object of mass 60g is placed in the ground it lengths become 22.05cm.Calculate the mass of the scale pan g as 10m/s
To calculate the mass of the scalepan, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to its extension.
The extension of a spiral spring can be calculated using the formula:
ΔL = (k * L * m) / g
Where:
ΔL = change in length of the spring (in meters)
k = spring constant (in N/m)
L = natural length of the spring (in meters)
m = mass on the scalepan (in kilograms)
g = acceleration due to gravity (in m/s²)
In this case, the masses applied to the spring are 40g and 60g, and the change in length is 1.8cm and 2.05cm respectively.
First, let's convert the units to the SI system. 40g is equal to 0.04kg, and 60g is equal to 0.06kg. The change in length is 1.8cm or 0.018m, and 2.05cm or 0.0205m.
Now, we can calculate the spring constant (k) using the first set of data:
0.018m = (k * 0.2m * 0.04kg) / 10m/s²
Simplifying the equation:
k = (0.018m * 10m/s²) / (0.2m * 0.04kg)
k = 9 N/m
Now, let's calculate the mass of the scalepan using the second set of data:
0.0205m = (9 N/m * 0.2m * m) / 10m/s²
Simplifying the equation:
m = (0.0205m * 10m/s²) / (9 N/m * 0.2m)
m ≈ 0.0114 kg
Finally, let's convert the mass back to grams:
mass_in_grams = 0.0114 kg * 1000g/kg
mass_in_grams ≈ 11.4 g
Therefore, the mass of the scalepan is approximately 11.4 grams.