A spring balance has a scale that reads from 0 to 5 kg. The length of scale is 20 cm.a body suspended from this spring, when displaced and released ,oscillates with period of 0.60s.what is the weight of body.
Period = 2PI(sqrt(mass/k)
Now for k, full scale is 5kg, of length 20cm, k=5*9.8/.2 N/kg
solve for mass.
Now the Weight of the mass is mass*9.8 ON Earth.
To find the weight of the body, we can use the formula:
Weight = Mass × Acceleration due to gravity
First, we need to find the mass of the body. We can use the equation of motion for a simple harmonic oscillator to do that.
The equation for the period of a simple harmonic motion is:
T = 2π√(m/k)
Where:
T = Period of oscillation
m = Mass of the body
k = Spring constant
Given: T = 0.60s, k = Weight range of spring balance = 5 kg (since the spring balance reads from 0 to 5 kg)
We can rearrange the equation to solve for the mass:
m = (T^2 × k) / (4π^2)
Substituting the given values:
m = (0.60^2 × 5) / (4π^2)
Now, let's calculate the mass:
m = (0.36 × 5) / (4π^2)
Next, we can find the weight using the formula:
Weight = m × Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Weight = m × 9.8
Now, let's calculate the weight of the body:
Weight = (0.36 × 5) / (4π^2) × 9.8
Weight ≈ 0.55 kg
Therefore, the weight of the body is approximately 0.55 kg.