Respuesta :
Answer:
The magnitude of the restoring force per unit mass is 5.175 m/s².
Explanation:
To solve the question, we note that from Hooke's law
F = -k·x
Where:
F = Restoring force
k = Constant of restoration and
x = Displacement of the particle
Therefore when we have, F = m × a, this gives
m × a = -k·x or
a = [tex]-\frac{k}{m} \times x[/tex]
That is the restoring force per unit mass is given by;
a = [tex]-\frac{k}{m} \times x[/tex]
Where:
a = Acceleration
m = mass of the object.
For a given mass, [tex]\frac{k}{m}[/tex] is also constant
Therefore, when a = 7.9 m/s²
x = 3.2 cm = , we have
a = [tex]-\frac{k}{m} \times x[/tex] → 7.9 m/s² = [tex]-\frac{k}{m}[/tex] × 0.032 m or
[tex]\frac{k}{m}[/tex] = (7.9 m/s²)/(0.032 m ) = 225
Therefore when x = 2.30 cm = 0.023, we have
a = [tex]-\frac{k}{m} \times x[/tex] = 225×0.023 m = 5.175 m/s²
The restoring force per unit mass = 5.175 m/s².
