An object with mass 500g less hang from the spring with force constant 20N/m . What is the mass of an object that stretch the spring 35cm long (take g=0.01N/g)
The force required to stretch a spring is given by Hooke's Law: F = kx, where F is the force, k is the force constant, and x is the displacement.
Given that the force constant is 20 N/m and the displacement is 35 cm, we need to convert the displacement to meters:
35 cm = 0.35 m
Thus, the force required to stretch the spring is:
F = kx = 20 N/m * 0.35 m = 7 N
Now, we need to find the mass of the object that would exert a force of 7 N on the spring.
Since force is equal to mass multiplied by acceleration (F = ma), we can rearrange the equation to solve for mass:
mass = F / acceleration
Given that acceleration due to gravity, g, is 0.01 N/g, we can substitute this value into the equation:
mass = 7 N / (0.01 N/g) = 700 g
Therefore, the mass of the object that would stretch the spring 35 cm long is 700 g.
To determine the mass of an object that stretches a spring by 35cm, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The mathematical representation of Hooke's law is as follows:
F = k * x
Where:
F is the force exerted by the spring (in Newtons),
k is the force constant of the spring (in N/m),
and x is the displacement of the spring from its equilibrium position (in meters).
Given that the force constant of the spring, k, is 20 N/m and the displacement, x, is 35 cm (which is equivalent to 0.35m), we can calculate the force exerted by the spring using Hooke's law:
F = k * x
F = 20 N/m * 0.35 m
F = 7 N
Now, to determine the mass of the object, we can use Newton's second law, which states that the force (F) applied on an object is equal to the mass (m) of the object multiplied by the acceleration due to gravity (g):
F = m * g
Given that the acceleration due to gravity, g, is 0.01 N/g, we can rearrange the equation to solve for mass:
m = F / g
m = 7 N / 0.01 N/g
m = 700 g
Thus, the mass of the object that stretches the spring by 35 cm is 700 grams.