When a 9.00 kg mass is placed on top of a vertical spring, the spring compresses 4.5cm, FIND THE FORCE CONSTANT OF THE SPRING.
(9.00kg) x (9.81m/s^2)= 88.29
88.29/4.5= 19.62N/cm
or .1962N/m
19.6
I will be happy to critique your thinking.
I would use Hooke's law: F=kx
To find the force constant of the spring, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.
The formula for Hooke's Law is:
F = -kx
Where:
F is the force exerted by the spring,
k is the force constant of the spring, and
x is the displacement from the equilibrium position.
In this case, the spring is compressed by 4.5 cm, which can be converted to meters by dividing by 100:
x = 4.5 cm = 4.5 / 100 m = 0.045 m
The force exerted by the spring can be calculated using the equation:
F = kx
We can rearrange the equation to solve for the force constant:
k = F / x
Now, we need to find the force exerted by the spring, F. To do that, we can use the weight of the mass, since the spring balances the force of gravity.
The weight of the mass can be calculated using the equation:
F = m * g
Where:
m is the mass (9.00 kg) and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values, we have:
F = 9.00 kg * 9.8 m/s^2 = 88.2 N
Now we can substitute the force and displacement values into the equation for the force constant:
k = 88.2 N / 0.045 m = 1960 N/m
Therefore, the force constant of the spring is approximately 1960 N/m.