Answer :
The maximum distance the block falls can be determined using the equation for the potential energy stored in the spring. the maximum distance the block falls is 5.05 times the square of the distance x
The potential energy stored in the spring is given by the formula:
Potential Energy = (1/2) * k * x^2
Where:
- k is the force constant of the spring (99 N/m in this case)
- x is the displacement from the equilibrium position (which is the maximum distance the block falls in this case)
In this problem, the block starts from rest and falls vertically. At the maximum distance, the potential energy stored in the spring is equal to the gravitational potential energy of the block.
The gravitational potential energy of the block is given by the formula:
Gravitational Potential Energy = m * g * h
Where:
- m is the mass of the block (1 kg in this case)
- g is the acceleration due to gravity (9.8 m/s^2)
- h is the maximum distance the block falls vertically
Setting the potential energy of the spring equal to the gravitational potential energy, we have:
(1/2) * k * x^2 = m * g * h
Rearranging the equation to solve for h, we get:
h = (1/2) * k * x^2 / (m * g)
Substituting the given values, we have:
h = (1/2) * 99 N/m * x^2 / (1 kg * 9.8 m/s^2)
Simplifying the equation, we get:
h = 5.05 x^2
Therefore, the maximum distance the block falls is 5.05 times the square of the distance x.
To know more about the gravitational potential energy
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