# Max Distance Calculated for Spring Mass System of K=450N/m, m=2.2kg

• samdiah
In summary, a 202kg block is attached to a vertically hanging spring with a spring constant of 450N/m. When the block falls, it gains momentum and will reach its maximum velocity at the equilibrium position, a distance of 0.05m below the initial position. The maximum distance the block will fall before moving upward will be twice this distance, where x satisfies the equation 450x=2.2(9.8).
samdiah
A spring with K=450N/m hangs vertically. You attach 202kg block to it and allow the mass to fall. What is the maximum distance the block will fall before it begins moving upward?

ans-
k=450N/m
m=2.2kg
x=?

Fnet=mg
=2.2kg*9.8N/m
=21.56 N

F=+/- kx
x=f/k
x=0.05m

Is this the max distance I calcul;ated or the new equilibrium distance? Can u give me a hint.

The equilibrium position will be where the force equals the weight:
450x= 2.2(9.8), measured below the initial position. Since the mass gains momentum as it falls, it will have its maximum velocity when it passes there, a distance x below it's initial position. It will continue to fall until the spring overcomes that momentum. Because of the symmetry of the situation, that distance below equilibrium will also be x. The "maximum distance the block will fall before it begins moving upward" will be 2x where x satisfies 450x= 2.2(9.8).

HallsofIvy, I don't understand what you are saying.

## 1. What is the formula for calculating the maximum distance of a spring mass system?

The formula for calculating the maximum distance (x) of a spring mass system is x = F/k, where F is the applied force and k is the spring constant.

## 2. How do you determine the spring constant (k) for a spring mass system?

The spring constant (k) can be determined by dividing the force applied (F) by the displacement (x) of the spring. This can be represented by the equation k = F/x.

## 3. Can the maximum distance of a spring mass system be negative?

No, the maximum distance of a spring mass system cannot be negative. It represents the maximum displacement of the spring from its equilibrium position.

## 4. How does the mass of the object affect the maximum distance in a spring mass system?

The mass of the object (m) does not directly affect the maximum distance in a spring mass system. However, it does affect the force applied (F) and therefore the spring constant (k), which in turn affects the maximum distance. A heavier mass will require a higher force to reach the same maximum distance compared to a lighter mass.

## 5. What is the significance of the maximum distance in a spring mass system?

The maximum distance in a spring mass system represents the potential energy stored in the spring. It is also used to determine the period and frequency of the oscillations of the system.

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