# Find the minimum value of the quantity

• gourish
In summary, the problem presents two cubes of mass m tied together by a string and separated by a spring with a compression of ε and coefficient of stiffness k. The goal is to find the minimum value of εk/mg so that when the string is cut and the spring is released, the lower cube will jump off the ground. To solve this, use energy conservation and consider the natural length of the spring as "l" and the center of mass of the lower cube as the reference line. By setting up equations and considering the distance x of the top cube from the relaxed spring, the minimum force required for the lower cube to jump can be determined.
gourish

## Homework Statement

There are two cubes of mass m. They are initially tied by a string tightly. They are kept from joining into each other because of a spring (which in this tied up state has a compression of ε) of coefficient of stiffness k. Find the minimum value of the quantity εk/mg so that when the string is cut and the spring is let loose to act, the lower cube jumps off the ground

## Homework Equations

consider the natural length as "l" of the spring and the center of mass of lower cube as the reference line
total mechanical energy (initial)=1/2 k ε^2+mg (l-ε)
total mechanical energy (after)=1/2kx^2+mg(l-x)

## The Attempt at a Solution

i found that k(e+x)/mg=2 but i did not get to the quantity to become εk/mg and did not understand how to relate the equations to the condition "the lower cube jumps off the ground" can anybody please help me

hi gourish! welcome to pf!
gourish said:
… did not understand how to relate the equations to the condition "the lower cube jumps off the ground" can anybody please help me

hint: it won't jump unless it's pulled! …

with what (minimum) force must it be pulled?

1. Use energy conservation. What is the initial energy in the spring?
2. What is the criterion on x for the bottom mass to just start moving?
Let x = 0 is when the spring is relaxed. x is the distance of the top m above the level where the spring is relaxed.

initial spring energy = final spring energy + gain in potential energy of top mass.

Last edited:

## 1. What does "minimum value" mean?

The minimum value of a quantity refers to the smallest possible numerical value that the quantity can have within a given range or set of values.

## 2. How do you determine the minimum value of a quantity?

To find the minimum value of a quantity, you can use mathematical methods such as differentiation or optimization techniques. Alternatively, you can graph the function or set of data points and visually identify the lowest point.

## 3. Can the minimum value of a quantity be negative?

Yes, the minimum value of a quantity can be negative if the quantity itself can have negative values or if the range of values includes negative numbers. However, it is also possible for the minimum value to be zero or a positive number.

## 4. What is the significance of finding the minimum value of a quantity?

Calculating the minimum value of a quantity can provide important information about the behavior or characteristics of the quantity. It can also help in making decisions or predictions based on the data.

## 5. Can the minimum value of a quantity change?

Yes, the minimum value of a quantity can change depending on the given range of values or the parameters of the function. As the range or parameters change, the minimum value may shift to a different value.

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