Force Constant k of Spring - Potential Energy Homework

In summary, a 2 kg rock shot straight up with a compressed spring attains a maximum height of 500m. Using the given values and equations, the force constant of the spring is calculated to be 20,000 N/m.
  • #1
themadhatter1
140
0

Homework Statement


A spring is compressed a distance of 1m and a 2 kg rock is shot straight up with the spring. The rock attains a maximum height of 500m. What is the force constant k of the spring?

Use g=10m/s^2

Homework Equations


P.E.= mgh
P.E. elastic= (1/2)(k)(x^2)

The Attempt at a Solution



P.E.= mgh
P.E.=(2000g)(10m/s^2)(500m)
P.E.= 10000000 Newtons

P.E. elastic= (1/2)(k)(x^2)
k= P.E elastic/ (1/2)(x^2)
k= 10000000/ (1/2)(1)
k=2000000 Newtons ?
 
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  • #2
themadhatter1 said:
P.E.= mgh
P.E.=(2000g)(10m/s^2)(500m)
P.E.= 10000000 Newtons
Use SI units ie kilogram, not gram. Furthermore, energy is in joules, not Newtons! Also, the spring constant k is in Newtons per meter, not Newtons. Please read up on units, okay?
 
  • #3
Fightfish said:
Use SI units ie kilogram, not gram. Furthermore, energy is in joules, not Newtons! Also, the spring constant k is in Newtons per meter, not Newtons. Please read up on units, okay?

Thanks,

So, if I correct my units I would have:

P.E.= mgh
P.E.=(2kg)(10m/s^2)(500m)
P.E.= 10000 joules

P.E. elastic= (1/2)(k)(x^2)
k= P.E elastic/ (1/2)(x^2)
k= 10000/ (1/2)(1)
k=20000 N/m ?

Is this correct?
 
  • #4
Looks good; that is one very strong spring indeed.
 

FAQ: Force Constant k of Spring - Potential Energy Homework

1. What is the definition of the force constant k of a spring?

The force constant k of a spring is a measure of the stiffness of the spring, or how much force is required to stretch or compress the spring by a certain distance. It is represented by the letter k and is measured in units of newtons per meter (N/m).

2. How is the force constant k related to the potential energy of a spring?

The force constant k is directly proportional to the potential energy of a spring. This means that as the force constant increases, the potential energy of the spring also increases, and vice versa. The relationship between force constant and potential energy can be represented by the equation: U = 1/2 * k * x^2, where U is the potential energy, k is the force constant, and x is the displacement of the spring from its equilibrium position.

3. What factors affect the value of the force constant k?

The value of the force constant k is affected by several factors, including the material of the spring, the dimensions of the spring (such as length and diameter), and the number of coils in the spring. The force constant is also affected by the temperature and the applied load or force on the spring.

4. How is the force constant k calculated or measured?

The force constant k can be calculated using the equation k = F/x, where F is the force applied to the spring and x is the resulting displacement of the spring. It can also be measured experimentally by using a force sensor or a spring balance to measure the force applied to the spring and a ruler or measuring tape to measure the displacement of the spring.

5. How does the force constant k affect the behavior of a spring?

The force constant k determines how much force is required to stretch or compress a spring by a certain distance. A higher force constant means the spring is stiffer and requires more force to stretch or compress, while a lower force constant results in a more flexible spring. This affects the behavior of the spring in terms of its response to external forces and its ability to return to its original shape after being stretched or compressed.

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