Question

A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the potential energy of the spring Usp and gravitational potential energy of the mass, Ug?

Answer 1

Complete Question

A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring's potential energy Us and the gravitational potential energy Ug of the mass?

A. both Us and Ug decrease

B. Us increases and Ug decreases

C Both Us and Ug increase

D Us decreases and Ug increases

E Us increases and Ug is constant

Answer:

Option B is the correct Answer

Explanation:

    The Gravitational Potential energy is mathematically represented as  

                    $U_g = mgh$

Where m is the mass , g is the acceleration due to gravity while and h is the height

 And in term of the spring  this energy represents the workdone against gravitational Force

 The Spring potential energy is mathematically represented as

                     $U_s = \frac{1}{2} k x^2$

Where k is the spring constant ans  x is the extension in the spring

   And energy represents the work that is being done to stretch the spring

 If the system as state in the question is setup and $U_s$ is being increased then $U_g$ decreases

   

Answer 2

Answer:

An increase in Ug causes a decrease in Usp. Also a decrease in Ug causes an increase in Usp of the spring.

Explanation:

For this system, the total mechanical energy of the system is conserved since the only force acting on the system is the force of gravity. As a result the total sum of the potential energies at all times must be equal.

E = Usp1 + Ug1 = Usp2 + Ug2

Now suppose the mass falls through a height h, its potential energy decreases by a magnitude mgh. Because energy is conserved this causes an increase in the potential energy stored in the spring

Ug2 – Ug1 = Usp2 – Usp1 = mgh

Usp2 = -mgh + Usp1

If instead the potential energy of the mass increased this will bring about a reduction in the potential energy of the spring.

In that case

So in essence the mechanical energy of the system always distributes itself in such a way that whatever increases in one accounts for the decrease in another.

So an increase in Ug causes a decrease in Usp. Also a decrease in Ug causes an increase in Usp of the spring.