Help please with my understanding the solution of this mass on a vertical spring

[hello478]

Homework Statement

a light spring of unextended length id 14.2cm and is suspended vertically from a fixed point as illlustrated
a mass of weight 3.8 N is hung from the end of the spring as shown
an additional force f then extends the spring so that its length becomes 17.8 cm as shown
springs constant is 1.8 N/cm
for extension from length 16.3 to 17.8 cm what is the change in gravitational potential energy
what is the change in elastic potential energy of the spring
determine work done by force f
i know the steps of these questions i dont understand them
i need explainations for them and also in gpe why dont we take account for the force f which is additional??
and why is work done by subtracting both energies??
and how is the elastic potential energy calculated by subrtracting 0.036 ^2 and 0.021^2

Relevant Equations

gpe = 3.8*0.015 = 0.057J
elastic potential energy => 0.1 ∆EP = mg∆h or W∆h
= 3.8 × 1.5 × 10-2
= 0.057 J

elastic potential energy = ½ × 1.8*100 *(0.036^2– 0.021^2)
= 0.077 J

work done = 0.077 – 0.057
= 0.020 J

 

[PeroK]

Can you tell us what you do know about these things:

What is GPE? And how do you calculate it?

What is the elastic PE of a spring? And how do you calculate it?

What is the work done by a force? And how do you calculate it?

 

[hello478]

Can you tell us what you do know about these things:

What is GPE?

What is the elastic PE of a spring?

What is the work done by a force?

gpe is the gravitational potential energy = mgh
elastice potential energy is equal to the enregy stored in a spring = 1/2 fx
work done by a force is distance moved times the force

 

[PeroK]

gpe is the gravitational potential energy = mgh

Okay. So, how do you calculated the difference in GPE?

elastice potential energy is equal to the enregy stored in a spring = 1/2 fx

How do you calculate the difference in elastic PE?

work done by a force is distance moved times the force

Not quite. For motion in one dimension, it is the force times the displacement. Force and displacemet being one-dimensional vectors.

 

[hello478]

Okay. So, how do you calculated the difference in GPE?

How do you calculate the difference in elastic PE?

Not quite. For motion in one dimension, it is the force times the displacement. Force and displacemet being one-dimensional vectors.

you calculate the difference in gpe by using the formula mgh
but i dont get why that mg used is 3.8N , what is the additional force f
doesnt it have an effect on the gpe of the mass
i cant quite comprehend...

 

[PeroK]

you calculate the difference in gpe by using the formula mgh

This is not right. The difference is GPE moving from $h_1$ to $h_2$ is:
$$\Delta GPE = mg\Delta h = mg(h_2 - h_1)$$

but i dont get why that mg used is 3.8N

In this context, the weight of an object of mass $m$ is given by $mg$. Some textbooks give the weight of an object in newtons, rather than giving the mass in kg.

 

[hello478]

This is not right. The difference is GPE moving from $h_1$ to $h_2$ is:
$$\Delta GPE = mg\Delta h = mg(h_2 - h_1)$$

In this context, the weight of an object of mass $m$ is given by $mg$. Some textbooks give the weight of an object in newtons, rather than giving the mass in kg.

what about the force f?? its confusing me, why is it there, why should i ignore it in my calculations even though it is being pulled by that force f

 

[PeroK]

what about the force f?? its confusing me, why is it there, why should i ignore it in my calculations even though it is being pulled by that force f

GPE is the potential energy at a given height. It doesn't depend on how an object got to that point or what force is holding it there. If you hold an object at a height $h$ above the ground, then it's GPE (relative to the ground) is $mgh$. You need to apply an upward force $mg$ to keep it there. And, if you carry an object upstairs, then it gains GPE. And if you carry it downstairs, then it loses GPE. The force you apply is necessary to move the object, but doesn't affect the GPE at a given height.

 

[hello478]

GPE is the potential energy at a given height. It doesn't depend on how an object got to that point or what force is holding it there. If you hold an object at a height $h$ above the ground, then it's GPE (relative to the ground) is $mgh$. You need to apply an upward force $mg$ to keep it there. And, if you carry an object upstairs, then it gains GPE. And if you carry it downstairs, then it loses GPE. The force you apply is necessary to move the object, but doesn't affect the GPE at a given height.

thanks alotttt
i think i sort of understand it
also can you please explain the remaining 2 parts of the question

 

[PeroK]

thanks alotttt
i think i sort of understand it
also can you please explain the remaining 2 parts of the question

The elastic potential of the spring is similar to GPE: it depends only on the extension of the spring. It doesn't matter how the spring was stretched to that length.

The other concept here is that gravity and the elastic force both do work on the mass when it moves. You should have learned this when you studied these forces individually. This problem is slightly more advanced and your difficulties perhaps come from not having fully understood the previous course work.

The work done by a force depends on the direction of the force and the direction of motion. If you throw an object upwards, then the gravitational force does negative work on the object. Negative work means that the KE of the object is reduced by gravity. When it reaches the highest point it has zero KE and gravity starts to do positive work on the object. Positive work means that the KE of the object increases (as it falls).

Likewise, an elastic spring alternately does positive and negative work on a object as it oscillates on the spring.

In both cases, the work done (whether positive or negative) depends on the change in GPE or elastic PE.

You need to study these concepts. These are core concepts that much of physics relies on.

In this case you have three forces at work: gravitational, elastic and the the third force. You can calculate how much work the third force does by calculating how much work gravity and the spring do. Note that there is an assumption here that the hanging mass starts and ends with zero KE.

 

[hello478]

The elastic potential of the spring is similar to GPE: it depends only on the extension of the spring. It doesn't matter how the spring was stretched to that length.

The other concept here is that gravity and the elastic force both do work on the mass when it moves. You should have learned this when you studied these forces individually. This problem is slightly more advanced and your difficulties perhaps come from not having fully understood the previous course work.

The work done by a force depends on the direction of the force and the direction of motion. If you throw an object upwards, then the gravitational force does negative work on the object. Negative work means that the KE of the object is reduced by gravity. When it reaches the highest point it has zero KE and gravity starts to do positive work on the object. Positive work means that the KE of the object increases (as it falls).

Likewise, an elastic spring alternately does positive and negative work on a object as it oscillates on the spring.

In both cases, the work done (whether positive or negative) depends on the change in GPE or elastic PE.

You need to study these concepts. These are core concepts that much of physics relies on.

In this case you have three forces at work: gravitational, elastic and the the third force. You can calculate how much work the third force does by calculating how much work gravity and the spring do. Note that there is an assumption here that the hanging mass starts and ends with zero KE.

thank you soo much
ill work on these concepts more :)