# Spring Force and mass

## Homework Statement

A 5.3kg mass hangs vertically from a spring with spring constant 720N/m. The mass is lifted upward and released. Calculate the force and acceleration the mass when the spring is compressed by 0.36m.
Note: I already solved for acceleration and I got the correct answer- a=58.70566038m/s^2

I tried to solve for the spring force but I got the wrong answer and I'm not sure what I did wrong.

m=5.3kg, k=720N/m, Δx=0.36m.

I used Fnet=ma

## The Attempt at a Solution

Fnet=ma
ma=-Fg-Fx
(5.3)(58.70566038)=-mg-Fx
311.14=-(5.3)(9.8)-Fx
311.14=-51.94-Fx
311.14+51.94=-Fx
363.08=-Fx
-363.08N=Fx
363.08N[down]=Fx

The correct answer is 310N[down]. Can someone tell me what I did wrong? Also, I'm confused about whether a put the negative signs infront of the correct variables(Fg and Fx are both pointing downwards in this problem, so I put a negative sign infront of both). Should I put a negative sign infront of Fnet too since Fnet points downwards in this case? Are you even supposed to put negative signs infront of variables based on direction when doing calculations?

## Answers and Replies

It looks like you have some serious fundamental misunderstandings.

Firstly, how'd you manage to find the acceleration of the mass without knowing the net force acting on the mass? What does Newton's Second Law tell us about how the net force acting on object is related to that object's acceleration?

To answer your other question, yes you should keep track of your signs, you'll end up with wrong answer if you don't. In fact, your value of Fx is wrong because you're not using the right signs. Subtracting versus adding a quantity makes a big difference, so yes they are important.

While we're at it, what force does Fx represent and why are you solving for it? The problem asks for the mass's acceleration, not the force by the spring.

haruspex
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Are you sure it is asking for the spring force, not the net force on the mass?
If it does want the spring force, you have a sign wrong.

Calculate the force and acceleration the mass when the spring is compressed by 0.36m.
Note: I already solved for acceleration and I got the correct answer- a=58.70566038m/s^2

I tried to solve for the spring force but I got the wrong answer and I'm not sure what I did wrong.

i wonder how you got acceleration of the mass ;

as usually when one draws a free body diagram the net force gets calculated and finally acceleration is equated with F/mass.
mark the underlined question .... when spring is compressed...

so the spring force will oppose compression and gravitational pull will be downward(opposed to compression), but the motion is upward; so calculate the net force which will be addition of the above two but acting opposed to displacement (effective deceleration)
and if you divide the net force by mass you get acceleration.
a look at the numbers gives an impression that you will get correct answer.

Are you sure it is asking for the spring force, not the net force on the mass?
If it does want the spring force, you have a sign wrong.
It wants the spring force

i wonder how you got acceleration of the mass ;

as usually when one draws a free body diagram the net force gets calculated and finally acceleration is equated with F/mass.
mark the underlined question .... when spring is compressed...

so the spring force will oppose compression and gravitational pull will be downward(opposed to compression), but the motion is upward; so calculate the net force which will be addition of the above two but acting opposed to displacement (effective deceleration)
and if you divide the net force by mass you get acceleration.
a look at the numbers gives an impression that you will get correct answer.

i wonder how you got acceleration of the mass ;

as usually when one draws a free body diagram the net force gets calculated and finally acceleration is equated with F/mass.
mark the underlined question .... when spring is compressed...

so the spring force will oppose compression and gravitational pull will be downward(opposed to compression), but the motion is upward; so calculate the net force which will be addition of the above two but acting opposed to displacement (effective deceleration)
and if you divide the net force by mass you get acceleration.
a look at the numbers gives an impression that you will get correct answer.

I did:

Fnet=ma
ma=-mg-k(deltax)

I knew all the values except acceleration, so i just used algebra to solve for it

It looks like you have some serious fundamental misunderstandings.

Firstly, how'd you manage to find the acceleration of the mass without knowing the net force acting on the mass? What does Newton's Second Law tell us about how the net force acting on object is related to that object's acceleration?

To answer your other question, yes you should keep track of your signs, you'll end up with wrong answer if you don't. In fact, your value of Fx is wrong because you're not using the right signs. Subtracting versus adding a quantity makes a big difference, so yes they are important.

While we're at it, what force does Fx represent and why are you solving for it? The problem asks for the mass's acceleration, not the force by the spring.

It asks for 2 things: acceleration and spring force(Fx)

Here's how I found acceleration:

ma=-mg-k(deltax)

I knew all the above values except a, so I just used algebra to solve.

Also, what mistake did I make with my negative signs?

I knew all the values except acceleration, so i just used algebra to solve for it

therefore you also knew the force as mass was known.
by newtons laws if you know acceleration and mass then you know the force.
so what value of force you get ?

therefore you also knew the force as mass was known.
by newtons laws if you know acceleration and mass then you know the force.
so what value of force you get ?

Fnet is 311.14N, which I should in my calculations in the original post

The correct answer is 310N[down]. Can someone tell me what I did wrong? Also, I'm confused about whether a put the negative signs infront of the correct variables(Fg and Fx are both pointing downwards in this problem, so I put a negative sign infront of both). Should I put a negative sign infront of Fnet too since Fnet points downwards in this case? Are you even supposed to put negative signs infront of variables based on direction when doing calculations?

so you are getting an approx. correct answer. regarding the negative sign - in force equations as they are vectors ,one has to use sign convention.
suppose the body is going up and you are writing mass xacceleration = the net force '
then the forces in the direction of motion may be taken as positive and opposed to the motion as negative.
the sign of the accelaration after calculation can tell you whether the net force is helping the motion or otherwisei.e. retarding the motion.
so the question you posed is perhaps asking for the net force rather than spring force;
the wording of the question suggested that they need net force-

It asks for 2 things: acceleration and spring force(Fx)

Here's how I found acceleration:

ma=-mg-k(deltax)

I knew all the above values except a, so I just used algebra to solve.

Also, what mistake did I make with my negative signs?

What you posted says to find the force and acceleration of the mass. The two answers you provided agree with the values for both the force and the acceleration of the mass (F = -210N and a = -58). It also makes more sense that they'd ask for the force and then the acceleration of the mass (in that order) as what you posted suggests. Unless you're leaving something out, why do you think you need to find the spring force? It's impossible to help you if you don't post the entire problem exactly the way it was worded.

Do note that -211.14 N is the same thing as 210 N (downward) once you take into account that the problem uses only two significant figures, so your final answer should only contain two significant figures.

That aside, if you wanted to find the spring force, there's no need to work backward from the net force on the object. The spring force is given by Hooke's law and is independent of the acceleration of the mass and gravity. It only depends on how much the spring is compressed, which you know.

$$F_s=-kx$$

so you are getting an approx. correct answer. regarding the negative sign - in force equations as they are vectors ,one has to use sign convention.
suppose the body is going up and you are writing mass xacceleration = the net force '
then the forces in the direction of motion may be taken as positive and opposed to the motion as negative.
the sign of the accelaration after calculation can tell you whether the net force is helping the motion or otherwisei.e. retarding the motion.
so the question you posed is perhaps asking for the net force rather than spring force;
the wording of the question suggested that they need net force-

It just asks for force and since the lesson was about the spring force, I assumed that that's what they wanted. Also, the only 2 forces acting on the mass are spring force and gravity, so it makes sense that they'd ask for the spring force.

What you posted says to find the force and acceleration of the mass. The two answers you provided agree with the values for both the force and the acceleration of the mass (F = -210N and a = -58). It also makes more sense that they'd ask for the force and then the acceleration of the mass (in that order) as what you posted suggests. Unless you're leaving something out, why do you think you need to find the spring force? It's impossible to help you if you don't post the entire problem exactly the way it was worded.

Do note that -211.14 N is the same thing as 210 N (downward) once you take into account that the problem uses only two significant figures, so your final answer should only contain two significant figures.

That aside, if you wanted to find the spring force, there's no need to work backward from the net force on the object. The spring force is given by Hooke's law and is independent of the acceleration of the mass and gravity. It only depends on how much the spring is compressed, which you know.

$$F_s=-kx$$

The question I posted is exactly as written in the textbook

so you are getting an approx. correct answer. regarding the negative sign - in force equations as they are vectors ,one has to use sign convention.
suppose the body is going up and you are writing mass xacceleration = the net force '
then the forces in the direction of motion may be taken as positive and opposed to the motion as negative.
the sign of the accelaration after calculation can tell you whether the net force is helping the motion or otherwisei.e. retarding the motion.
so the question you posed is perhaps asking for the net force rather than spring force;
the wording of the question suggested that they need net force-
So, I should put a negative sign infront of the acceleration too

The question I posted is exactly as written in the textbook
I didn't get F=210N, I got 363.08N

So, I should put a negative sign infront of the acceleration too
you do not have to put in a sign- its the result of your calculation that acceleration = - number m/s^2
and this carries a meaning that it is in a direction opposite to the motion.

you do not have to put in a sign- its the result of your calculation that acceleration = - number m/s^2
and this carries a meaning that it is in a direction opposite to the motion.

Oh ok, so then I put the negative signs in the correct places, but still got the wrong answer

The correct answer is 310N[down]. Can someone tell me what I did wrong?

Oh ok, so then I put the negative signs in the correct places, but still got the wrong answer

no you got 311 N for the net force and its close to 310 which was expected.
It is the spring force pushing downward because of compression of spring , there was no term of 210 N in the discussion.and 363 is the wrong answer.

=

no you got 311 N for the net force and its close to 310 which was expected.
It is the spring force pushing downward because of compression of spring , there was no term of 210 N in the discussion.and 363 is the wrong answer.

=
Why does spring force=net force? or does the question just want us to solve for net force?

The question I posted is exactly as written in the textbook

The problem asks you to find the net force acting on the mass and the mass's acceleration. The answers given are for the force and acceleration of the mass.

I don't understand why you think you're finding the spring force. Even then, you can't find the correct value for it because you aren't using the acceleration you claimed to have found, which is a claim I'm now very skeptical of. In fact, you had to use the spring force in order to find the acceleration, so the fact that you're having trouble finding it is concerning.

Last edited:
Why does spring force=net force? or does the question just want us to solve for net force?

i do not know whether you have done simple hamonic motion with a mass hanging on the spring;
i quote a simple way to look at it

the spring is normally supporting a mass by some stretching increase in length - any disturbance leads to oscillations ,if it is during compression stage the net downward force will be provided by the spring as all the time it is holding the mass

i do not know whether you have done simple hamonic motion with a mass hanging on the spring;
i quote a simple way to look at it

the spring is normally supporting a mass by some stretching increase in length - any disturbance leads to oscillations ,if it is during compression stage the net downward force will be provided by the spring as all the time it is holding the mass

Got ahead of myself.

This is not correct. The net downward force is not provided by the spring alone. For a hanging system, the forces acting on the mass are the gravitational force and the spring force. If the spring is compressed, the spring force is downward and so is the gravitational force. Therefore, the net force in the downward direction is Fs + Fg, which also happens to be the net force acting on the mass.

you are right about the force mg acting downward but in oscillatory motion the equilibrium point gets shifted and the initial condition supports the mass
see
Assume a mass suspended from a vertical spring of spring constant k. In equilibrium the spring is stretched a distance x0 = mg/k. If the mass is displaced from equilibrium position downward and the spring is stretched an additional distance x, then the total force on the mass is mg - k(x0 + x) = -kx directed towards the equilibrium position. If the mass is displaced upward by a distance x, then the total force on the mass is mg - k(x0 - x) = kx, directed towards the equilibrium position. The mass will execute simple harmonic motion. The angular frequency ω = SQRT(k/m) is the same for the mass oscillating on the spring in a vertical or horizontal position. The equilibrium length of the spring about which it oscillates is different for the vertical position and the horizontal position.
ref.http://labman.phys.utk.edu/phys135/modules/m9/oscillations.htm

The problem asks you to find the net force acting on the mass and the mass's acceleration. The answers given are for the force and acceleration of the mass.

I don't understand why you think you're finding the spring force. Even then, you can't find the correct value for it because you aren't using the acceleration you claimed to have found, which is a claim I'm now very skeptical of. In fact, you had to use the spring force in order to find the acceleration, so the fact that you're having trouble finding it is concerning.

Well, I did find the acceleration first and I got the correct answer, so I don't understand why that's hard to believe