# How do i work out the magnitude of a force

• ems1312
In summary, calculating the magnitude of a force involves using the formula F=ma, where F is force, m is mass, and a is acceleration. This can be applied to both linear and rotational motion, and can also be used to determine the net force acting on an object in a given direction. Additionally, the direction of the force can be determined using trigonometric functions and vector analysis. Understanding and accurately calculating force magnitude is crucial in various fields of physics and engineering, as it is a fundamental concept in explaining the behavior of objects in motion.
ems1312
how do i work out the magnitude of the force that has to be applied to compress a spring?

ems1312 said:
how do i work out the magnitude of the force that has to be applied to compress a spring?

Welcome to the PF. You use the spring constant and Hooke's Law:

http://en.wikipedia.org/wiki/Spring_(device )

.

Last edited by a moderator:
is it 0.5kxsquared or just -kx?

ems1312 said:
is it 0.5kxsquared or just -kx?

The restorative force is -kx. The energy stored in the spring is the 1/2 kx^2. What course is this for? Or is it for a project of yours?

predicting motion course, struggling abit. i even worked out the spring constant on the question before. now its asking me to work out the speed which means combining equations at a guess. its an open university course, so a lot of reading involved which doesn't suit me really. As soon as someone explains it in a different way i normally understand it. advice is good on here though!

ems1312 said:
predicting motion course, struggling abit. i even worked out the spring constant on the question before. now its asking me to work out the speed which means combining equations at a guess. its an open university course, so a lot of reading involved which doesn't suit me really. As soon as someone explains it in a different way i normally understand it. advice is good on here though!

Glad to help. I'm going to go ahead and move this thread to the Homework Help forums, since it's about schoolwork. Let us know if you have follow-up questions. As always, it's best to show us as much of your work as possible, since we can often guide you better after we see how you are working out the problems.

everything......!
its about a small toy attached to a spring with a suction device on the bottom.
the total compression of the spring is 1.2 cm
when the toy pops off the device it reaches a maximum height of 34 cm
the mass of the toy is 0.65g
the spring is ideal and air resistance and other losses are negligible.

the first part was to work out the constant of the spring,
i used these equations...
Strain potential energy: E = 0.5kx2 and gravitational potential energy: E = mgh
Re-arranging this equation to give k (spring constant) as the subject i get:
K = 2 mgh/ x2
Inserting these values into the equation i get:
K = 2 x(6.5 x 10-4 kg) x 9.81 m s-2 x 0.34 m / (0.012 m)2
giving the value of the spring constant as 30.1 N m

the next part was to work out the magnitude of the force that has to be applied in order to compress the spring sufficiently so the toy can be pressed down to the table.

F = Kx
F = 30.1 kg m2 s-2 x 0.012 m
giving 0.36 N as the answer.

the next part is to calculate the speed in which the toy leaves the table, working on that bit now, hope I'm right so far!

ems1312 said:
everything......!
its about a small toy attached to a spring with a suction device on the bottom.
the total compression of the spring is 1.2 cm
when the toy pops off the device it reaches a maximum height of 34 cm
the mass of the toy is 0.65g
the spring is ideal and air resistance and other losses are negligible.

the first part was to work out the constant of the spring,
i used these equations...
Strain potential energy: E = 0.5kx2 and gravitational potential energy: E = mgh
Re-arranging this equation to give k (spring constant) as the subject i get:
K = 2 mgh/ x2
Inserting these values into the equation i get:
K = 2 x(6.5 x 10-4 kg) x 9.81 m s-2 x 0.34 m / (0.012 m)2
giving the value of the spring constant as 30.1 N m

the next part was to work out the magnitude of the force that has to be applied in order to compress the spring sufficiently so the toy can be pressed down to the table.

F = Kx
F = 30.1 kg m2 s-2 x 0.012 m
giving 0.36 N as the answer.

the next part is to calculate the speed in which the toy leaves the table, working on that bit now, hope I'm right so far!

Looking pretty good so far, but the units on K are not quite right. Should be N/m, not Nm. Double check that you worked the equation right, and check your units as you carry them along (and cancel them just like you do real numbers).

To calculate the speed with which the toy leaves the table i will have used the following equation:
E = ½ m v2
Re-arranged to give:
V =√ E / 0.5 x m
V =√ 0.36 N / 0.5 x (6.5 x 10-4)
V = 33.3 m s-1
So the speed is 33.3 m s-1

This seems quite fast!?

ems1312 said:
To calculate the speed with which the toy leaves the table i will have used the following equation:
E = ½ m v2
Re-arranged to give:
V =√ E / 0.5 x m
V =√ 0.36 N / 0.5 x (6.5 x 10-4)
V = 33.3 m s-1
So the speed is 33.3 m s-1

This seems quite fast!?

The energy in the compressed spring is not 0.36N (wrong number, wrong units).

not sure now. thought i was doing ok! do i work out the magnitude of the force like the following or am i off the mark?!

F = Kx
F = 30.1 kg m2 s-2 x 0.012 m
F = 0.36 N (is N supposed to be in joules?)

or do i use the 0.5kx-2 equation.

are you online tomorrow evening to help at all?

are you ok to help? got another question, or do i put that on a different message?

The potential energy PE in the compressed spring is converted to kinetic energy KE as the spring is released. Say that all of the PE is converted to KE, what does that give you for the takeoff velocity?

i really don't understand. getting confused with it.

You have your toy on its spring, the spring is compressed and the toy is not moving.

All the energy in the system is stored as potential energy in the spring. As you release this toy the spring starts to "uncompress" itself. As the spring uncompresses itself your toy begins to move upwards.

So what's happening behind the scenes in terms of energy conservation?

We know that all energy is conserved.

So the energy is going from potential energy (stored in the COMPRESSED spring), to kinetic energy (the toy moving upward). The moment your spring is relaxed (x=0) you could say that all the potential energy in the spring has been converted to kinetic energy.

We can also predict the energy transfer after all the energy is become kinetic energy. Since all the energy is now stored in kinetic energy the toy is going to be moving upwards (kinetic energy is not 0, therefore it has a NONZERO VELOCITY) when the toys reachs its maximum height it won't be moving(VELOCITY=0).

All the energy is now gravitational potential energy!

PE Compressed Spring -> Kinetic -> Gravitational PE

Hope this helps.

ems1312 said:
... got another question, or do i put that on a different message?
Questions unrelated to this topic should be posted separately. Otherwise, they are quickly going to get lost in the abyss (black hole).

## 1. How do I calculate the magnitude of a force?

To calculate the magnitude of a force, you need to know the mass of the object and its acceleration. You can use the formula F=ma, where F is the force, m is the mass, and a is the acceleration. Plug in the values and solve for F to find the magnitude of the force.

## 2. What units are used to measure force?

The SI unit for force is the Newton (N). Other commonly used units include pounds (lb) and kilogram-force (kgf). It is important to use consistent units when calculating the magnitude of a force.

## 3. How does the direction of a force affect its magnitude?

The direction of a force does not affect its magnitude. The magnitude of a force only depends on the mass and acceleration of the object. However, the direction of a force does affect its overall effect on an object, as it can change the object's velocity or direction of motion.

## 4. Can I use the magnitude of a force to determine the direction?

No, the magnitude of a force only tells you the strength of the force. To determine the direction of a force, you will need to know the angle or vector components of the force. This can be done using trigonometry or vector addition.

## 5. How do I measure the magnitude of a force in real-world situations?

In real-world situations, you can use tools such as a spring scale or a force sensor to measure the magnitude of a force. These tools typically have units in either Newtons or pounds, which you can use to determine the force's strength.

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