# A Couple of Basic Questions about Mechanics

• syberraith
In summary, the conversation discusses the concept of work and kinetic energy, with specific calculations and examples given. There is also a mention of using the Feynman Lectures as a resource for better understanding these concepts.

#### syberraith

I'm writing a paper on a propulsion device and I could use some F/P ratio comparisons, like typical values for Newtons per Watt for propeller driven, jet driven, and rocket driven craft.

Also I ran into a confusing point involving work and kinetic energy. if kinetic energy is 1/2 m v^2, then say a 1kg mass that is traveling at 1m/s, then according to the formula the mass has a kinetic energy of 0.5 joules.

Now let say the mass was accelerated from a velocity of zero to the velocity of 1m/s, by a force of 1 Newton applied for one second. The definition of work state that the work applied to a mass increases the kinetic energy of that mass. So the 1 Newton force applied for one second, resulted mass moving one 1 meter. The formula for work states that force times distance equals the energy added to the system, Thus 1 Newton times 1 meter should equal one joule of energy added to the mass.

This is how I get two different answers for the kinetic energy of a 1kg mass that is moving at 1m/s.

Could someone point out my mistake in this please.

Best regards,

FredB

Your mistake is that a 1 N force applied for one second means that the body travels one meter. Your "jerk" (rate of change of acceleration) for 0 < t < 1, is 1. So integrating that 3 times you get:
$$s(t) = \frac{x^3}{3}$$ for 0 < t < 1

So the displacement is s(1) = $\frac{1}{3}$
Now an easier way to get work from this:
$$Work = \delta E_k$$

$$v(t) = \frac{x^2}{2}$$

this should clear things up.

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I'm still confused.

Maybe could you point me to a good article on the subject. Wikipedia is what has confused me.

Then again maybe I can just ignore the N*m approach and use the delta Ek method instead.

I could still use some ball park figures for F/P ratios for propeller planes. jets, and rockets...

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All you need to know is that $a(t) = v'(t) = s''(t)$ and that $s(t) = \int v(t) dt = \int \int a(t) dt^2$.

And for work, there are a couple of formulas you can use.

$$W = \int F \cdot dx = \int F \cdot v dt$$
$$W = \Delta E_{k}$$

In terms of a good article, I know of none but i'll look. Best description I've ever seen of work is in the Feynman Lectures - Volume 1. (Maybe because I'm a huge sucker for Feynman :P)

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gordonj005 said:
Your mistake is that a 1 N force applied for one second means that the body travels one meter. Your "jerk" (rate of change of velocity) for 0 < t < 1, is 1. So integrating that 3 times you get:
The rate of change of velocity is called "acceleration". Jerk is the rate of change of acceleration.
In the example described in the OP there is a constant acceleration 1m/s^2.
The distance traveled in 1 s is 0.5 m and the work is 0.5 J, equal to the change in kinetic energy.

To the OP: just look up uniform accelerated motion.

IF you are still confused, igmore posts #2 and #4, which are also confused and/or wrong.

To repeat what #5 said, in slightly different words:

The velocity increases linearly from 0 to 1 m/s over 1 second.
So the average velocity over the second is (0 + 1)/2 = 0.5 m/s
Distance traveled = average speed x time = 0.5 meters.
The work done = force x distance = 0.5 joules.
And that is the same as the kinetic energy = $mv^2/2$.

I see.

So I erred in presuming that 1N applied to 1kg for one second would result in a displacement of 1m. It actually results in a displacement of 0.5m, and 1N acting through a distance of 1m would increase the kinetic energy by 1 joule it would just take longer than 1 second if the origninal velocity was zero.

Thanks, that's a relief. At least I know where to look now.

the calculus text I have on hand is rather poor. Barely a paragraph about the dot product of N*m. It's single variable calculus for non-science/engineering majors.

Feyman, I'm a fan. I'll see if I can find any of his basic physics lectures that were taped.

AlephZero said:
IF you are still confused, igmore posts #2 and #4, which are also confused and/or wrong.

#4 is correct. Some of #2 is incorrect.

## 1. What is mechanics?

Mechanics is a branch of physics that deals with the motion and behavior of physical objects under the influence of forces.

## 2. What are the two main types of mechanics?

The two main types of mechanics are classical mechanics and quantum mechanics. Classical mechanics deals with the motion of macroscopic objects, while quantum mechanics deals with the behavior of subatomic particles.

## 3. What are the fundamental principles of mechanics?

The fundamental principles of mechanics are Newton's laws of motion, which state that an object will remain at rest or in uniform motion unless acted upon by an external force, and that the force applied to an object is equal to its mass multiplied by its acceleration.

## 4. How is mechanics applied in real-life situations?

Mechanics is used in various fields such as engineering, astronomy, and biomechanics to understand and predict the behavior of physical systems. It is also used in the design and development of machines, structures, and vehicles.

## 5. What are some common applications of mechanics?

Some common applications of mechanics include designing and building bridges, cars, airplanes, and other forms of transportation. It is also used in the study of celestial mechanics to understand the motion of planets and other celestial bodies. In addition, mechanics is used in sports to analyze and improve the performance of athletes.