# How much energy is needed to move an object in lossless environment?

How much energy is needed to move a 1 kg object for a distance of 1 meter horizontally in a constant speed (assuming no energy is wasted)?

Does it matter what is the movement speed (assuming not zero)?

Does it matter whether the object accelerates or decelerates as long as the direction of the movement isn't altered?

• Do you want the object to go only 1 meter? very little energy will get the object moving and it will ontinue to move forever if there is no friction. Newton's laws. – Peter R Nov 13 '15 at 21:15

If no energy is wasted, it will take no energy to move the object.

You started by saying "at constant speed". This must mean that the object has speed at the start of your time interval - otherwise it would have to accelerate and speed is not constant. Ditto at the other end - it can't decelerate at the end.

And in between there is no dissipation ("waste") of energy.

The conclusion is that this is an idealized scenario in which Newton's first law applies: absent any forces, an object continues in a straight line at constant speed. And if there are no forces, then no work is done.

Note that the last part of your question "does it matter whether the object accelerates or decelerates..." is inconsistent with the conditions of the first paragraph ("at constant speed"). If the object decelerates, it is actually giving up energy to "something": if it is not "wasted", it must be transferred to something else (for example a spring is being compressed). In that case, energy is extracted from the object, and the moving "required negative energy". Similarly, if it accelerates (perhaps a loaded spring gave it a push) then it will have more energy at the end than at the beginning, and it took work to move it. The amount of work in either of these cases would be

$$W = \frac12m(v_2^2 - v_1^2)$$

• From your answers, I realized that I didn't know how to ask what I really wanted to know. Let's say there is some friction, the body starts at rest and accelerates in time t to some speed v, and decelerates in time t to zero (assume there is time t_1 > 0 where the object is at constant speed). How much energy, in this case, will be needed, assuming friction, t, v are variables in the formula for the energy ? – Moti Berger Nov 14 '15 at 9:38
• Is the friction and the distance known? Does friction depend on velocity? In the simple case (known distance and constant force of friction) the work done will just be $F_f\cdot x$ - force of friction times distance. The extra energy needed to accelerate at the beginning is "given back" as the object decelerates at the end. – Floris Nov 14 '15 at 13:50

How much energy is needed to move a 1 kg object for a distance of 1 meter horizontally in a constant speed (assuming no energy is wasted)?

No more than $mv^2/2$.

Does it matter what is the movement speed (assuming not zero)?

Yes it matters. The higher the speed the more energy the mass needs.

Does it matter whether the object accelerates or decelerates as long as the direction of the movement isn't altered?

Yes, because $Work = F*d = m*a*d$. As you see the higher the acceleration the more work is needed.