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jinx007 · 2010-06-13 13:55:17

Dynamics question please help i am stuck...!

A model helicopter of mass 5.0 kg rises with constant acceleration from rest to a height of 60 m in 10 seconds. Find the thrust exerted by the rotor blades during the ascent.

The answer in the book is 55 N

Astro · 2010-06-20 08:42:52

Ok, i won't do this for you, you can work it out, but i can help.

Thrust is simply a force, just like weight, and this is in 55 Newtons then a solution.

So weight and gravity can be taken into account, including the gravitational potential and height.

working with a constant acceleration makes things a lot easier, so you know the mass - a constant acceleration can be appliable to the equation of motion:

$F=Ma$

Since we have a height involved, we also have the idea of kinetic energy and potential energy - in your condition, your object began stationary, so it's height from the ground must began as:

$gh=v*^2$ because $v=0$ and $g$ is the gravitational acceleration. From this, we find the height equation given as $-\frac{h}{2}= \frac{v*^2 - v^2}{-2g}$ states that something is $\frac{h}{2}$ units from the ground. To find the work done for the force of thrust, one might also want to use the equation $W_k=Fh$ which is the work due to the kinetic energy, so equally $W_k=mgh$ because $GPE=Wh$ where $GPE$ is the gravitational potential energy and $W$ is the work, and inversely related also is the height $h$ .

So for any object which for arguements sake has a force applied where the acceleration is an upwards motion, the unit of the gravitational potential energy is the same measurement of the work done; so we must apply it an amount of potential energy equal to the work applied to it to begin with.