Finding out the power by using average velocity....

[albertlee]

How to find out the power by using average velocity?

given info: object:1kg, average velocity:1m/s, distance:10m


Aprciate for the responds

[wolfson]

Kinetic energy = 1/2 mv^2

m= mass
v= velocity

Units of Joule

PE = mgh

m= mass
g= gravity (9.81ms^-2)
h = height (metres)

Unity joule

Average power = workdone / time (secs)

Work done = force (9.81) * distance moved.

If a force F acting on a particle has accelerated the particle to a velocity v , the instantaneous power expended is:
power = F * v
There's a few off the top of my head.

[darkbob5150]

How to find out the power by using average velocity?

given info: object:1kg, average velocity:1m/s, distance:10m




I take it you mean frictionless horizontal motion so no gravity issues.

Power is the rate of doing work - and is also given by Force x (average)
Velocity.

What I'd do is work out what constant acceleration over a distance of 10m you need to produce an average velocity of 1m/s.

Average velocity over a period of constant acceleration is given by (Final velocity - initial velocity)/2. In this case (assuming you start from rest) the final velocity is 2m/s and the time taken to travel the 10m would be distance/average velocity = 10sec. So the acceleration (change in velocity with time) would be 0.2 m/s^2

You now have the force you would have to apply to produce this acceleration (assuming frictionless horizontal motion) from F = ma.

Put the numbers into Power = Force x average velocity and that'll be it.

Work is given by Force x Distance moved (in the direction of the Force) so if you wanted to do it that way then you have to divide by the time to get the Power.

[albertlee]

Thx Dark........But the equation from Wolfson confused me: k.e. = 1/2mv^2
since m=1kg, v=av*2=2m/s
Can I work it as k.e.=1/2(1)(2^2)?

But what I wonder is where does this equation take the distance into acount?

Any help? thx

[dave]

It doesn't, it just takes into account the kinetic energy an object has at a specific instant in time.

[albertlee]

Ok, just for sure, is my way of doing correct in my previous message?

[darkbob5150]

Thx Dark........But the equation from Wolfson confused me: k.e. = 1/2mv^2
since m=1kg, v=av*2=2m/s
Can I work it as k.e.=1/2(1)(2^2)?

But what I wonder is where does this equation take the distance into acount?

Any help? thx


Ok, the equation for kinetic energy - as Dave said - gives you the energy that the object has, at a particular time, because it is moving. You would use the KE in a question when there are no external force acting because energy would then be a conserved quantity - the amount of energy (kinetic + potential) would remain constant allowing you to work nice little things out.

Because this question is about average velocities it means that the velocity changes (accelerates) as the object moves which would indicate that there are external (unbalenced) forces acting. External forces mean that you can't apply the conservation of energy because the force will either add energy to the system (your moving object) like pushing it to make it go faster, or take it away like friction.

If you take the extra energy that the force introduces to the system into account then you can use the energy formula:

Work done on an object is really just the change in energy of that object due to the applied force. It only depends on the initial and final states which is a useful and important feature.

In this case (if you take the setup I had earlier where the object starts at rest, constantly accelerates and reaches a top speed of 2m/s after 10m) you can take the work done on the object as the change in KE ( = Final - Initial = 1/2 x m x 2^2 - 0 ) and you get the same answer as before for the work. Divide by the time taken to get the power.

[darkbob5150]

sorry, just read the numbers in your reply properly. Yeah, you had it right - didn't need all that boring crap I wrote, but it explains a little bit as to why it's right!

Soz

[albertlee]

Thx Dark, the information is relavant and helpful.........

Anyway, I have also problems with the direction of forces.................

Can anyone tell me the basic concepts of the direction of force? for eg, how can an object move diagonally? or move in an indefined route, since it makes even harder to measure the distance and to say the direction of the force.........


Aprciate for furthur helps!

[albertlee]

Anybody?

[swansont]

Thx Dark, the information is relavant and helpful.........

Anyway, I have also problems with the direction of forces.................

Can anyone tell me the basic concepts of the direction of force? for eg, how can an object move diagonally? or move in an indefined route, since it makes even harder to measure the distance and to say the direction of the force.........


Aprciate for furthur helps!

The net force is always in the direction of the acceleration, but this doesn't mean that it has to be in the direction of the displacement (which is given by the velocity vector)

"Diagonal" motion is just an artifact of a coordinate system, which is arbitrary.

[darkbob5150]

Sounds like you need Newton's first law of motion:

A body will continue in a state of rest or uniform motion in a straight line unless acted on by an unbalanced external force.

When an unbalanced force acts on a body it will cause it to accelerate in the direction of the applied force. The acceleration lasts for as long as the force is applied.

[The important thing about forces are that they are vectors, that means that every force must have both a magnitude (how hard you push it) and a direction (what direction you push it in).]

So forces tend to change the direction something travels in and/or change the objects speed. I'm not too sure what you mean by your questions......an object travelling in a diagonal line is not under the influence of an unbalanced force (unless it's speed is changing). Do you mean it's moving under gravity?

An undefined force that is changing it's magnitude / direction would cause the object to change it's speed / direction accordingly and travel in an undefined path.

Here's an example that might help...?

If you throw a ball diagonally up into the air (like you were throwing it to someone a few metres away) then think about what that would do. The gravitational force acts straight down with a magnitude of: Mass of the ball x Acceleration due to Gravity (from Newton's 2nd law F = Ma). So the vertical (up and down) motion of the ball is subject to an acceleration and will therefore cause the ball to slow down when heading for the sky, stop and then speed up towards the ground. The force due to gravity is constant, so the speed of the ball is always changing by a constant amount.
The horizontal motion has no gravitational force acting on it, so the ball's direction / speed parallel to the ground does not change - your friend catches it with the same horizontal speed as you threw it with.
This technique (resolving components of motion) allows you to resolve an objects motion into directions at right angles to each other to make a problem simpler. Here you can make the horizontal motion separate to the vertical motion so the horizontal motion is just a constant motion in a straight line problem, and the vertical motion is just acceleration in one dimension.

[albertlee]

ok,maybe my question is not complete enough........How can explain the direction of force of a plane flying diagonally? if the direction of force is horizontal?

Please help

[albertlee]

If the previous message is not clear enough, here is an example which i confuse:
http://a.domaindlx.com/supershare/d.bmp

How can we find the work done? according to direction of force and the distance?


Please help!

apreciate

[wolfson]

Work = F * Cos degrees

Thus:

Work = (400 N) * (30m) * (Cos 30) = 10392.30 J = 10.39 KJ

[albertlee]

Wolfson, What is Cos degree? and How does it work as a concept to the direction of the force?

Please help.

[wolfson]

You need to use |cos| to calculate the force, it is used as you have a angle, and the only way we can calculate 400N on a 30 degress elavation is by using cosine, (you may also need to use |sine| in other parts of physics), have you come accross trigonometry?, same concept here. So by using cos (seen an your calculator as cos), we can use Equation 1.

Work = F * Cos theta
EQUATION 1

thus

We can find out the work done (SI unit joules) do you understand?

[albertlee]

Ok, wolfson, the key to this whole question is the problem of cos.....
First of all, I know nothing about "cos"...And i dont know what it is used for, and how,,,
The only thing I know is that i can see a cos button on my calculator.......:-)

Any futhur help on cos?

[swansont]

You need to break the forces down into their x and y components. Only the net force in the x direction (horizontal) does any work for displacement in that direction. Any components in the y direction make no contribution.

[wolfson]

You have not done trig so just imagine it as if you have a degree on the horizontal you NEED to use cosine.

[wolfson]

Or i could teach you trig.

[albertlee]

Ok....Got a bit of sense.........it sounds like vectorial analysis....

Anyway, I am still very fresh with cosine.......

Any body helps?

[albertlee]

Oh, forget about my previous message...........
I know the concept of cosine just now...............it is adj./hyp. in a right-angled triangle, but.......

What i really confused is still about how does it do to the direction of the forces and distance.

Any help?

[albertlee]

Any body?

[wolfson]

it is adj./hyp. in a right-angled triangle

So you have done trig :-)

[albertlee]

Again, What i really confused is still about how does it (cosine) do to the direction of the forces and distance.........in the solution of work?


Any help?

[swansont]

Again, What i really confused is still about how does it (cosine) do to the direction of the forces and distance.........in the solution of work?


Any help?

The dot product, that gives you the cosine, tells you what the projection of the vectors are onto each other. i.e. how much of the force is in the same direction as the displacement. A force that is perpendicular to the displacement can't add or remove energy, thus it does no work. A force that is in the exact same direction as the displacement does the maximum work possible. The cosine, in essence, tells you how efficiently you are doing the work with that force.

[albertlee]

Sorry Swansont, I still dont get it, you say that a force that is perpendicular does no work, but why you cannot do cos 90 then?
On the other hand, I know this is impossible because it is not in the direction of the force, but by that, if in my case(see in the picture of the 1st page in the thread), why we should do "cos"? we can just force times distance, because the distance is in the direction of the force................


Any more helps?


Really apreciate for the responds

[swansont]

Sorry Swansont, I still dont get it, you say that a force that is perpendicular does no work, but why you cannot do cos 90 then?
On the other hand, I know this is impossible because it is not in the direction of the force, but by that, if in my case(see in the picture of the 1st page in the thread), why we should do "cos"? we can just force times distance, because the distance is in the direction of the force................


The cosine tells you the component of the force doing the work. The perpendicular component doesn't contribute.

[albertlee]

Ok, Swansont, in ur previous message, the most confusing word is "component", I dont get what u r talking about component in this case.......Can u explain it?

How can something doing not in the direction of force still can move a distance that is not in the direction?
in my case, the trolly is moving horizontally, but the force's direction is diagonal.....

[swansont]

Ok, Swansont, in ur previous message, the most confusing word is "component", I dont get what u r talking about component in this case.......Can u explain it?

How can something doing not in the direction of force still can move a distance that is not in the direction?
in my case, the trolly is moving horizontally, but the force's direction is diagonal.....

A force that is at some angle is the same as the sum of two forces, one horizontal and the other vertical, and whose magnitude is given by the Pythagorean theorem if you were to draw the right triangle with the three vectors. The horizontal and vertical parts are the components. How big any given component is depends on the angle - you can use trig to figure that out.

In your example there are other forces present that are not named. Gravity, for instance, exerts a force downward. The upward component of the force the rope exerts acts against gravity, and makes no contribution to the forward motion. That component would be given by the sine of the angle (400N * sin30). The component of the forward force is given by the cosine (400N * cos30) (using the angle in your drawing)

(400*sin30)2+(400*cos30)2=4002
so you can see the component forces add (as vectors) to be the total force of 400N

[albertlee]

So..............Why the trolley does not move upwards but only forwords as the force is exerting diagonally?

[albertlee]

Any body?

[albertlee]

any body?

[swansont]

any body?

Prompting people when they're offline doesn't do any good.

The object would accelerate vertically if the vertical component of the force is greater than the weight. But that information isn't in the diagram.