How Long Does a 25% Efficient 750W Motor Take to Lift a 45kg Object to 9m?

[Jabababa]

Homework Statement

A 45 kg object is lifted vertically at a constant speed to a height of 9.0m by a 750 W electric motor. If this motor is 25% efficient in converting electric energy to mechanical energy, how long does the motor take to lift the object?

Homework Equations

The Attempt at a Solution

I have no idea how to even start this question. I don't understand why it is in electric circuit unit.

 

[PeterO]

Homework Statement

A 45 kg object is lifted vertically at a constant speed to a height of 9.0m by a 750 W electric motor. If this motor is 25% efficient in converting electric energy to mechanical energy, how long does the motor take to lift the object?

Homework Equations

The Attempt at a Solution

I have no idea how to even start this question. I don't understand why it is in electric circuit unit.

The mass being raised will be gaining Gravitational Potential Energy. The electric motor will be supplying energy at the stated rate - allowing for the efficiency - so you can calculate how long it takes to supply the requisite amount of energy.

 

[Jabababa]

sooo is it like this?

P= W/t
W= Ep = mgh
P= mgh/t

since its 25% efficient then its p*0.25
750/4=(45)(9.8)(9)/t
t=(45)(9.8)(9)/(750/4)
t=21.168sec
=21sec

is this what u got?

 

[PeterO]

sooo is it like this?

P= W/t
W= Ep = mgh
P= mgh/t

since its 25% efficient then its p*0.25
750/4=(45)(9.8)(9)/t
t=(45)(9.8)(9)/(750/4)
t=21.168sec
=21sec

is this what u got?

I didn't get anything - you are the one calculating the numbers, I am just explaining the situation.

 

[Jabababa]

alright, does my work look good? Just need some confirmations.

 

[PeterO]

alright, does my work look good? Just need some confirmations.

At this stage you need some care and some confidence. Were you careful with the values you used? Does the answer look reasonable?

 

[Jabababa]

At this stage you need some care and some confidence. Were you careful with the values you used? Does the answer look reasonable?

Sigh, just need some confirmations...if u don't want to confirm no need to reply with all those confidence and care stuff. I am being very cautious because this will affect my mark and unlike you, i need good marks to get into universities. So this will have a big effect on my life.

 

[PeterO]

Sigh, just need some confirmations...if u don't want to confirm no need to reply with all those confidence and care stuff. I am being very cautious because this will affect my mark and unlike you, i need good marks to get into universities. So this will have a big effect on my life.

Rather than head to a final formula and then substitute number s and hope consider the following:

What is the total gain in energy of the mass (in Joules).

At 750 W, how long would it take to gain that energy?

What is THEN the effect of the efficiency of the motor.

 

[Jabababa]

hmm well at 750W it takes 5.292 seconds...and its 25% efficient...then its 5.292 * 0.25 = 1.323 seconds

so the answer is either 1.323 seconds or 21 seconds...

In real life i have never actually worked with motors lifting objects and such...so I am not sure which is more plausible.

 

[PeterO]

hmm well at 750W it takes 5.292 seconds...and its 25% efficient...then its 5.292 * 0.25 = 1.323 seconds

so the answer is either 1.323 seconds or 21 seconds...

In real life i have never actually worked with motors lifting objects and such...so I am not sure which is more plausible.

THINK !

If the motor was 100% efficient it would take 5.292 seconds.

If the motor didn't work at all it would take for ever - not happen instantaneously!

So how long will it take if the motor is 25% efficient ?

 

[Jabababa]

oh ok now i get it, if its 100% efficient its at 5.292 seconds...so if its at 0% then its not going to do anything. Then 25% is between 100% and 0% then it must take longer, 21seconds.

...so my 1st answer was right...anyways thanks for the help. Sorry if i snapped before and offended you. Its almost 5am, haven't gotten any sleep.

 

[PeterO]

oh ok now i get it, if its 100% efficient its at 5.292 seconds...so if its at 0% then its not going to do anything. Then 25% is between 100% and 0% then it must take longer, 21seconds.

...so my 1st answer was right...anyways thanks for the help. Sorry if i snapped before and offended you. Its almost 5am, haven't gotten any sleep.

It is always useful to break the question into parts, like I indicated, so you can assess if the answers you are getting are reasonable.

It is very easy to make a slip and multiply by 1/4 rather than divide, but if you calculate on the way you should notice.

While re-arranging the formulae the substituting gives an answer you often don't know whether it is reasonable.

What I would have done is a rough check using g = 10 for simplicity, and a height of 10m.

mgh then becomes 45 x 10 x 10 = 4500.

With a 1000W motor that would take 4.5 seconds.

25% efficiency would means 4 times as long - or 18 seconds.

[note that all those figures can be calculated as mental arithmetic - no calculator needed].

Now reality: g is a little less than 10, and the height is a little less than 10 - so the time would be smaller. But the motor is only a nominal 750W so that would make it longer. SO I expect an answer about 20 seconds.

Your formula manipulation gave 21, so I would have been happy with that figure.