The Question:
An escalator is used to transport people between two floors of a shopping center.
Work out the minimum power required to operate the escalator.
(Little note on the side: Try to avoid using the internet to gather data, as the question wants you to estimate everything. Genuinely, this is a real question from my physics textbook. Enjoy)

You'll have to make a lot of assumptions, like how many people at one time, avg weight of the people, and some loss to the friction and efficiency of the motor. Then it's just weight lifted a meter in time t. What is minimum, get someone to the top in less than 10 years?

Better answer, assume they're able to walk on, so forward velocity is 3-4 mph, and assume the escalators are 45 degrees, probably more lie 30, that'll give you the vertical velocity.

I can only wish we've had such textbooks, because what everything is is the real question.

I bet the answer isn't a number. I bet it's this: The minimum power used is when the escalator is empty of people. Or, you could do a good estimate of the number of exposed steps on an escalator, estimate the average weight of a person, figure two people per step, estimate the vertical lift, assume a 45% pitch, blah, blah,....

The answer is zero due to the people on the other side of the escalator descending to the lower floor at the same time...

Onyx8 wrote:The answer is zero due to the people on the other side of the escalator descending to the lower floor at the same time...

Indeed - M.C. Escher demonstrated this quite some time ago:

crank wrote:You'll have to make a lot of assumptions, like how many people at one time, avg weight of the people, and some loss to the friction and efficiency of the motor. Then it's just weight lifted a meter in time t. What is minimum, get someone to the top in less than 10 years?

What a terrible question.

Is the escalator in an american shopping centre?

Are you trying for mass estimates? And that would be shopping center, BTW.

This is probably on of those "show your work" questions. The final answer is not important, what is important is to show that you understand the subject matter sufficiently to take into account all the variables and parameters that go into solving the question.

crank wrote:Are you trying for mass estimates? And that would be shopping center, BTW.

Well, it'd be the centre of mass in the midwest?

Thomas Eshuis wrote:

crank wrote:You'll have to make a lot of assumptions, like how many people at one time, avg weight of the people, and some loss to the friction and efficiency of the motor. Then it's just weight lifted a meter in time t. What is minimum, get someone to the top in less than 10 years?

What a terrible question.

I'd agree its a rather terrible question.
Supposedly exam boards are judging our ability to make reasonable assumptions and estimations.
I could only even begin to answer the question when doing research on the average speed of escalators, their average angle. Weight of a person, and so on.

There is however, a worse question in the book. I'll quote both part a & b, but its just part b that is the nasty one:

11. During a spacewalk, an astronaut, of mass 60kg, becomes detached from the spacecraft and is floating out into space. She has the presence of mind to throw a spanner, of mass 1kg, at a velocity of 4m/s
a. In which direction should she throw the spanner?
b. Calculate her velocity after she has thrown the spanner.

Now, you could argue that we are meant to make a reasonable assumption as to her velocity floating away from the spacecraft, as they haven't given us that, however I'm fairly sure there isn't a normal speed to be floating away from a spacecraft at. If your floating away from your spaceship and your only hope is a spanner, then "Houston, we really do have a problem". She could be floating away at 0.1m/s, 4m/s or 50m/s. Her velocity afterward could be anything at all!

Corneel wrote:This is probably on of those "show your work" questions. The final answer is not important, what is important is to show that you understand the subject matter sufficiently to take into account all the variables and parameters that go into solving the question.

If I hadn't seen any other of these questions, then I'd agree, and we've been comforted with the fact that supposedly the most marks on pure estimation will be a 1 or 2 mark question, but this book, genuinely wants us to have correct working AND accurate estimations.

c. What day is it?

I'd throw it at my mask, depending on how far I was from the spacecraft.

Seriously, I think they're just looking to see if you consider all the correct factors, whether or not all the data is available. There IS an answer however incomplete it may be.

a) She must throw the spanner in a direction that is exactly opposite the direction of a line drawn from her center of mass to the spacecraft.

b) her velocity would be 1/60th of the velocity of the spanner. 150 mm/s

No?

<edit: read the next two posts before commenting on this one. I corrected myself>

Oops... no, I don't think that was right at all.

Her velocity would be REDUCED by 150 mm/s. It depends on how fast she is drifting. You could write a formula that would include her velocity as a variable. I may be wrong about the 150 mm/s as I didn't actually do the math, but the answer is a formula. That is what they are looking for.

Like most physics problems, the spanner / spacewalk one only serves to demonstrate principals (conservation of momentum) and not reality - in reality, it is nearly impossible to throw an object so the vector passes through your own center of gravity; thus instead of obtaining a neat vector solution you'd mostly have a rotational component robbing you of effective direction change.

LjSpike wrote:

Corneel wrote:This is probably on of those "show your work" questions. The final answer is not important, what is important is to show that you understand the subject matter sufficiently to take into account all the variables and parameters that go into solving the question.

If I hadn't seen any other of these questions, then I'd agree, and we've been comforted with the fact that supposedly the most marks on pure estimation will be a 1 or 2 mark question, but this book, genuinely wants us to have correct working AND accurate estimations.

Oh in that case I take back what I said. How is accurate estimation of importance is beyond me. That is what Google is for unlike for working it out.

Rumraket wrote:Is the escalator in an american shopping centre?

Then you would have to double the mass of the people using it...