Weighing a ceiling fan

Classical Mechanics Level 1

A ceiling fan is hung on a hook through a spring balance, which reads $M$ kg when the fan is off.

If the fan is switched on and rotates at a constant speed, then what will be the reading on the balance?

Details and Assumptions:

Ignore the effects of torque.
The fan blows the air downwards.

Less than

M

kg Equal to

M

kg Greater than

M

8 solutions

Marta Reece
Jun 1, 2017

The fan is pushing the air down, so the air is lifting the fan up.

A simple answer...perfect for my tiny brain!

William Huang - 4 years ago

Yeah, that is true, as the air is blown downwards, the air pushes the fan upwards and the fan would feel lighter. Can you give an estimate of how much difference of weight should generally occur for an average sized fan?

Rohit Gupta - 4 years ago

I assumed it was talking about M in Mass (As it was in kg) and not weight - if the answer required was for weight, the question should've been in Newtons

Imtiaz Hasham - 4 years ago

The weighing scales are generally calibrated to give the readings in kilograms.

Rohit Gupta - 4 years ago

It was the result of a measurement by a scale. So that fact, rather than the units used on the scale, was the key clue in this case.

Marta Reece - 4 years ago

Is this a test of our knowledge of fans? If we are we supposed to infer from the picture that this fan pushes air down, then we can also imagine that it is positioned in a stairwell with a strong down-draft. An unfair question.

s j - 4 years ago

Well, it is mentioned that it is a ceiling fan, also the diagram makes it clear.

Rohit Gupta - 4 years ago

Ignoring assumptions about directions (which have since been addressed in the problem's description), even if it were positioned in a stairwell with a strong down-draft, its weight would still be $M$ kg when turned off (because it's the first reference point we have for the fan's weight), then it would also still be less than $M$ kg when turned on (because the drag of the fan against the air is less).

Jonathan Quarrie - 4 years ago

Jonathan Quarrie
Jun 2, 2017

The spring balance is measuring the fan's weight, which is a product of the fan's mass and the net forces acting upon it - in this case, when the fan is off, the net force on the fan can be considered to be Gravity.

Using Newton's 3rd Law , we can determine that when the fan is on and interacts with the air, forcing the air downwards, there is an equivalent force acting upon the fan in the opposite direction, which contributes to the net force acting on the fan. This new force on the fan opposes Gravity, thus decreasing the fan's measured weight - $\boxed{\text{Less than M kg}}$

This solution has been reworded, now that the problem includes an assumption about the direction in which the fan blows.

Jonathan Quarrie - 4 years ago

Yes, that was indeed necessary to mention. Otherwise, the fan may weigh greater than $M \text{ kg}$ .

Rohit Gupta - 4 years ago

David Conaway
Jun 4, 2017

I assumed correctly but my fans on my ceiling can spin either way for up or down draft. They should have stipulated which direction

Thanks, for pointing it out. The problem statement has been updated.

Rohit Gupta - 4 years ago

Did they recently add this assumption.

Walter Neilsen-Steinhardt - 4 years ago

Correct! Fans can rotate in either direction depending on what the user wants

Stephen Garramone - 4 years ago

Rotation direction is immaterial. The problem statement indicates that the air is blown "downwards"

Adrian Donen - 3 years, 12 months ago

Travis Donnelly
Jun 4, 2017

Most ceiling fans have the capability to rotate in either direction. So the force could be greater or less. The question assumes a downward flow of air. Unfortunately from growing up around cigarette smokers I know that ceiling fans are often run in 'reverse' such that the weight would be more than M.

Thanks, for pointing it out. The problem statement has been updated.

Rohit Gupta - 4 years ago

Mainak Chaudhuri
Jun 4, 2017

The fans when switched on and rotates pushes the air just below them. Now the pushed air exerts an equal and opposite force on the fan in the upward direction against the direction in which the weight acts. So the system gets a lift and the spring is contacted showing the reading of weight less than original weight i.e < M kg

Exactly, this is also extended to helicopters. Where the wings rotate at such a high speed that they generate enough lift to carry the weight of the helicopter.

Rohit Gupta - 4 years ago

Bassit Ali
Jun 13, 2017

Turing effect of force is acting in downward direction hence the fan is being pushed in upward direction

Amjed Almousa
Jun 13, 2017

The answers should not be in Kg. Mass does not change weight (Newtons) is what changes.

The spring balances are calibrated to show their readings in kilograms.

Rohit Gupta - 3 years, 12 months ago

The problem is solvable as stated but I agree that more precise language would be nice. The problem as stated facilitates the further confusion between weight and mass. Even in some of these solutions people are stating things like "weighs M kg."

george palen - 2 years, 11 months ago

Chuck Malo
Jun 6, 2017

The fan blade is working like the propeller on an airplane, providing thrust - in this case downward - pushing the fan assembly up thus reducing the weight.

I would say it works more like the fan of a helicopter which provides a lift to the helicopter. So, if the fan speed is sufficiently increased, then we may have the spring balance show zero reading as well.

Rohit Gupta - 4 years ago

Weighing a ceiling fan

8 solutions

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