# Help calculating power required to lift a mass

#### CantBeRocketScience

Hello,
I realize that this is a Physics 101 pop quiz problem, but it's been 45 years since I was in Physics 101

I'm trying to figure out what size of a 12VDC motor to purchase to perform the following work.

I have a 40 Kg tool that I want to lift 30cm within 60 seconds.

If you need the length of a lever arm to calculate this, then assume a gear wheel of 2.5 cm in diameter.

Any help would be appreciated.

Thanks,
John

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#### benit13

Minimum work done for lifting:
$$\displaystyle \Delta W = m_{tool} g \Delta h$$

If this is to be achieved in a time limit, then the minimum power is:
$$\displaystyle P = \frac{\Delta W}{\Delta t} = m_{tool} g \frac{\Delta h}{\Delta t}$$

Therefore, the minimum power of the generator,

$$\displaystyle P_{generator} = P = m_{tool} g \frac{\Delta h}{\Delta t}$$

Substituting values:

$$\displaystyle P_{generator} = 40 \times 9.81 \times \frac{0.3}{60} = 1.962 W$$

However, this doesn't take into account many things, such as:

i) efficiency of the power generator and other equipment that may be involved;
ii) a driving force that may not be perpendicular to the vertically upwards direction;
iii) additional forces that oppose the driving force (like friction);

#### CantBeRocketScience

Thank you benit13

Hmm,
The math seems right.
40kg x 9.81 = 392.4 Newtons
392.4 Newtons X 0.3 meters = 117.72 Newton-meters
117.72 Newton-meters / 60 seconds = 1.962 Newton-meters/second
1 Newton-meter/second = 1 W
thus 1.962 Watt

However,
1.962 W doesn't seem like very much if 1 HP = 746 Watts.
I would have ballparked it in the vicinity of 1/4 hp (+/- 1/8hp) or 10 times the calculated power needed.
John

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#### Cervesa

Hmm, 1.962 W doesn't seem like very much if 1 HP = 746 Watts.
I would have ballparked it in the vicinity of 1/4 hp (+/- 1/8hp)
John
A lift of 30cm in 60 seconds is pretty slow.

Ignoring any non-conservative losses, a power of 1/8 HP would raise the 40kg mass 30 cm in a little over a second.

#### benit13

However,
1.962 W doesn't seem like very much if 1 HP = 746 Watts.
I would have ballparked it in the vicinity of 1/4 hp (+/- 1/8hp) or 10 times the calculated power needed.
John
Agreed, it's a minimum power; it's the value required to raise the object without any waste energy over the whole 60 seconds.

If the additional factors taken into account at the end of my post are considered, the model will become more sophisticated, but will yield larger power values that will be more realistic.

#### oz93666

This motor is perfect for what you want ... 7W ..too much power ...24V or 12V ... there are dozens of different designs on eBay , many different RPMs https://www.ebay.co.uk/itm/FJ-107RPM-Aluminum-electrifying-Gearbox-DC-Gear-Motor-Micro-Speed-Reduction-Hig/233206052001?hash=item364c29f4a1:g:2xYAAOSwsQNcviTH

The one above has built in gears.... Motors of the size pictured above have an efficiency better than 80%( output feeding gears/electrical power IxV) ... Then losses in the gears perhaps 30% .... maybe 10% loss in mechanism to lift ....So a 4Watt motor wold do it ...lets say 5W to be sure....

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