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11 Jan 2020 : If my washing machine were a car, how fast would it travel? #
In Finland I live in a small flat, so spend more time in close proximity to my washing machine than I'd really like. But as the drum spun up to create its highest pitched whine this morning while I was cleaning my teeth, the speed of it impressed me.
So I wondered: if it were a vehicle, how fast would it be travelling? It shouldn't be too hard to calculate with the information available. What are the pieces needed? The radius of the drum and the angular velocity should be enough.
For the angular velocity we just need to check out the technical specs from the manual. That was easy as I already carry a copy around with me on my phone to help me figure out which programme to use.
Today I was running a 30°C Cotton wash, which spins at 1200 rpm.
$$
1200 {\rm\ rpm} = \frac{1200 \times 2 \pi}{60 {\rm\ s}} = 40 \pi {\rm\ radian} {\rm\ s}^{-1}
$$
There's nothing in the manual about the drum size, so I reverted to a tape measure.
So that's a diameter of 47cm, or a radius of 0.235m. That's the inside of the drum of course, but that is the bit the clothes have to deal with.
This gives us a linear velocity of
$$
40 \pi \times 0.235 = 20.5 {\rm\ m}{\rm s}^{-1} = 106.3 {\rm\ kph} = 66.1 {\rm\ mph}.
$$
So if my washing machine were an electric car, it'd be zipping along at nearly the speed limit. That's surprisingly nippy!
So I wondered: if it were a vehicle, how fast would it be travelling? It shouldn't be too hard to calculate with the information available. What are the pieces needed? The radius of the drum and the angular velocity should be enough.
For the angular velocity we just need to check out the technical specs from the manual. That was easy as I already carry a copy around with me on my phone to help me figure out which programme to use.
Today I was running a 30°C Cotton wash, which spins at 1200 rpm.
$$
1200 {\rm\ rpm} = \frac{1200 \times 2 \pi}{60 {\rm\ s}} = 40 \pi {\rm\ radian} {\rm\ s}^{-1}
$$
There's nothing in the manual about the drum size, so I reverted to a tape measure.
So that's a diameter of 47cm, or a radius of 0.235m. That's the inside of the drum of course, but that is the bit the clothes have to deal with.
This gives us a linear velocity of
$$
40 \pi \times 0.235 = 20.5 {\rm\ m}{\rm s}^{-1} = 106.3 {\rm\ kph} = 66.1 {\rm\ mph}.
$$
So if my washing machine were an electric car, it'd be zipping along at nearly the speed limit. That's surprisingly nippy!
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