## Piston

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Jayraj
Posts: 15
Joined: Sun Oct 21, 2018 11:06 am UTC

### Piston

You have a rectangular shaped piston placed against the wall.

1 inch of the wall just above the piston is covered with grease.

The range of motion of the piston is only one inch up and back to its original place.

Once switched on, the piston performs this motion 3 times per second.

Given that the grease does not diminish or dry,

how many inches of the piston will be lubed with grease in 2 seconds.

bjazz
Posts: 7
Joined: Fri Jul 08, 2011 8:40 pm UTC

### Re: Piston

Making sure I understand the question correctly - the piston will move up get the top inch of it greased, then smear the grease down the wall on its return stroke, making the grease spot 2 inches tall on the wall, so when it moves up again you would say two inches of the piston will be greased, and so on... correct? If so:
Spoiler:
With each up-stroke, the piston will cover the existing grease spot, and drag it down the wall on the return stroke, extending it by 1 inch each time. After 1/3 second (the first complete stroke), the top 1 inch is greased. Each successive stroke extends it by 1 inch. In 2 seconds, the piston completes a total of 6 strokes, so after another 5 strokes, an additional 5 inches is greased, for a total of 6 inches. Am I missing anything?