I am often a DIY’er and I have a really heavy hatch (32 kg) at home that I want to open automatically with an electric actuator. Something like the hatch in the image below. You can buy these actuators for 50 to 100 euros online: but which one do I need? or: What is the minimal and maximal length (and stroke) that I need? What is the force the actuator should be able to push? I made a schematic model, with ...
My local supermarket runs a campaign where you can collect stickers for a photo album 📔 with historic pictures of our pitoresk town. For every 10 euros you get a package of 4 stickers and in total there are 229 unique stickers. My question is: How many stickers including doubles do you need to get a full album? 💁 This is known as the Coupon collector’s problem (a variant of the birthday problem). The first card you will always have a new unique card. The change that the second card is a new unique card is $1$ minus the change that you have the same card as the first: ...
While skiing in the Swiss Alps last winter, I got into a discussion about speed. Following my engineering knowledge, your skiing speed does not depend on your own mass. Without the intention to offend anyone, skiing is basically a form of falling at an angle. We can build a model based on Newton’s second law where acceleration times mass is equal to the resultant force. We can see that mass ($m$) will drop out of the equation: ...