2th Round of 25th year

Select year

Series

1. ... rainbow(2 points)

What would a rainbow look like if it was raining oil, sulfuric acid or glass instead of water?

2. ... green gnome(2 points)

What would you see if you were standing at one end of a rainbow?

3. ... lifting boats(4 points)

figure

A small Scottish town decided to build an elevator for boats. It consists of two big containers filled with water that are suspended from the ends of a long rod. This rod is attached in the middle to a motor that can rotate the whole system. A boat enters one of the containers and waits to be lifted. What is the minimum power of the motor for this lift to work?

4. ... ball on a train(4 points)

figure

Small weight of mass m is suspended from the ceiling of a train on a string of length $l$. The weight is hanging a distance $d$ from a wall (see picture). Suppose the train starts to accelerate in the direction perpendicular to the wall. Find a condition on the acceleration such that the weight eventually touches the wall. How long does it take before this happens? Assume that $d$ is less than $ l/5$.

5. ... hair(4 points)

A hair with a lot of curls can be approximated by a spring (in other words it can be described by the exact same parameters – radius, inclination and material constants). How much longer is the hair if it hangs vertically in a gravitational field compared to the case that it lies horizontally on a table? Assume that the inclination is very small.

P. ... elevator(5 points)

Suppose that you are in an elevator when the rope that holds it breaks. Can you save yourself from dying by jumping right before the elevator hits the ground? What is the maximum speed of the falling elevator such that you could save yourself this way? You will need to look up or estimate the maximum impact velocity that a human can survive.

E. ... lenses(8 points)

Determine type and focal length of enclosed lenses. (If you're new to FYKOS just send as an email to <tt>cocky@fykos.cz</tt> and we will send you a set of lenses.)

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