Search

Water flows through a water channel of rectangular cross-section, and width $d=10 \mathrm{cm}$. A leaf falls on its surface and starts moving with a velocity of $60 \mathrm{cm\cdot s^{-1}}$. The height of the water in the channel is $h=1{,}3 \mathrm{cm}$. Estimate how long it will take to fill up a $50 \mathrm{l}$ bucket. Comment on the assumptions used in comparison with the real situation.

Let us have an ideal scale which we calibrate using a state standard (etalon) with a mass $m\_e = 1,000~000~165 kg$ and a density $\rho \_e = 21~535,40 kg.m^{-3}$. By calibration, we mean that after placing the standard on the scale, we assign to the measured value the mass $m\_e$. The unknown object is weighed under the same conditions in which its volume is $V_0 = 3,242~27 dl$. What mass did we measure if we measured the weight $G = 1,420~12 N$? What is the actual mass of the object? The experiment is conducted at a place with standard gravitational acceleration $g = 9,806~65 m.s^{-2}$ and air density $\rho \_v=1,292~23 kg.m^{-3}$. Take into account that the calibration is linear, and the unloaded scale shows zero.

Measure the density of ice.

Estimate the consumption of electrical energy for one trip of the IC Opavan train. The train set consists of seven passenger cars, a 151-series locomotive and is capable of reaching a speed of $v\_{max} = 160 \mathrm{km\cdot h^{-1}}$. For simplicity, consider that all passengers are going from Prague to Opava.

A cylindrical capsule (Puddle Jumper) with a diameter $d = 4 \mathrm{m}$, a length $l = 10 \mathrm{m}$ and with a watertight partition in the middle of its length is submerged below the ocean surface and falls to the seabed at a speed of $v = 20 \mathrm{ft\cdot min^{-1}}$. At the depth $h = 1~200 ft$, the glass on the front base breaks and the corresponding half of the capsule is filled with water. At what speed will it fall now? How long will it take for the capsule to sink to the bottom at the depth $H=3~000 ft$? Assume that the walls of the capsule are very thin against its dimensions.

There are several movie scenes where a car falls into water together with its passengers. Calculate the torque with which a person must push the door in order to open it at the bottom of a lake if the bottom of the door's frame is $8,0 \mathrm{m}$ deep underwater. Assume that the door is rectangular with dimensions $132 \mathrm{cm} \times 87 \mathrm{cm}$ and opens along the vertical axis.

The water level in bath reaches height $15{,} \mathrm{cm}$. The plug has a shape of a conical frustum which perfectly fits the hole in the base of the bath. Its radii of bases are $16,0 \mathrm{mm}$ and $15,0 \mathrm{mm}$ and its mass is $11,0 \mathrm{g}$. What force does the bath bottom act on the plug? Assume that the drain pipe below contains air of atmospheric pressure.

Measure viscosity (in $\textrm{Pa}\cdot\textrm{s}$) of two different oils using Stokes' method.

We are sorry. This type of task is not translated to English.

What period of small oscillations will water in a glass container (shown on the picture) have? The dimensions of the container and the equilibrium position of water are shown. Assume that there is room temperature and standard pressure and that water is perfectly incompressible.