Search

In the winter, Matěj found a $0{,}5 \mathrm{m^3}$ bale of polystyrene and decided to use it. He made a cube-shaped box out of it. Then he cut the ice from a frozen pond, which he stored in the polystyrene cube in the cellar, where the temperature is constant $9{} \mathrm{\C }$. How big should Matěj make the cube so that he has the largest amount of ice left in it after half a year? And how many kilograms of ice will he have left? Suppose that the ice from the pond has a temperature of exactly $0{} \mathrm{\C }$. Ignore the volume of polystyrene used for the edges of the cube.

Hint:: The thermal conductivity coefficient is the easiest parameter of polystyrene to find.

Using current technology, how much fuel would it take to carry an object of mass $m=1 \mathrm{kg}$ into low Earth orbit?

What is the smallest amount of gadolinium $148$ needed to put together to cause local melting from the heat generated by its nuclear decay? Assume that only $\alpha $ decays take place and the material is at room temperature in the air.

Estimate the upper limit of work that can be done on Earth over the long term. The planet must remain habitable and, if possible, with the same climate for future generations.

The FYKOS-bird arrived at his cottage in the middle of winter with only $T_1 = 12 \mathrm{\C }$ indoors. So he lit a fire in the fireplace by using wood of heating value $Q_0 = 14{,}23 \mathrm{MJ\cdot kg^{-1}}$. How much wood does he need to burn to heat the air inside to $T_2 = 20 \mathrm{\C }$? The cottage is in the shape of a rectangular cuboid with dimensions $a = 6 \mathrm{m}$, $b = 8 \mathrm{m}$ and $c = 3 \mathrm{m}$. A roof is in the shape of an irregular recumbent triangular prism with a height of $v = 1{,}5 \mathrm{m}$, the upper edge of which is the axis of the cottage layout. The air occupies $87 \mathrm{\%}$ of the volume of the cottage and its specific heat capacity is $c_v = 1 \mathrm{007 J\cdot kg^{-1}\cdot K^{-1}}$. Does the result match the expectation? Discuss the simplicity of the model used.

What parameters does a planet need to have to keep its atmosphere comparable to the Earth? What conditions are essential for the planet to gain such an atmosphere?

A cylindrical jar made of glass has a height $h = 7,0 \mathrm{cm}$ and an inner radius $r = 2,5 \mathrm{cm}$. We pour hot apricot jam at temperature $T_0 = 80 \mathrm{\C }$ into the jar, we close the lid and let it cool down. Note that we didn't fill the jar to the top, but left some air between the jam and the lid. If a force of at least $F = 4 \mathrm{N}$ is applied, a sound is heard as the lid suddenly incurves. We heard this sound $t\_i = 30 \mathrm{min}$ after the jar had been closed. If jam hardens at temperature $T\_h = 60 \mathrm{\C }$, was it to be already hard when the lid incurved?

Bonus: How long after closing the jar will the jam harden? Assume that the temperature is evenly distributed throughout the jar and that the cooling rate only depends on the difference in temperatures of the jar and its surroundings $T\_{s} = 25 \mathrm{\C }$.

We have a U-tube with length $l$ and cross-sectional area $S$. We pour volume $V$ of water into the tube. The volume $V$ is large enough that the whole U-turn is filled with water but $Sl > V$. When water levels in both arms of the tube are at rest, we seal one of the arms. What is the period of small oscillations of water in the tube?

A lid has a shape of a hollow cylinder of radius $6,00 \mathrm{cm}$. The lid under which is an air of atmospheric pressure $1~013 \mathrm{hPa}$ is placed in a horizontal washbasin. While doing the dishes, we start filling the washbasin with water at room temperature. The water also gets under the lid and compresses the air trapped inside. At a certain moment, the lid starts floating. At what height is the water level at that moment? The lid weighs $200 \mathrm{g}$, its height is $2,00 \mathrm{cm}$ and negligible volume.

Come up with as many physics reasons as possible on why an asteroid might have a higher temperature than its surroundings.