For a id system like a linear polymer, we write d sigma = du-fdl, where is the "natural" temperature r = k_b t, f is the external force on the line, and l is the extension of the line. from this, we get f= - . consider a polymer chain in id with n links of length a, where each link can be oriented to the left or the right with equal probability. the total end-to-end extension of the polymer is given by l = 2|s|a, where. v is the excess oflengths pointing to the right. show that for |s| n, we can write the entropy as sigma(l) = ln[2g(n, 0)] -l^2/(2na^2) where g(n, s) - n! /(1/2 n+s)! {1/2n-s)! ] analogously to the spin system studied in class. show that the force at extension l is given by f = l/(na^2). what does this mean physically will happen to the polymer as the temperature is increased?

a

explanation:

because they are cartillidge

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: