Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 11 rubs a distance of 7.50 cm each and with a frictional force averaging 71.3 N, what is the temperature increase? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers. The specific heat of the tissue is 3500 J/(kg · °C).

0.168°C

Explanation:

The frictional force between the palms enables rubbing and initiates the heat deposed.

The energy generated per rub is;

The force × distance

Hence we have; 71.3 N×0.0750m

Hence for 11 rubs we have; 11× 71.3 N×0.0750m= 58.82J

Now this heat acquired by the tissue is the same as mass of tissue × specific heat capacity of tissue × temperature rise;

Expressed mathematically as;

58.82=0.100 kg×3500 J/(kg · °C)×∆T

∆T= 58.82/ 0.100 ×3500 =0.168°C

a 2,000 calorie based diet.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.