Know how friction and friction area calculate power
there are positive and negative work to do, positive work to do power, negative work to do resistance, it can also be said that the object overcomes this force to do (positive) work
hope you understand, hope to adopt!
Assuming that the mass flow rate of coal falling onto the conveyor belt per second is m
and the speed of the conveyor belt itself remains unchanged, the increased power is used to transport the coal falling per unit time to the top of the conveyor belt
to reach the same speed as the conveyor belt, And provide the heat consumption generated by friction in the process
!! the energy increased by motor per second = the potential energy increased by coal + the kinetic energy increased by coal + the heat generated by friction
(strictly speaking, the kinetic energy of the coal when it falls from the hopper should be dected, but the title says that the hopper is above the conveyor belt,
so the distance between the hopper and the conveyor belt is short by default, and the kinetic energy of coal falling is very small, Ignore)
if the speed of conveyor belt is V and the height difference of coal from the falling point to the top of conveyor belt is h,
△ e = △ EP + △ EK + △ EF, i.e. △ e = MGH + 1 / 2 * MV ^ 2 + f * s,
where f is the friction force of coal with mass m and S is the distance it passes when it reaches the same speed V as the conveyor belt μ， The belt inclination is α， Then there is f= μ N= μ mgcos α
let the acceleration of coal before reaching the velocity v be a, and according to the force analysis,
MA = f-mgsin α=μ mgcos α- mgsin α=& gt; a=( μ cos α- sin α) G
(since a and V have the same direction, a is a positive number, i.e μ cos α- sin α& gt; 0, i.e μ& gt; tan α
In the process of coal velocity from 0 to V,
V = at, s = 1 / 2 * at ^ 2, s = V ^ 2 / (2a) = V ^ 2 / [2G] μ cos α- sin α)]
∴△Ef=f*s= μ mgcos α* v^2/[2g( μ cos α- sin α)]= 1/2*mv^2/[1-tan α/μ]
∴△E=mgh+1/2*mv^2+1/2*mv^2/[1-tan α/μ]
this is the energy that the conveyor belt needs to increase per second, that is, the power that the motor needs to increase
the heat generated by the friction between coal and conveyor belt is △ EF per second, then the heat generated by the friction between coal and conveyor belt is △ EF1 = 60 * △ EF = 60 * 1 / 2 * MV ^ 2 / [1-tan] α/μ]
P = FV is used to calculate instantaneous power, and the total power obtained is also instantaneous total power
Fmax is the maximum static friction force, n is the positive pressure, where the proportional constant μ It's called static friction coefficient. It's a value with no unit. μ It is related to the material of contact surface, smooth roughness, dry and wet conditions, but not to the size of contact surface.
generally speaking, textbooks think that it is not relevant, and examinations also think that it is good to not be relevant.
1. For two separate books, f = MGU (U is the coefficient of friction)
but if the book has 100 pages, each contact surface will have its own friction, It can be calculated with F = nu (the formula is an arithmetic sequence), so of course it is much larger
2 because the tension will have a radial component. To be simple, there will be pressure on the pile, so there will be friction (because there is a tendency to move) along the tangent direction, that is, the opposite direction of the tension, and the pressure is proportional to the tension, for a small angle, The change of pulling force is equal to the friction force, which is proportional to itself in the end. After learning calculus, we can strictly prove that the pulling force grows exponentially, so we can hold it
as for whether the friction force is related to the area, from the macroscopic point of view, the ideal model can not consider the area, and from the microscopic point of view, it's really hard to say. When it comes to practice, you will find that the situation described in the book can't be realized. I'm tired. Over. I hope it will help you
friction is related to contact area and pressure, and increases with the increase of contact area and pressure
therefore, when the contact area becomes smaller and the pressure becomes larger, it is not sure whether the friction force becomes larger or smaller.