Question

Тело соскальзывает с наклонной плоскости,которая составляет с горизонтом угол 30 градусов,с постоянной скоростью.Чему равен коэффициент трения k тела о плоскость?

Answer 1

Коэффициент трения соответствует тангенсу угла наклона плоскости:
tg30=k=√3/3=0,58

Answer 2

Calculation of the Coefficient of Friction

To determine the coefficient of friction (k) between the body and the inclined plane, we can use the given information that the body is sliding down the inclined plane at a constant speed.

The angle between the inclined plane and the horizontal surface is 30 degrees

Let's denote the coefficient of friction as k. The force of friction (F_friction) can be calculated using the equation:

F_friction = k * F_normal

where F_normal is the normal force exerted by the inclined plane on the body.

The normal force (F_normal) can be calculated using the equation:

F_normal = m * g * cos(theta)

where m is the mass of the body, g is the acceleration due to gravity, and theta is the angle between the inclined plane and the horizontal surface.

Since the body is sliding down the inclined plane at a constant speed, the net force acting on the body in the horizontal direction is zero. Therefore, the force of gravity acting down the inclined plane (F_gravity) is balanced by the force of friction (F_friction):

F_gravity = F_friction

The force of gravity (F_gravity) can be calculated using the equation:

F_gravity = m * g * sin(theta)

Setting F_gravity equal to F_friction and substituting the expressions for F_friction, F_normal, and F_gravity, we can solve for the coefficient of friction (k):

k * m * g * cos(theta) = m * g * sin(theta)

Simplifying the equation:

k = tan(theta)

Substituting the value of theta (30 degrees) into the equation:

k = tan(30) = 0.577

Therefore, the coefficient of friction (k) between the body and the inclined plane is approximately 0.577.

Please note that the value of the coefficient of friction can vary depending on the nature of the surfaces in contact and other factors. The value provided here is a general approximation based on the given information.

Conclusion

The coefficient of friction (k) between the body and the inclined plane is approximately 0.577.