Question

Какой скоростью должен обладать шар, катящийся без скольжения, чтобы подняться по наклонной плоскости, составляющей с горизонтом угол 30 градусов, на высоту 2м, если сила трения равна 0.2 силы давления шара на плоскость? чему равно время подъема?

Answer 1

Пусть масса шара m; Тогда вес - mg Сопротивление 0.2mg Получаем - ma=mgsin A+0.2 mg=(0.5+0.2)mg=0.7mg a=0.7g Высота 2 метра, тогда длин горки -L=H/sin A=2/0.5=4 L=vt-at^2/2 0=v-at; t=v/a; L=v^2/a-v^2/2a=v^2/2a; v^2=2aL=1.4gL=1.4*10*4=56 v=|56|=2|14| t=|2aL|/a=|2L/a|=|2L/0.7g|=2*4/0.7*10=8/7

Answer 2

Calculation of the Required Speed

To calculate the speed required for a ball to roll up a inclined plane without slipping, we can consider the forces acting on the ball. The main forces involved are the force of gravity and the force of friction.

Let's denote the mass of the ball as m, the acceleration due to gravity as g, the angle of the inclined plane as θ, the height of the inclined plane as h, and the coefficient of friction as μ.

The force of gravity acting on the ball can be calculated as mg. The force of friction can be calculated as μmg.

To lift the ball up the inclined plane, the net force acting on the ball should be equal to the force required to overcome the force of gravity and the force of friction. This net force can be calculated as:

F_net = mg + μmg

The net force can also be expressed in terms of the acceleration of the ball (a) as:

F_net = ma

Since the ball is rolling without slipping, the acceleration of the ball can be related to its linear speed (v) and the radius of the ball (r) as:

a = v^2 / r

By equating the two expressions for the net force, we can solve for the required speed (v) of the ball:

mg + μmg = m(v^2 / r)

Simplifying the equation, we get:

v = sqrt((g * r * h) / (1 + μ))

Now, let's substitute the given values into the equation to calculate the required speed.

Given: - Angle of the inclined plane (θ) = 30 degrees - Height of the inclined plane (h) = 2m - Coefficient of friction (μ) = 0.2

Using the equation above, we can calculate the required speed (v).

v = sqrt((g * r * h) / (1 + μ))

Let's calculate the value of v.

Calculation:

First, let's convert the angle from degrees to radians:

θ_rad = θ * (π / 180) = 30 * (π / 180) radians

Next, let's substitute the given values into the equation:

v = sqrt((g * r * h) / (1 + μ))

v = sqrt((9.8 * r * 2) / (1 + 0.2))

Simplifying further:

v = sqrt((19.6 * r) / 1.2)

Now, we need to find the radius of the ball (r). Unfortunately, the radius of the ball is not provided in the question. Without this information, we cannot calculate the required speed accurately.

Please provide the radius of the ball so that we can proceed with the calculation.