Question

На нити длиной 50 см висит шарик. Какую минимальную скорость следует придать шарику в горизонтальном направлении, чтобы она сделала полный оборот в вертикальной плоскости? Считайте, что g=10 м/с2. Сопротивлением воздуха и размером шарика пренебрегите. Ответ запишите в метрах за секунду

Answer 1

Дано R=L=0,5 м  Vo- ?

для того чтобы тело сделало поный оборот в верхней точке оно должно двигаться с центростремительным ускорением а=Fт/m=g
V^2/R=g
V^2=g*R
по закону сохранения энергии
m*Vo^2/2=m*V^2/2 +m*g*2*R
Vo^2=V^2+4*g*R
Vo=√5*g*R=√5*10*0,5=5 м/с

Ответ Vo=5 м/с - ответ

Answer 2

Calculation of Minimum Speed for the Ball to Make a Full Revolution

To calculate the minimum speed required for the ball to make a full revolution in the vertical plane, we need to consider the centripetal force acting on the ball. The centripetal force is provided by the tension in the string.

The centripetal force can be calculated using the formula:

F = m * v^2 / r

Where: - F is the centripetal force - m is the mass of the ball - v is the velocity of the ball - r is the radius of the circular path

In this case, the radius of the circular path is equal to the length of the string, which is 50 cm or 0.5 m.

The mass of the ball is not given in the question. However, we can assume a mass for the ball to proceed with the calculation. Let's assume the mass of the ball is 0.1 kg.

Using the acceleration due to gravity, g = 10 m/s^2, we can calculate the tension in the string:

T = m * g

Substituting the value of m = 0.1 kg, we get:

T = 0.1 kg * 10 m/s^2 = 1 N

Since the tension in the string provides the centripetal force, we can equate the tension to the centripetal force:

T = F

Substituting the value of T = 1 N and r = 0.5 m, we can solve for v:

1 N = (0.1 kg * v^2) / 0.5 m

Simplifying the equation, we get:

v^2 = 10 m^2/s^2

Taking the square root of both sides, we find:

v = √10 m/s

Therefore, the minimum speed required for the ball to make a full revolution in the vertical plane is approximately 3.16 m/s.