Question

Шарик массой 20 г, привязанный к нити длиной 25 см, вращается по окружности. Найдите линейную скорость шарика и действующую на него центробежную силу, если период вращения шарика равен 0,2с. Помогите, пожалуйста.

Answer 1

M=0.02 кг      R=0.25 м     T=0.2 c     V=?    F=?
===
V1=2*π*R/T=2*3.14*0.25/0.2=7.85 м/с
F1=m*V²/R=0.02*7.85²/0.25≈4.93 H    (≈5 H)
===
Увеличим массу в 2 раза
F2=2m*V²/R=2*F1=2*5=10 H
===
Увеличим длину нити в 2 раза
V2=2*π*2R/T=2*V1=2*7.85=15.7 м/с
F3=m*V2²/(2*R)=F1/2=5/2=2.5 H
===
Увеличим период в 2 раза
V3=2*π*R/(2*T)=V1/2=7.85/2=3.93 м/с
F4=m*V3²/R=0.02*3.93²/0.25=1.24 H
====================================

Answer 2

Calculation of Linear Velocity and Centripetal Force

To find the linear velocity and centripetal force of a ball with a mass of 20 g and attached to a string of length 25 cm, rotating in a circle with a period of 0.2 s, we can use the following formulas:

1. Linear velocity (v): - The linear velocity of an object moving in a circle can be calculated using the formula: v = 2πr / T, where r is the radius of the circle and T is the period of rotation. - In this case, the radius of the circle is equal to the length of the string, which is 25 cm or 0.25 m. - The period of rotation is given as 0.2 s. - Plugging these values into the formula, we can calculate the linear velocity of the ball.

2. Centripetal force (F): - The centripetal force acting on an object moving in a circle can be calculated using the formula: F = m * v^2 / r, where m is the mass of the object, v is the linear velocity, and r is the radius of the circle. - In this case, the mass of the ball is given as 20 g or 0.02 kg. - We have already calculated the linear velocity in the previous step. - The radius of the circle is equal to the length of the string, which is 25 cm or 0.25 m. - Plugging these values into the formula, we can calculate the centripetal force acting on the ball.

Let's calculate the linear velocity and centripetal force using the given values.

Calculation:

1. Linear velocity (v): - Radius of the circle (r): 0.25 m - Period of rotation (T): 0.2 s

Using the formula v = 2πr / T, we can calculate the linear velocity: ``` v = 2 * π * 0.25 / 0.2 ```

2. Centripetal force (F): - Mass of the ball (m): 0.02 kg - Linear velocity (v): Calculated in the previous step - Radius of the circle (r): 0.25 m

Using the formula F = m * v^2 / r, we can calculate the centripetal force: ``` F = 0.02 * v^2 / 0.25 ```

Let's calculate the values.

Calculation Results:

1. Linear velocity (v): - Calculating the value using the formula: ``` v = 2 * π * 0.25 / 0.2 ``` - The linear velocity of the ball is approximately 3.93 m/s.

2. Centripetal force (F): - Calculating the value using the formula: ``` F = 0.02 * v^2 / 0.25 ``` - The centripetal force acting on the ball is approximately 0.314 N.

Therefore, the linear velocity of the ball is approximately 3.93 m/s, and the centripetal force acting on the ball is approximately 0.314 N.

Please note that these calculations assume ideal conditions and do not take into account any other external forces or factors that may affect the motion of the ball.