Question

Шарик массой m=0,15 кг на нити длиной L=0,4 м раскачивают так , что каждый раз, когда шарик проходит положение равновесия, на него в течение короткого промежутка времени t=0,01 с действует сила F=0,2 Н, направлена параллельно скорости.Через сколько полных колебаний шарик на нити отклонится на 60 градусов?

Answer 1

Из рисунко видно что чтобы маятник отклонился на 60 градусов он должен подняться на высоту L/2=0,2 м
найдем скорость которая для этого потребуется   m*V^2\2= m*g* L/2
V = корень из g*L = корень из 10*0,4= 2 м\с
найдем время из  второго закона Ньютона
F*t= m*V  t=0,15*2/0,2=1,5
найдем число толчков N=t/t1=1,5/0,01=150
За период маятник проходит положение 2 раза
значит число колебаний n=150/2=75
Решение верное, а все остальные можно выкинуть

Answer 2

Problem Analysis

We are given a mass m = 0.15 kg ball swinging on a string of length L = 0.4 m. The ball is subjected to a force F = 0.2 N for a short period of time t = 0.01 s when it passes through the equilibrium position. We need to determine the number of complete oscillations the ball will make before deviating by 60 degrees.

Solution

To solve this problem, we can use the equation for the period of a simple pendulum:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

First, let's calculate the period of the pendulum using the given length L:

T = 2π√(0.4/9.8) ≈ 0.899 s.

Next, we need to find the angular frequency (ω) of the pendulum. The angular frequency is given by:

ω = 2π/T

Substituting the value of T, we get:

ω = 2π/0.899 ≈ 7.001 rad/s.

Now, we can calculate the time it takes for the ball to deviate by 60 degrees. Since the force acts for a short period of time t = 0.01 s, we can assume that the ball reaches its maximum displacement in this time.

The angular displacement (θ) of the ball can be calculated using the equation:

θ = ωt

Substituting the values of ω and t, we get:

θ = 7.001 * 0.01 ≈ 0.070 radians.

To convert this angular displacement to degrees, we can use the conversion factor:

1 radian ≈ 57.296 degrees.

Therefore, the angular displacement in degrees is:

θ_degrees = 0.070 * 57.296 ≈ 4.01 degrees.

Since the ball deviates by 4.01 degrees in one oscillation, we can calculate the number of complete oscillations required to reach 60 degrees:

Number of oscillations = 60 / 4.01 ≈ 14.96 oscillations.

Therefore, the ball will complete approximately 14.96 oscillations before deviating by 60 degrees.

Answer

The ball will complete approximately 14.96 oscillations before deviating by 60 degrees.

Note: The calculations in this response are based on the assumption that the force acts for a short period of time and the ball reaches its maximum displacement in that time.