A particle of mass 4 kg is attached to one end of an inelastic string and a particle of mass 2 kg is attached to the other end of the string.The string has length 4m and is hung over a smooth pivot at its midpoint. The Pivot lies 3m above the ground.How long does it take for one of the particles to hit the ground?
To determine how long it takes for one of the particles to hit the ground, we can analyze the motion of both particles and find the time when either of them reaches the ground.
First, let's consider the motion of the particle with a mass of 4 kg. It moves in a circular path due to the string's length and the pivot at its midpoint. The radius of this circular path is half the length of the string, which is 4m/2 = 2m. The mass of the particle is not relevant here since it does not affect the time it takes to hit the ground.
The particle will make one complete revolution around the pivot before it reaches the ground. The time taken for this revolution is determined by the formula for the period of a simple pendulum:
T = 2π√(L/g)
Where:
T = period of the pendulum
π = pi (approximately 3.14)
L = length of the pendulum
g = acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values for length and acceleration due to gravity, we have:
T = 2π√(2/9.8)
T = 2π√(1/4.9)
T = 2π/2.213
T ≈ π/1.107
The period of the pendulum is approximately π/1.107 seconds. Since it takes one period for the particle to make a complete revolution, the time it takes for the particle to hit the ground is equal to the period:
Time = T ≈ π/1.107 seconds
Therefore, it takes approximately π/1.107 seconds for one of the particles to hit the ground.