A 1.5 m long frictionless pendulum of mass 1.6 kg is released from point A at an angle 0 of 10 degrees.
To solve this problem, we can use the principle of conservation of mechanical energy.
At point A, the pendulum has only potential energy. The potential energy at point A is given by:
U(A) = mgh
Where:
m = mass of the pendulum (1.6 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of point A from the reference point (Assuming the reference point is at the lowest point of the pendulum)
Since the pendulum is released from rest, the total mechanical energy at point A is equal to its initial potential energy.
E(A) = U(A)
E(A) = mgh
Next, we can calculate the potential energy at the lowest point, point B. At point B, the pendulum has only kinetic energy. The kinetic energy at point B is given by:
K(B) = (1/2)mv^2
Where:
v = velocity of the pendulum at point B
Using conservation of energy, we can equate the initial potential energy to the final kinetic energy:
E(A) = E(B)
mgh = (1/2)mv^2
Canceling the mass term and substituting the given values:
(1.6 kg)(9.8 m/s^2)(1.5 m) = (1/2)(1.6 kg)v^2
23.52 J = (0.8 kg)v^2
Dividing both sides by 0.8 kg:
29.4 J/kg = v^2
Taking the square root of both sides:
v ≈ 5.42 m/s
Therefore, the velocity of the pendulum at point B is approximately 5.42 m/s.