Question

A 1.5 m long frictionless pendulum of mass 1.6 kg is released from point A at an angle 0 of 10 degrees.

Answer 1

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.