A frictionless pendulum with a mass of 1.2 kg is released from point A, which is at a height of h = 0.4. What is the speed of the pendulum as it passes through point C?
A. 7.8 m/s
B. 4.7 m/s
C. 2.8 m/s
D. 2.0 m/s
To find the speed of the pendulum as it passes through point C, we can use the principle of conservation of mechanical energy.
At point A, the pendulum has gravitational potential energy (mgh), where m is the mass, g is the acceleration due to gravity, and h is the height.
At point C, all of the potential energy is converted to kinetic energy.
Since the pendulum is frictionless, no energy is lost due to friction or other forces.
Therefore, we can set the initial gravitational potential energy equal to the final kinetic energy:
mgh = (1/2)mv^2
Where v is the velocity of the pendulum at point C.
Simplifying the equation:
mgh = (1/2)mv^2
gh = (1/2)v^2
v^2 = 2gh
v = sqrt(2gh)
Plugging in the given values:
v = sqrt(2 * 9.8 * 0.4)
v = sqrt(7.84)
v = 2.8 m/s
Therefore, the speed of the pendulum as it passes through point C is 2.8 m/s.
The correct answer is C. 2.8 m/s.