A ball bearing of mass m is suspend as a pendulum. It is initially held stationary at a height h above the lowest point of its trajectory. Assuming that energy is conserved, which of the equations below can used to determine the speed of the ball, v3, at the lowest point
Question
A ball bearing of mass m is suspend as a pendulum. It is initially held stationary at a height h above the lowest point of its trajectory. Assuming that energy is conserved, which of the equations below can used to determine the speed of the ball, v3, at the lowest point
Solution
The principle of conservation of energy states that the total energy in a closed system remains constant. This principle can be applied to the ball bearing pendulum problem.
Initially, when the ball bearing is held stationary at a height h, it has potential energy but no kinetic energy. The potential energy (PE) can be calculated using the formula:
PE = m * g * h
where: m = mass of the ball bearing g = gravitational acceleration (approximately 9.8 m/s^2 on Earth) h = height above the lowest point of the trajectory
When the ball bearing is released and swings down to the lowest point of its trajectory, it has maximum kinetic energy and zero potential energy. The kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * m * v^2
where: v = speed of the ball bearing
According to the conservation of energy, the potential energy at the highest point should be equal to the kinetic energy at the lowest point. Therefore, we can set the two equations equal to each other and solve for v:
m * g * h = 0.5 * m * v^2
Solving for v gives:
v = sqrt(2 * g * h)
So, the speed of the ball bearing at the lowest point of its trajectory can be determined using the equation v = sqrt(2 * g * h).
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