in vertical circular motion ratio of kinetic energy of particle at highest point to lowest point is

The ratio of kinetic energy of a particle at the highest point to the lowest point in vertical circular motion is given by the principle of conservation of mechanical energy.

Step 1: Understand the principle of conservation of mechanical energy The principle of conservation of mechanical energy states that the total mechanical energy in a closed system—i.e., a system not affected by external forces—is constant and conserved. In the context of vertical circular motion, this means that the sum of kinetic energy (KE) and potential energy (PE) at any two points in the motion must be equal.

Step 2: Apply the principle to the highest and lowest points At the highest point of the motion, the particle has maximum potential energy (PE_max) and minimum kinetic energy (KE_min). At the lowest point, it has maximum kinetic energy (KE_max) and minimum potential energy (PE_min).

Step 3: Set up the equation According to the conservation of mechanical energy, we have:

PE_max + KE_min = PE_min + KE_max

Step 4: Solve for the ratio We want to find the ratio of KE_min to KE_max. We can rearrange the equation to find this:

KE_min/KE_max = (PE_min + KE_max - PE_max) / KE_max

Assuming the motion starts from rest at the highest point (which means PE_min = 0), and the reference point for potential energy is at the lowest point (which means PE_max = mgh, where m is the mass of the particle, g is the acceleration due to gravity, and h is the height of the circular path), the equation simplifies to:

KE_min/KE_max = (KE_max - mgh) / KE_max

This is the ratio of the kinetic energy of the particle at the highest point to the lowest point in vertical circular motion.

The kinetic energy of a particle in vertical circular motion is given by the equation KE = 1/2 mv^2, where m is the mass of the particle and

The ratio of kinetic energy of a particle at the highest point to the lowest point in vertical circular motion is given by the principle of conservation of mechanical energy.

Step 1: Understand the principle of conservation of mechanical energy The principle of conservation of mechanical energy states that the total mechanical energy in a closed system—i.e., a system not affected by external forces—is constant and conserved. In the context of vertical circular motion, this means that the sum of kinetic energy (KE) and potential energy (PE) at any two points in the motion must be equal.

Step 2: Apply the principle to the highest and lowest points At the highest point of the motion, the particle has maximum potential energy (PE_max) and some kinetic energy (KE_high). At the lowest point, the particle has minimum potential energy (PE_min, often zero in these problems) and maximum kinetic energy (KE_max).

Step 3: Set up the equation According to the conservation of mechanical energy, we have: PE_max + KE_high = PE_min + KE_max

Step 4: Solve for the ratio We want to find the ratio KE_high / KE_max. We can rearrange the equation to find this: KE_high / KE_max = 1 - (PE_max - PE_min) / KE_max

Without specific values for the potential and kinetic energies, we can't provide a numerical ratio. However, we can say that the ratio of kinetic energy at the highest point to the lowest point is equal to 1 minus the change in potential energy divided by the kinetic energy at the lowest point.