A particle of mass m=5.00 kg is released from point A and slides on the frictionless track shown

step 1 Delta K is given by all the work done which is the work done due to gravity which is m g delta h

A particle of mass m=5.00 kg is released from point A and...

A particle of mass $m=5.00 \mathrm{kg}$ is released from point ${A}$ and slides on the frictionless track shown in Figure $\mathrm{P} 8.24$ . and slides on the frictionless track shown in Figure P8.24 Determine (a) the particle's speed at points $B$ and $C$ and (b) the net work done by the gravitational force in moving the particle from $A$ to $C$.

A particle of mass $m=5.00 \mathrm{kg}$ is released from point ${A}$ and slides on the frictionless track shown in Figure $\mathrm{P} 8.24$ . and slides on the frictionless track shown in Figure P8.24
Determine (a) the particle's speed at points $B$ and $C$ and (b) the net work done by the gravitational force in moving the particle from $A$ to $C$.

Key Concepts

Work Done by Gravity

The work done by a force, such as gravity, is defined as the product of the force component in the direction of displacement and the displacement itself. In this context, the net work done by gravity on the particle is equal to the change in its gravitational potential energy, which is then converted into kinetic energy during the sliding motion.

Kinetic Energy

Kinetic energy is the energy of motion, defined as one half the product of the mass of an object and the square of its velocity. In energy conservation scenarios, the increase in kinetic energy of the particle is directly related to the decrease in gravitational potential energy as it slides downward.

Conservation of Mechanical Energy

In a frictionless system, the total mechanical energy (the sum of kinetic and potential energy) remains constant throughout the motion. This principle allows us to equate the gravitational potential energy lost by the particle to the kinetic energy gained at different points along its path, thereby facilitating the calculation of speeds at various positions.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field relative to a reference level. In problems like this, changes in height correspond to changes in gravitational potential energy, which then convert into kinetic energy as the particle moves along the track.

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