91Ó°ÊÓ

Kinetic energy is a type of energy that an object possesses due to its motion. Whenever an object moves, like a golf ball being driven from a tee, it has kinetic energy. The formula to calculate kinetic energy is \( K.E = \frac{1}{2}mv^2 \), where \( m \) represents mass and \( v \) is the velocity of the object. This formula tells us that kinetic energy depends on how fast an object is moving and its mass.

In the original exercise, the golf ball's initial kinetic energy is found using its mass (47 g or converted to 0.047 kg) and its initial speed of 52 m/s. Plug these values into the formula to find the ball's initial kinetic energy. As it rises and reaches its highest point, the ball slows down, transforming some of its kinetic energy into potential energy.

• The less speed, the less kinetic energy.
• Kinetic energy is always positive or zero.

Thus, when the ball is at its highest point, the kinetic energy calculated is important to complete understanding of its motion when combined with potential energy.

Potential energy is stored energy that an object has because of its position or state. In the context of the original problem, we focus on gravitational potential energy, which is energy due to the height an object gains or loses. The formula for calculating gravitational potential energy is \( P.E = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity (approximately 9.81 m/s² on Earth), and \( h \) is height.

When the golf ball in the exercise approaches its maximum height, its potential energy is at its peak because it has risen to the highest point above ground level. The potential energy at the top can be calculated by multiplying the ball's mass, the gravitational pull, and the height it reached (24.6 m). This height is pivotal because it shows how much of the initial kinetic energy was converted to potential energy.

• The higher the object, the more potential energy it has.
• Potential energy can increase or decrease with height.

Understanding potential energy helps in comprehending how energy is transformed in motion, especially as the ball descends and potential energy converts back into kinetic energy.

Mechanical energy is the total energy that an object has due to its movement and position. It is the sum of kinetic and potential energy, emphasizing that energy is conserved within a system like in the exercise. According to the conservation of energy principle, in the absence of external forces, the total mechanical energy remains constant.

In practical terms, for the golf ball problem, as the ball launches, its mechanical energy is the sum of its kinetic energy (movement) and its initial potential energy (position initially taken as zero). As it rises, part of its kinetic energy converts into potential energy until it reaches its maximum height, where the total mechanical energy is shared between the kinetic energy remaining and the increased potential energy.

• Mechanical energy stays constant in a closed system without external forces.
• Mechanical energy is helpful in predicting motion's future states.

For the golf ball 8 m below its highest point, using this conservation helps determine its speed by accounting for the mechanical energy shift between kinetic and potential forms.