Final answer:
The questions involve calculating kinetic and potential energy using the formulas PE = mgh and KE = 1/2 mv^2, and discussing the role of friction and the conservation of mechanical energy.
Step-by-step explanation:
The subject matter of these questions lies within Physics, specifically focusing on kinetic energy, potential energy, friction, and the Principle of Conservation of Mechanical Energy in various practical scenarios such as sledding, ball rolling, and bullets being shot.
Estimating Kinetic and Potential Energy
The potential energy at the beginning of the hill for the sledding contest can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height from which the sled starts. To determine the kinetic energy at the bottom of the hill, we use the formula KE = 1/2 mv^2. Friction would act to reduce the total mechanical energy of the system, thus decreasing the sled's speed.
Effects of Friction and the Principle of Conservation of Mechanical Energy
Ignoring friction and using the Principle of Conservation of Mechanical Energy, which states that the total mechanical energy in an isolated system remains constant, one can deduce that the potential energy lost by an object falling a certain height will be converted to kinetic energy, which can then be used to calculate its velocity at the bottom of the hill. This principle also applies to the bullet example where the initial kinetic energy can be used to determine the maximum height reached by the bullet.
Friction affects the sled's motion by doing work against the direction of motion, diminishing the sled's mechanical energy, which results in a loss of speed. For example, the work done by friction as a sled moves along the hill can be calculated using the formula Work = friction force × distance.