Final answer:
Using the law of conservation of mechanical energy, the velocity of a 10kg box sliding down a 10m high frictionless incline when it is 1m above the ground can be calculated. Friction would slow down the box as it converts some mechanical energy into other forms, such as heat.
Step-by-step explanation:
According to the law of conservation of mechanical energy (ME), the total ME of an object remains constant if no external forces (like friction or air resistance) do work on it. Since the incline is frictionless, we can apply this principle to the 10kg box on the incline.
At the top of the incline, the box's ME consists entirely of gravitational potential energy (PE), which is given by PE = mgh, where m is mass, g is acceleration due to gravity (9.81 m/s2), and h is the height above the ground. As the box slides down, this PE is converted into kinetic energy (KE), which is given by KE = 1/2mv2, where v is the velocity.
At 1m above the ground, the box still has some PE left (PE = 10kg * 9.81 m/s2 * 1m) and the rest is KE. By setting the initial total ME equal to the combined PE and KE at the point 1m above the ground, we can solve for the box's velocity at that point. If friction were present, the box would not be going as fast due to friction converting some of its ME to other forms of energy, such as heat.