Final answer:
To find the distance a 200-gram rock stops moving in the snow under a force of 12 Newtons, one must apply the work-energy principle. By calculating the kinetic energy at the point of impact and equating it to the work done by the force of the snow, we can solve for the distance.
Step-by-step explanation:
To determine after how many meters a 200-gram rock stops moving in the snow when an average force of 12 Newtons is exerted on it, we can use the work-energy principle. The work done by the snow on the rock equals the kinetic energy the rock had just before it hit the snow. This is expressed as Work = Force × Distance, where Force is the average force exerted by the snow and Distance is what we want to find out.
The kinetic energy of the rock just before hitting the snow can be calculated using the formula Kinetic Energy = 0.5 × mass × velocity^2. However, since we are given the height from which the rock was dropped and not the velocity, we must first calculate the velocity using the equations of motion for objects under gravity. For an object falling from rest (initial velocity = 0) and ignoring air resistance, the final velocity just before impact can be found with velocity = ∙(2 × gravity × height), where gravity is 9.81 m/s^2.
Once we have the velocity, we can determine the rock's kinetic energy at the moment it hits the snow. Then using the work-energy principle, we set the work done by the snow equal to this kinetic energy and solve for the distance the rock moves in the snow:
Work = Kinetic Energy
Force × Distance = 0.5 × mass × velocity^2
By substituting all known values and solving for Distance, we can determine after how many meters the rock stops moving.