In which case is potential energy increasing?
A.
a skydiver jumps from an airplane that is 4 kilometers above the Earth
B.
a 20 kilogram boulder rolls down a hill that is 430 meters high
C.
a spring of a dart gun launches a dart in a straight line from rest position
D.
a weightlifter lifts a 20 kilogram barbell above his head
The correct answer is A.
In this case, the potential energy of the skydiver increases as he jumps from an airplane that is 4 kilometers above the Earth.
In all of these cases, the potential energy is increasing, but let's break it down step by step:
A. In case A, a skydiver jumps from an airplane that is 4 kilometers above the Earth. As the skydiver moves downwards, the potential energy is increasing because the skydiver is moving closer to the Earth's surface, where the gravitational force is stronger.
B. In case B, a 20 kilogram boulder rolls down a hill that is 430 meters high. As the boulder rolls downhill, its height decreases, and therefore its potential energy is converted into kinetic energy. However, at the beginning of its descent, when it is at the top of the hill, the potential energy is at its maximum because the boulder is at its highest point.
C. In case C, a spring of a dart gun launches a dart in a straight line from the rest position. In this case, the potential energy of the spring is initially stored in the compressed state of the spring. As the dart is released, the potential energy is gradually transformed into kinetic energy.
D. In case D, a weightlifter lifts a 20 kilogram barbell above his head. The potential energy here increases because the weightlifter is lifting the barbell against the force of gravity. The higher the barbell is lifted, the greater its potential energy.
Therefore, potential energy is increasing in all of these cases.
To determine in which case potential energy is increasing, we need to understand the factors that affect potential energy. Potential energy depends on two main factors: the height of an object and its mass.
In option A, a skydiver jumps from an airplane that is 4 kilometers above the Earth. In this case, the height of the skydiver increases as they jump from the plane. Since potential energy is directly proportional to height, the potential energy of the skydiver increases.
In option B, a 20 kilogram boulder rolls down a hill that is 430 meters high. As the boulder rolls down the hill, its height decreases. Since potential energy is directly proportional to height and inversely proportional to mass, the potential energy of the boulder decreases in this case.
In option C, a spring of a dart gun launches a dart in a straight line from a rest position. The potential energy of the dart is stored in the compressed spring, and when released, it transforms into kinetic energy rather than potential energy. Therefore, the potential energy of the dart decreases.
In option D, a weightlifter lifts a 20 kilogram barbell above his head. As the weightlifter lifts the barbell, its height increases. Similar to the skydiver's situation, the potential energy of the barbell increases.
Therefore, the answer is A, where the potential energy is increasing as the skydiver jumps from an airplane.