Under what conditions would a rope remain in equilibrium during a tug of war
2 answers:
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Answer:
Position A/Position E
,
Position B/Position D
,
, for
Position C
,
Explanation:
Let suppose that ball-Earth system represents a conservative system. By Principle of Energy Conservation, total energy () is the sum of gravitational potential energy (
) and translational kinetic energy (
), all measured in joules. In addition, gravitational potential energy is directly proportional to height (
) and translational kinetic energy is directly proportional to the square of velocity.
Besides, gravitational potential energy is increased at the expense of translational kinetric energy. Then, relative amounts at each position are described below:
Position A/Position E
,
Position B/Position D
,
, for
Position C
,
Answer:
E. Zero Maximum
Explanation:
At the point of maximum displacement, the speed is zero while the restoring force is maximum. In fact:
- The restoring force is given by , where k is the spring constant and x is the displacement - at the point of maximum displacement, x is maximum, so F is maximum as well
- the total energy of the system is sum of kinetic energy and elastic potential energy:
where m is the mass of the system and v is the speed. Since E (the total energy) is constant due to the law of conservation of energy, we have that when K increases, U decreases, and viceversa. As a result, when x increases, v decreases, and viceversa. At the point of maximum displacement, x is maximum, so v will have its minimum value (which is zero, since the system is changing direction of motion).