A 36-kg girl is bouncing on a trampoline. During a certain interval after she leaves the surface of the trampoline, her kinetic energy decreases to 185 J from 460 J. How high does she rise during this interval? Neglect air resistance.
m*g = 36 * 9.8 = 352.8 N.
KE+PE = 460 J.
185 + PE = 460
PE = 275 J. = mg*h
mg*h = 275
352.8h = 275
h = 0.779 m.
To determine the height the girl rises during this interval, we need to use the principle of conservation of energy. According to this principle, the total mechanical energy (potential energy + kinetic energy) remains constant if no external forces, such as air resistance, are present.
In this case, the decrease in kinetic energy must be compensated by an increase in potential energy. Since there is no air resistance, we can assume that the only energy loss during the interval is due to the work done against gravity as the girl rises.
The initial kinetic energy is given as 460 J, and the final kinetic energy is given as 185 J. The loss in kinetic energy is then:
Loss in kinetic energy = Initial kinetic energy - Final kinetic energy
= 460 J - 185 J
= 275 J
This loss in kinetic energy is equal to the work done against gravity as the girl rises. The work done against gravity is given by the formula:
Work = Force × Distance
In this case, the force is the weight of the girl, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
= 36 kg × 9.8 m/s²
= 352.8 N
The work done against gravity is equal to the weight of the girl multiplied by the vertical distance she rises. Therefore:
Work = Weight × Distance
Since the vertical distance is what we want to find, we can rearrange the formula:
Distance = Work / Weight
Substituting the values, we can calculate the distance:
Distance = 275 J / 352.8 N
= 0.7804 m
Therefore, the girl rises approximately 0.7804 meters during this interval.