The potential energy of the spring when a mass of m hangs vertically from it is equal to the gravitational potential energy of the mass.
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Yes, bungee jumping involves potential energy, specifically gravitational potential energy. When the jumper is hoisted up to a significant height before plunging down, they accumulate gravitational potential energy due to their elevated position above the ground. This potential energy is then converted into kinetic energy as they fall, creating the thrilling bungee jump experience.
The potential energy of the apple while hanging is given by mgh, where m=0.95 kg, g=9.8 m/s^2, and h=3 m. At the moment it reaches the ground, all this potential energy will have converted to kinetic energy, thus the kinetic energy would be equal to the initial potential energy. Calculating mgh gives a potential energy of 27.93 J, which would be the kinetic energy just before hitting the ground.
As the juggler pin rises, it gains gravitational potential energy as it moves against gravity. Since total mechanical energy is conserved in the absence of external forces like air resistance, the kinetic energy decreases to compensate for the increase in potential energy. This decrease in kinetic energy is evident as the pin rises higher and its velocity decreases.
A spring scale measures weight by using the principle of Hooke's law, which states that the force needed to extend or compress a spring by a certain distance is proportional to that distance. As an object hangs from the scale, the spring stretches or compresses, and the scale measures the amount of force needed to do so. This force is then converted into a weight reading in units such as grams or Newtons.
The potential energy of the apple can be calculated using the formula PE = mgh, where m is the mass of the apple (0.95 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the ground (3.0 m). Substituting the values into the formula, the potential energy of the apple is 28.14 Joules.