A 0.28-kg stone is held 1.5 m above the top edge of a water well and then dropped into it. The well has a depth of 4.8 m.
(a) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone–Earth system before the stone is released?
J
(b) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone–Earth system when it reaches the bottom of the well?
J
(c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
J
Actually,
** GPE = mgh
a) GPE = mgh
as height of well is taken to be area of 0 GPE.
sign is positive.
GPE = mgh = 0.28*9.8*1.5
b) GPE = mgh
as height is now below area of 0 GPE, h changes to -h.
therefore sign is negative
GPE = 0.28*9.8*(-4.8)
c) GPE = mgh
here, mg(-h1-h2)
therefore,
GPE = 0.28*9.8*(-1.5-4.8)
(a) Well, the gravitational potential energy of the system before the stone is released is pretty high because it's holding itself up! It's like a magician trying to keep a bowling ball balanced on their nose. So, let's calculate the potential energy using the formula PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height. Plugging in the values, we get PE = 0.28 kg * 9.8 m/s^2 * 1.5 m. Do some quick math and you'll find that the potential energy is approximately 4.116 J.
(b) Ah, the stone finally takes the plunge! Now it's going to unleash its inner potential energy as it falls to the bottom of the well. The potential energy at the bottom would be zero because the stone has reached its lowest point and doesn't have anywhere else to fall. So, the gravitational potential energy at the bottom of the well is approximately 0 J.
(c) The change in the gravitational potential energy of the system from release to reaching the bottom of the well is simply the difference between the potential energies at those two points. So, 0 J - 4.116 J gives us approximately -4.116 J. That negative sign means that the stone has lost potential energy as it descended into the well. Maybe it left it behind as a tip for the well-dwelling creatures? Who knows!
To answer these questions, we need to calculate the gravitational potential energy at different points in the stone-Earth system. Let's go step by step:
(a) To find the gravitational potential energy of the stone-Earth system before the stone is released, we'll consider the stone at its initial position, 1.5 m above the top edge of the well. The formula for gravitational potential energy is given by:
PE = mgh
Where:
PE is the gravitational potential energy,
m is the mass of the object (0.28 kg in this case),
g is the acceleration due to gravity (approximately 9.8 m/s²),
and h is the height of the object from the reference point (1.5 m).
Substituting these values into the formula, we get:
PE = (0.28 kg) × (9.8 m/s²) × (1.5 m)
Now, calculate the product of these numbers to find the gravitational potential energy before the stone is released.
(b) To find the gravitational potential energy of the stone-Earth system when it reaches the bottom of the well, we need to calculate the height of the stone from the reference point, which is at the top edge of the well. The height can be calculated as follows:
Total Height = Height of well + Initial height of the stone
Given that the depth of the well is 4.8 m and the stone is initially held 1.5 m above the well, we have:
Total Height = 4.8 m + 1.5 m
Now, substitute this value into the formula for gravitational potential energy:
PE = (0.28 kg) × (9.8 m/s²) × (Total Height)
Calculate the product of these numbers to find the gravitational potential energy when the stone reaches the bottom of the well.
(c) The change in gravitational potential energy of the system from release to reaching the bottom of the well can be found by subtracting the initial gravitational potential energy (found in part a) from the final gravitational potential energy (found in part b).
a. PE = mgh = 0.28 * 9.8 *1.5 = 4.1J.
b. PE = 0.28 * 9.8 * 4.8 = 13.2 Joules.
c. Change = mg(h1+h2) - 0 =
0.28 * 9.8 * (1.5+4.8) - 0 = 17.3J.