a 15kg rock falls from the top of a building 8.0m high. Find its PE and KE
a.when at rest at the top of the building
b. halfway down the ground
c. when it reaches the ground
d.speed when it reaches the ground
What is it you do not understand.
To find the potential energy (PE) and kinetic energy (KE) of the falling rock in different situations, we can use the formulas for gravitational potential energy and kinetic energy.
1. When the rock is at rest at the top of the building:
a. The potential energy (PE) of the rock at rest at the top of the building can be determined using the formula:
PE = mgh
where m is the mass of the rock (15 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the building (8.0 m).
So, PE = (15 kg) * (9.8 m/s^2) * (8.0 m) = 1176 Joules
b. At halfway down the building, the potential energy decreases by half, and half of that potential energy is converted into kinetic energy (assuming no energy losses due to air resistance). So, the rock's potential energy at this point is:
PE = (15 kg) * (9.8 m/s^2) * (8.0 m) / 2 = 588 Joules
c. When the rock reaches the ground, it has no potential energy left since it is at the lowest point. Therefore, the potential energy is zero (PE = 0 Joules).
d. To find the speed of the rock when it reaches the ground, we can use the law of conservation of energy. At the top of the building, all of the rock's initial potential energy is converted into kinetic energy at the bottom.
The initial potential energy (PE) is equal to the final kinetic energy (KE):
PE = KE
mgh = (1/2)mv^2
where v is the speed of the rock.
Since the mass cancels out, we can solve for v:
v = sqrt(2gh)
v = sqrt(2 * 9.8 m/s^2 * 8.0 m) = 19.8 m/s
Therefore:
a. PE = 1176 Joules, KE = 0 Joules
b. PE = 588 Joules, KE = 588 Joules
c. PE = 0 Joules, KE = 1176 Joules
d. The speed when it reaches the ground is 19.8 m/s.