(a) How much gravitational potential energy (relative to the ground on which it is built) is stored in the Great Pyramid of Cheo
1 answer:
Answer:
(a)
(b) The gravitational energy stored in the Great Pyramid of Cheops is times greater than the daily food intake of a person (in Joules).
Explanation:
(a) Gravitational potential energy (with respect to the earth) is the energy possessed by an object due to its position from the surface of the earth.
It is given as:
where m = mass of object
g = acceleration due to gravity
h = height above the ground
∴
(b) A person's daily food intake = 2500 food calories
1 food calorie = 1000 regular calories
∴ 2500 food calories = 2500 * 1000 regular calories = 2500000 regular calories
We are given that :
1 regular calorie = 4.184 J
∴ 2500000 regular calories = 2500000 * 4.184 J =
Comparing this with the answer in (a) above:
The gravitational energy stored in the Great Pyramid of Cheops is times greater than the daily food intake of a person (in Joules).
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A) +5 J
B) +1 J
Explanation:
A)
The internal forces (interaction forces) acting on a system do not change the mechanical energy (sum of potential and kinetic energy) of the system.
However, these forces are responsible for converting the energy from one form into another; the work done by these forces is equal to the amount of energy converted from one form into the other.
In this problem, we have:
is the loss in potential energy of the system
is the gain in kinetic energy of the system
By looking at these numbers, this means that the internal forces have converted 5 J of energy from potential energy into kinetic energy (while the additional +1 J missing is due to external forces, as explained in part B).
Therefore, the work done by internal forces is
W = +5 J
B)
First of all, we calculate the change in mechanical energy of the system.
The mechanical energy of a system is the sum of its kinetic energy (K) and its potential energy (U):
So, the change in mechanical energy is equal to the sum of the changes of kinetic energy and the changes of potential energy:
In this problem:
So, the change in mechanical energy is:
According to the work-energy theorem, the work done by external forces on a system is equal to the change in mechanical energy of the system: therefore in this case, the work done by external forces is
Answer:
a) v_{p} = 2.83 m / s , b) 50.5º north east
Explanation:
This is a vector problem.
The speed of the ball with respect to the ground is the speed of the ball with respect to Mia plus the speed of Mia with respect to the ground
To make the sum we decompose the speed of the ball in its components
The angle of 30 east of the south, measured from the positive side of the x axis is
θ = 30 + 270 = 300
=
cos 300
= v_{b} sin. 300
v_{bx} = 3.60 cos 300 = 1.8 m / s
v_{by} = 3.60 sin 300 = -3,118 m / s
Let's add speeds on each axis
X axis
vₓ = v_{bx}
vₓ = 1.8 m / s
Y Axis
= v1 - vpy
v_{y} = 5.30 - 3.118
v_{y} = 2.182 m / s
The magnitude of the velocity can be found using the Pythagorean theorem
= √ (vₓ² + v_{y}²)
v_{p} = √ (1.8² + 2.182²)
v_{p} = 2,829 m / s
v_{p} = 2.83 m / s
b) for direction use trigonometry
tan θ = / vₓ
θ = tan ⁺¹ v_{y} / vₓ
θ = tan⁻¹ 2.182 / 1.8
Tea = 50.48º
This address is 50.5º north east