The definition of mechanical energy allows to find the results for the questions about the energy changes in the movement of the system are:
1) The midpoint of the path. Em = 784 J
2) Lowest point of the trajectory Em = 784 J
3) Acceleration of gravity is: g = 9.8 m/s²
4) The bowling ball has more kinetic energy as its height decreases.
Mechanical energy is the sum of the kinetic energy due to motion and the potential energies of the body. In the case of no friction the energy remains constant at all points, this is one of the most important principles of physics.
Em = K + U
Em = ½ m v² + m g h
Where Em is the mechanical energy, K and U the kinetic and potential energy, respectively, m the mass, v the velocity. G the acerleacion of gravity and h the height where the body is.
In this case when the ball is on top of the building of height y = 40 m, all its energy is potential.
Em = U = m g h
Em = 2 9.8 40
Em = 784 J
when the body falls it begins to acquire speed, therefore its kinetic energy increases and the height decreases, therefore its potential energy decreases, but the sum of the two remains constant.
1) Let's calculate the energy at the midpoint of the path.
They indicate that the speed is v= 19.8 m/s and the height is y2 = 20m
Em = ½ m v² + m g h
em = ½ 2 19.8 ² + 2 9.8 20
em = 392 + 392
Em = 784 J
We see that the kinetic and potential energy have the same value and the mechanical energy maintains its initial value.
2) We calculate the energy at the lowest point of the trajectory.
They indicate that the speed is v= 28 m/s and = height is zero h=0
Let's calculate
Em = ½ m v² + m g h
Em = ½ 2 28² + 0
Em = 784 J
At this point, all energy is kinetic and mechanical energy is conserved.
3) The acceleration of gravity comes from Newton's second law where the force is the universal attraction.
F = [tex]G \frac{Mm}{r^2}[/tex]
F= ma
[tex]\G frac{Mm}{R^2}[/tex]
In the case of a body near thesurfacee of the distance of the radius of the planet and the acceleration is called gravity
g = a = [tex]G \frac{M}{R_e^2 }[/tex]
g = [tex]\frac{ 6.67 \ 10^{-11} \ 5.98 \ 10^{24}}{6.37 \ 10^6 }[/tex]
g = 9.81 m/s²
4) The bowling ball has more kinetic energy as its height decreases, at the point where the height is half the kinetic and potential energy are equal.
In conclusion using the definition of mechanical energy we can find the results for the questions about the energy changes in the movement of the system are:
1) The midpoint of the path. Em = 784 J
2) Lowest point of the trajectory Em = 784 J
3) Acceleration of gravity is: g = 9.8 m/s²
4) The bowling ball has more kinetic energy as its height decreases.
Learn more about mechanical energy here: brainly.com/question/24443465
