1) Mechanical energy is conserved in all the 4 situations
2) True
3) The potential energy of the block is 490 J
Explanation:
1)
Mechanical energy is the sum of potential energy (PE) and kinetic energy (KE) of a body:
According to the law of conservation of energy, in absence of non-conservative forces (such as air resistance, friction...), the mechanical energy of a body is always conserved.
This means that the mechanical energy is conserved in all the situations described. More specifically:
- Child on a swing
: there is a continuous conversion between kinetic energy and gravitational potential energy
- Pendulum
: there is a continuous conversion between kinetic energy and gravitational potential energy
Bow and Arrow
: there is a conversion of energy from elastic potential (when the bow is stretched) to kinetic energy (when the arrow is shot)
Roller Coaster: there is a continuous conversion between kinetic energy and gravitational potential energy
2)
As we said, the mechanical energy of the object falling down at any point of the fall is
where KE is the kinetic energy and PE is the potential energy. The value of E is constant, since the mechanical energy is conserved.
The potential energy is given by
where m is the mass of the object, g is the acceleration of gravity, h is the height of the object above the ground.
As the object falls, its height 
decreases, and therefore, the potential energy PE also decreases. But we said that E must remain constant: therefore, if PE decreases, this means that KE increases, therefore as the object falls, the potential energy is converted into kinetic energy (in fact, the speed of the object increases). So the statement is true.
3)
The potential energy of an object is given by the equation
where
m is the mass of the object
is the acceleration of gravity
h is the height of the object relative to the ground
For the block in this problem, we have:
m = 10 kg
h = 5 m
Substituting, we find its potential energy:
Learn more about potential energy and kinetic energy:
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