The Mechanical Energy of an object is the total of all kinetic energy and all forms of potential energy.
Em = Ek + Ep Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations.
U = _____
Ek = _____
Em = ______
U = _____
Ek = _____
Em = ______
v = _______
U = _____
Ek = _____
Em = ______
v = _______
h = _______
The Mechanical Energy of an object is the total of all kinetic energy and all forms of potential energy.
Em = Ek + Ep Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations.
U = _____
Ek = _____
Em = ______
U = _____
Ek = _____
Em = ______
v = _______
U = _____
Ek = _____
Em = ______
v = _______
h = _______
In an Isolated system, there is no energy loss due to friction (heat), light, or sound.
Therefore in an Isolated system:
ΣEm before = ΣEm after
In a NON­isolated system, energy is either introduced into the system, or lost loss due to friction (heat), light, or sound.
Therefore in an non­isolated system:
ΣEm before ≠ ΣEm after
Therefore
ΔEm lost/gained = ΣEm after - ΣEm before
Since we've mainly been working with friction, and we know friction removes energy from the system:
ΔEm lost/gained = ΣEm after - ΣEm before
ΔEm lost/gained = ­ Em lost A negative value
Since we know friction is a force, and it is applied over a distance, it is safe to say that the energy lost in a system due to friction is equal to the work done by friction.
ΔEm lost = Wfriction
Rearranging:
ΣEm before+ ΔEm lost/gained = ΣEm after
with friction
ΣEm before ­ Wfriction = ΣEm after
or, depending how you like to look at it
ΣEm before = ΣEm after + Wfriction
The work­energy theorem states that the work done on a system is equal to the sum of the changes in the potential and kinetic energies of the system.
in other words,
W = ΔEk + ΔEp
W = (Ekf ­ Eki) + (Uf ­ Ui) + (Epf ­ Epi)
page 61
21. A bird flying at 4.00 m/s suddenly dies of a heart attack. When the bird strikes the ground it is travelling at 11.7 m/s. Disregarding air resistance, determine how high above the ground the bird was when it died.
Isolated system
Em before = Em after
page 60
12. In the given diagram, the 0.250 kg mass is 20.0 cm away from the spring bumper moving towards it at 2.00 m/s. The force of friction between the mass and the surface on which it is sliding is 0.240 N. If the mass compresses the spring 10.0 cm:
(a) What is the k­value for the spring?
(b) How fast will the mass be moving as it leaves the spring?
page 58
12. In the given diagram, the 0.250 kg mass is 20.0 cm away from the spring bumper moving towards it at 2.00 m/s. The force of friction between the mass and the surface on which it is sliding is 0.240 N. If the mass compresses the spring 10.0 cm:
(a) What is the k­value for the spring?
(b) How fast will the mass be moving as it leaves the spring?
Attachments
Potential Energy.swf