Transcript Document

-PotentialEnergy
-Conservation of
Mechanical
Energy in an
isolated system,
without friction.
AP Physics C
Mrs. Coyle
Gravitational Potential
Energy, ΔU g=mgh
• h=height
• Unit: Joule
• Compared to a Reference (Base)
level.
• When solving problems, be sure
to select the reference level.
Conservation of Mechanical
Energy
The mechanical energy of an isolated
and friction free system is conserved
U1 + K1 = U2 + K2
Note
In an isolated system there
are no energy transfers
across the boundaries.
Elastic Potential Energy
• The energy stored in a
compressed or stretched spring
is:
Us = ½
•
•
2
kx
k is the spring constant
x is the elongation or compression
from equilibrium
Problem 1- The loop-theloop (#5)
A bead slides with out friction around
a loop-the-loop. The bead is released
from a height h=3.5R.
a) What is the speed at the top of
the loop?
b) How large is the normal force on
it if its mass is 5.00g?
Ans: a) v=(3gR)
½,
b) 0.098N
Problem 2- Projectile(#17)
A 20.0 kg cannon ball is fired from a
cannon with a muzzle speed of 1,000m/s
at an angle of 370 above the horizontal.
A second ball is fired at an angle of 900
with the same speed.
Find: a) the maximum height reached by
each ball.
b) the total mechanical energy at the
maximum height for each ball. Set the
reference point to be at the cannon.
(Ans: a)1.85x104m, 5.10x104m, b) 1.00x107 J )
Problem 3- The pendulum
(#9)
A pendulum has a 2.00m long string
and the bob makes an initial angle of
300 with the vertical when the bob is
released (ignore air resistance).
Calculate the speed of the particle:
a) at the lowest point of the swing
and b) when the angle is 150.
Ans: a)2.29m/s, b)1.98m/s
Problem 4- Spring on an
inclined plane (#10)
• An object of mass m starts from rest
and slides a distance d down a
frictionless incline of angle θ. When
sliding, it compresses a spring, of
force constant k, a distance x at
which point is it momentarily at rest.
Find the initial separation d between
the object and the spring.
• Ans: d= ( kx2
) -x
2mgsinθ