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Class 24Review EquilibriumRequirements of Equilibrium
ReviewRotational Kinetic Energy
An object that rotates while its center of mass translates will have both translational and rotational kinetic energies.
Kinetic energy of pure rotation
Work done by constant torque
Power (constant torque)
Angular Momentum
if
Conservation of angular momentum
The total angular momentum of a rotating object remains constant if the net external torque acting on it is zero.
The net torque acting on an object is equal to the time rate of change of the angular momentum
x
2
An object with forces acting on it, but not moving, is said to be in static equilibrium.
The first condition for equilibrium is that the forces along each coordinate axis add to zero.
The second condition of equilibrium is that there be no torque around any axis; the choice of axis is arbitrary.
Requirements of Equilibrium
For static equilibrium the total momentum must be zero.
(P is constant)
(L is constant)
CT_E1: Which disks are in equilibrium?CT_E2: If the magnitude of the forces are adjusted properly (but not zero), in which situation can the rod be in equilibrium?
The lever and mechanical advantage
Rr
FPF
CT_E3: In the figure shown, how large should Fp be to lift the bolder?
3
Ex: A diver of weight 580 N stands at the end of a diving board of length L = 4.5 m and negligible mass. The board is fixed to two pedestals separated by a distance d = 1.5 m. Of the forces acting on the board, what is (a) the magnitude of the force from the left pedestal and (b) the magnitude of the force from the right pedestal?
y
x
CT_E4: A diver of weight mg stands at the end of a diving board of length L and negligible mass.
4
Ex: Suppose the length of a uniform bar is L = 3.00 m and its weight is 200 N. The block weights 300 N and = 30.0o. The wire can withstand a maximum tension of T = 500N.
(b) If the block is placed at the maximum x, what are the horizontal and vertical components of the force on the bar from the hinge at A?
y
x
(a) What is the maximum possible distance x before the wire breaks.
CT_E5: (a) In which case it the force on the rod from the cord the least?
5
Ex: A uniform beam of weight 500 N and length L = 3.0 m is suspended horizontally. The least tension that will snap the cable is 1200 N. What value of D corresponds to that tension.
y
x
L
D
CT_E6: In which case is the tension in the wire the least?
6
Ex: A uniform beam, of length L. and mass m = 1.8 kg, is at rest on two scales. A uniform block, with mass M = 2.7 kg, is at rest on the beam, with its center a distance L/4 from the beam’s left end. What do the scales read?
y
x
Center of GravityThe gravitational force mg on a body effectively acts at a single point, called the center of gravity of the body.If g is the same for all parts of a body, then the body’s center of gravity is coincident with the body’s center of mass.
CT_E8: Consider the two configurations of books shown below.CT_E9: A box, with its center-of-mass....
CT_E7: You are standing on two bathroom scales, one foot on each.
Note: if M was at L/2 each scale would read the same.
CT_E10: The figure show a block suspended by two wires, A and B, ...
7
Ex: A ladder of length L = 12 m and mass m = 45 kg leans against a frictionless wall. It rests on a floor with coefficient of friction m = 0.5. What is the minimum angle you can lean the ladder so that it does not slip?
y
x
8
x
y
m
Ex: A block of mass 15.0 kg hangs by a cord which is attached to two other cords which hang from the ceiling, as shown. The cords have negligible mass, 1 = 25o and 2 = 40o. What is the tension in the three cords?
cord 1
cord 3
cord 2
For m
For the knot
9
Ex: What magnitude for force applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 3.00 cm. r = 6.00 cm and m = 0.800 kg.
10
Requirements of Equilibrium
Review
(P is constant)
(L is constant)
Class 25Review Center of GravityElasticity
11
Elasticity
Tension and compression
Stress Strain
E - Young’s Modulus (units: N/m2)
Atoms in a solid form a lattice structure
The atoms are bonded together with electrons. These bond act like springs. There are three ways we can stress solids.We can pull/push, shear, or compress.In all cases
CT_E10: The figure show a block suspended by two wires, A and B, which are identical except for their original lengths.
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Shearing
Hydraulic Stress
G - Shear Modulus (units: N/m2)
- Bulk Modulus (units: N/m2)