physics reading quiz- centripetal force and centripetal acceleration

acceleration

change in velocity, either in its magnitude or in its direction, or both

UCM direction of velocity…

changes constantly, so there is always an associated acceleration even though the mag of the velocity might be constant

sideways acceleration in a car

holding wheel steady during a turn and move at a constant speed 

Centripetal Acceleration

points directly toward the center of rotation (the center of the circular path) 

Centripetal

toward the center or center seeking

Triangle formed by…

by the velocity vectors and the one formed by the radii r and Δs are similar

Triangles ABC and PQR 

isosceles triangles (two equal sides)

Two equal sides of the velocity vector triangle are

the speeds v1=v2=v

Ac formula

V²/r and rw²

Centripetal Acceleration is greater at 

at high speeds and in sharp curves (smaller radius), a sharp corner has a small radius, so that ac is greater for tighter turns

Centrifuge

rotating device used to separate specimens of different densities

High centripetal acceleration significantly decreases…

the time it takes for separation to occur, and makes separation possible with small samples

Applications of Centrifuges

science and medicine- single cell suspensions (bacteria, viruses, and blood cells from a liquid medium) and macromolecules- DNA and protein from a solution 

Centrifuges are often rated in terms of their

centripetal acceleration relative to acceleration due to gravity (g)

Maximum centripetal acceleration

of several hundred thousand g is possible in a vacuum.

Human centrifuges (extremely large centrifuges)

have been used to test the tolerance of astronauts to the effects of accelerations larger than that of Earth’s gravity.

Net external force is needed to cause

any acceleration (N2L), so it is needed to cause a centripetal acceleration

Any force or combination of forces

can cause a centripetal or radical acceleration

Centripetal force 

Any net force causing uniform circular motion, direction is toward center of curvature, same direction as the direction of centripetal acceleration 

Fc=mac

magnitude of centripetal force

acceleration ac from ac=v2r;ac=rω2, we get two expressions for the centripetal force Fc in terms of mass, velocity, angular velocity, and radius of curvature:

Fc=mv²/r; Fc=mrω²

Centripetal force Fc is always perpendicular

to the path and pointing to the center of curvature, because ac is perpendicular to the velocity and pointing to the center of curvature

r=mv²/Fc.

implies that for a given mass and velocity, a large centripetal force causes a small radius of curvature—that is, a tight curv

banked curves

where the slope of the road helps you negotiate the curve, the greater the angle θ, the faster you can take the curve

ideally banked curves

the angle θ is such that you can negotiate the curve at a certain speed without the aid of friction between the tires and the road

ideal banking

the net external force equals the horizontal centripetal force in the absence of friction.

The components of the normal force N in the horizontal and vertical directions must equal

the centripetal force and the weight of the car, respectively

If the angle θ is ideal for the speed and radius, then

the net external force will equal the necessary centripetal force

weight of car and normal force of road must add to give a net external force

that is horizontal toward the center of curvature and has magnitude mv²/t, crucial force and horizontal- must use vertical and horizontal axes

Because the car does not leave the surface of the road, the net vertical force must be zero,

meaning that the vertical components of the two external forces must be equal in magnitude and opposite in direction

A large θ will be obtained

for a large v and a small r, roads must be steeply banked for high speeds and sharp curves

Note that θ does not depend

on the mass of the vehicle

Friction helps, because it allows you to take the curve at

greater or lower speed than if the curve is frictionless