physics ch 8
give four examples of units of rotational speed
revolutions per second revolutions per minute rotations per second rotations per minute
people in the future live inside a rotating space structure that is 4 km in diameter. inside the structure, people on the inside of the outer edge will experience 3 g while people halfway to the axis will experience how much gravity?
1.5 g
mrs. corlew loves to make vanilla frappuccinos in her new blender. if she blends an 8.00 g ice cube on high so that it spins around the blender at 23.0 m/s with a centripetal force of 11.2 N. what is the radius of the blender?
ac = 11.2 / .008 = 1400 m/s^s r = (23)^2 / 1400 r = 0.378 m
to test their stamina, astronauts are subjected to many rigorous physical tests before they fly in space. one such test involves spinning the astronauts in a device called a centrifuge that subjects them to accelerations far greater than gravity. with what linear speed would an astronaut have to spin in order to experience an acceleration of 3 g's at a radius of 10.0 m?
ac = 3g = 3(9.8) = 30 m/s^2 ac = v^2 / r 30 = v^2 / 10 v = 20 m/s
what is centrifugal force?
an outward "force" that can attribute to circular motion
define centripetal force
any force that causes an object to follow a circular path
an object will always stop with its center of gravity where?
as low as possible
what is a straight line about which rotation takes place?
axis
why does the sun wobble as it moves through space?
because its orbiting planets cause a shift in the sun's center of mass
why is centrifugal force considered a fictitious force?
because the force has no agent such as mass and no interacting counterpart
why does a person weigh slightly less at the equator than at the poles?
because the tangential speed of the earth is greater at the equator, people are "pushed off" the scales
why does a tennis ball whirled on the end of a string move in a circle?
because there is an inward force acting on the ball
how can you locate the center of gravity of an object?
by drawing lines straight down from suspension points by looking at the intersecting lines drawn from suspension points by balancing it above your finger
what are three examples of objects that have their center of gravity located at a point where there is no mass?
donut, ring, boomerang, baseball
luigi twirls a round piece of pizza dough overhead with a frequency of 60 revolutions per minute. a) find the linear speed of a stray piece of pepperoni stuck on the dough 10 cm from the pizza's center. b) in what direction will the pepperoni move if it flies off while the pizza is spinning? explain the reason for your answer
f = 60rev / min = 1 rev/sec t = 1/f = 1/1 = 1 s a) v = 2pi(r)/t = 2pi(10) / 1 = 60 cm/s b) it will go tangent to the pizza because the pepperoni's inertia is tangent to the circle
what tangential speed must a 65.0 kg person have in order to feel weightless in a carnival ride that has a radius of 20.00 m and spins with 3.000 rotations in one minute?
fc = 65*9.8 = 657 N t = 3rot/1min = .05 rot/1sec = 20s/1rot fc = mv^2 / r 657 = (65)(v^2) / 20 v = 14.0 m/s
where is the center of mass of the solar system? is it in the same location as the center of gravity? why or why not?
it varies as the planets move, but usually slightly outside the center of the sun. CG is usually at the sun's center where the most mass is located
if the earth were to rotate more slowly about its axis, what would happen to your weight? why?
it would increase because there is a lower tangential speed
any object thrown into the air rotates about what point?
its center of gravity
the long heavy tail of a squirrel enables it to easily vary what?
its center of gravity
if an object is in neutral equilibrium, any displacement will do what to its center of gravity?
its center of gravity remains unchanged
which has greater linear speed, a ladybug near the outside of a turntable or an inchworm near the inside? why?
ladybug near the outside because it covers a longer distance during each rotation
in which direction on earth should you travel in order to decrease your weight when you live in the northern hemisphere?
south, go toward the equator to increase tangential speed
a rock polisher with a radius of 30.0 cm turns with a frequency of 0.35 Hz. what is the centripetal acceleration of a small rock wedged on the inside wall of the tumbler?
t = 1/0.35 = 2.9 s v = 2pi(.3) / 2.9 = 0.65 ac = (0.65)^2 / 0.3 = 1.4 m/s^2
if you whirl a ball on the end of a string and the string suddenly breaks, in what direction will the ball move?
tangent to the circular path
an astronaut hovers in space beside a rotating asteroid. both he or she and the center of mass of the asteroid are at relative reset. if the asteroid is in earth's orbit, does the astronaut also have to be in earth's orbit? why?
yes because if they are hovering together, they must be rotating together
a possible space habitat of the future is a doughnut shaped craft rotating about its axis. what is the relative gravitational field at the axis of this habitat?
zero
what is a center of gravity?
a point located at an object's average position of weight
a 3.20 kg hawk circles overhead in search of prey. a) if the hawk circles once every 10.0 s in a circle 12.0 m in radius, what is the linear speed of the hawk? b) what centripetal force allows him to remain in a circle? c) what is providing the centripetal force?
a) v = 2pi(r) / t = 2pi(12) / 10 = 7.54 m/s b) ac = v^s / r = 7.54^2 / 12 = 4.7 m/s^2 fc = m*ac = 3.20*4.7 = 15.0 N c) the air pushing up against his wings
a space habitat designed so that the variation in g between a person's head and feet is less than 2/1000 g. if the person is 5m tall, then what is the radius of the habitat?
g = h/r 2/1000 = 5/r r = 2500 m
if a plumb line is dropped from a suspension point of a square piece of cardboard, what can you say about the amount of weight and mass on each side of the line? where will the center of gravity be in relation to the line?
half of the weight and half of the mass will be on either side of the line and the center of gravity will be directly along the line
when you carry a heavy load with one arm, why do you tend to hold your free arm away from your body?
in order to move the center of gravity of your body and the load back over your support base which is your feet
what is the direction of the force that acts on lettuce while it's spinning in a salad spinner? what is this force called?
inward toward the center. centripetal force
you push a ping pong beneath the surface of water in a glass of water. what happens to the center of gravity of the glass of water?
it increases
if you would begin to sprint in the direction that the station rotates, what happens to the magnitude of the simulated gravity that you feel?
it increases because tangential speed is higher
as the rotational speed of a space habitat increases, what happens to the weight of people inside? why?
it increases because they are pushed down against the scale
what must be true of an object's center of gravity if it topples?
it is outside of the area of support
if an object is in unstable equilibrium, any displacement will do what to its center of gravity?
lower it
which has greater rotational speed, a ladybug near the outside or an inchworm near the inside? why?
neither. they both have the same rotational speed because they both have the same period
a box resting on the floor is in what kind of equilibrium?
neutral. as long as the displacement is pushing it across the floor, not lifting it
will a child on a turning merry-go-round make more turns per minute if he or she walks toward the center of the merry-go-round? why or why not?
no, rotational speed is equal at all points along a rotating object
is the center of gravity of an object equivalent to the object's geometric center? is it equivalent to its center of mass?
no. it has more to do with weight than shape no. usually true but not for very large objects that may have variations in gravity
do passengers on a rotating platform of a carnival ride need to be strapped in to keep from falling out?
no. the reaction force of the carnival ride pushing inward against their weight pushing outward keeps passengers in
when an irregularly shaped object is thrown spinning through the air, what path does its center of gravity follow?
parabolic path
if an object is in stable equilibrium, any displacement will do what to its center of gravity?
raise it
an inchworm rests on the bottom of a cup that is being whirled horizontally on the end of a string. since the inchworm, like the cup, moves in a circle, there must be a force on it. what exerts this force?
the cup
where is the center of gravity of a hammer located?
the more massive side
define rotational speed
the number of rotations per unit of time
a period of rotation is the time it takes for what to happen?
the time it takes for one full rotation / revolution of an object
if you try to pick a small object up off the floor while standing flat against a wall, you will probably fall over. why?
the wall doesn't allow you to change your body position in order to keep your center of gravity inside your area of support, so your cg goes outside your feet support and you topple
if a swing on a carnival ride travels in a circle with constant speed, in what direction is the net force on the swing directed?
toward the center of the ride
where is the center of mass of a human located?
usually 2-3 cm below the navel, but it changes based on body orientation
based on stability concepts, you would expect a very tall building to have what?
very deep underground supports
