Chapter 5
A particle moves at constant speed in a circular path. The instantaneous velocity and instantaneous acceleration vectors are
perpendicular
An object is moving on a circular path of radius π meters at a constant speed of 4 m/s. The time required for a half revolution is
pi^2/4s v=2pir/T Divide t by two
What is seen at the bottom of the cycle in a motorcycle stunt?
. At the bottom, the normal force and the weight oppose one another, giving a centripetal force of magnitude FN1 − mg
A circular airport luggage carousel has a radius of 5.7 m. A suitcase on the carousel is moving at 0.84 m/s. How many revolutions does the suitcase make in the 7.4 minutes that it is on the carousel before its owner claims it?
10 rev
A particle at the edge of a disk makes 1600 revolutions in one hour while traveling at 0.333 m/s. What is the radius of the disk in centimeters?
11.9 cm
A giant wheel, having a diameter of 40 m, is fitted with a cage and platform on which a man of mass m stands. The wheel is rotated in a vertical plane at such a speed that the force exerted by the man on the platform is equal to his weight when the cage is at X, as shown. The net force on the man at point X is
2 mg down
The apparent weight of passengers at the rim of a rotating space station is 73.1 % of their actual weight at the surface of the Earth. If the rim of the station is 73.9 m from its center, what is the speed of passengers at the rim?
23.0
What occurs if the speed is too small for a given theta?
A car would slide down a frictionless banked curve, at a speed that is too large, a car would slide off the top.
Passengers at the rim of a rotating space station feel as if they were on the surface of the Earth. Which one of the following statements is true about the magnitude ac of the centripetal acceleration at the rim of the station?
Ac=g Because of the rotational motion, any object located on the rim of this space station experiences a centripetal force directed toward the axis.The force produces a centripetal acceleration equal to g, making passengers feel as if they were on the surface of the Earth.
What does the word centripetal mean?
Moving toward a center
What kind of quantity is centripetal acceleration?
A vector quantity, therefore it has direction and magnitude. The direction is toward the center of the circle.
The iron ball shown is being swung in a vertical circle at the end of a 0.70-m string. How slowly can the ball go through its top position without having the string go slack?
At the top point of the vertical orbit the tension force T, the weight of the ball mg, and the centripetal force Fc are all directed downward.The sum of these forces acting in the y direction can be expressed by:ΣFy=-T-mg=-FcIn this scenario, the tension force at the top position is equal to 0 N. We are left withT=Fc-mg=0mv2r=mgv2r=gCalculate the velocity.v20.70m=9.8ms2v2=6.9v=2.6ms
What is seen at the top of the cycle in a motorcycle stunt?
At the top, the normal force and the weight reinforce each other to provide a centripetal force whose magnitude is FN3 + mg.
What is the acceleration referred to in uniform circular motion?
Centripetal acceleration because it points toward the center of the circle.
What force must a passenger experience in order to remain on the circular path?
Centripetal force
Does speed differ in satellites?
Consequently for a given orbit, a satellite with a large mass has exactly the same orbital speed as a satellite with a small mass.
In what case scenario, is where there isn't enough static friction to keep the passenger in place?
If the upholstery is very slippery, there may not be enough static friction to keep him in place, so it seems like the passenger is thrown outside of the curve. The passenger is sliding off the tangent circle until he encounters a centripetal force to keep him in place.
What is acceleration?
Is the change in velocity (f-i) divided by the elapsed time.
What connection is made between Newton's second law and uniform circular motion?
Newton states, whenever an object is accelerated, there must be a net force to create the acceleration. Thus in uniform circular motion, there must be a net force to produce the centripetal acceleration.
Other things being equal, would it be easier to drive at high speed around an unbanked horizontal curve on the moon than to drive around the same curve on the earth?
No
What is period T?
Of a satellite is the time required for one orbital revolution. As in any uniform circular motion, the period is related to the speed of the motion by v=2pir/T
A rotating space laboratory (like the one discussed in Example 13) has inner and outer rings. Compare the passenger speed vO at the outer ring to the passenger speed vI at the inner ring.
Passengers at any point on the rotating space laboratory experience the same centripetal force,Fc=mv2r. In order for them to experience the same force, because rO>rI, so too must vO>vI.
What must riders have in order to perform the loop-the-loop trick?
Riders who perform the loop-the-loop trick must have at least a minimum speed at the top of the circle to remain on the track. The speed is determined at point 3.
What is the relationship between period and speed?
Since speed v is the distance traveled divided by the time. v=2pir/T
What provides centripetal force for a satellite?
Since the gravitational force is the only force acting on the satellite in the radial direction, it alone provides the centripetal force.
An astronaut in training will be spun in a circle on the end of a 8.3 m boom. If the linear speed reaches a value of 30 m/s, how many g's of acceleration is the astronaut subjected to?
Step One:Calculate the astronaut's centripetal acceleration.ac=v2rac=(30ms)28.3mac=108ms2Step Two:Calculate the number, n, of g's of acceleration the astronaut is subjected to.ng=108ms2n=108ms29.8ms2n=11
A toy train follows a circular track, completing ten laps around the track in 5.1 minutes. The train traveled a total distance of 131.9 meters. Find the radius of the track
The distance traveled in one lap is the circumference of the track, so the distance traveled over 10 laps is 10 times the circumference, 2πr.
A penny is placed on a rotating turntable. Where on the turntable does the penny require the largest centripetal force to remain in place: at the center of the turntable or at the edge of the turntable?
The edge of the turntable
What changes as the cycle goes around in a motorcycle stunt?
The magnitude of the normal force changes because the speed changes and because the weight does not have the same effect at every point.
What is an example of uniform circular motion?
The motion of a model airplane flying at a constant speed on a horizontal circular path.
What allows for a car to travel without skidding around an unbanked curve?
The static frictional force between the tires and the road provides the centripetal force.
When using the term "uniform circular motion," what do we mean by the term "uniform"?
The net force on the moving object is zero newtons. The motion of the object is at a constant speed. The direction of the object's velocity is constant. The motion occurs without the influence of the gravitational force. The forces acting on the object are uniformly applied from all directions. B) The motion of the object is at a constant speed
A space station in is a circular orbit about the Earth. A passenger on the space station feels "weightless". Which one of the following statements is true?
The passenger is accelerating toward earth The passenger and the space station "fall" with the same acceleration toward the center of the Earth and cannot push against one another, thus why they feel "weightless".
Consider two people, one on the earth's surface at the equator and the other at the north pole. Which has the larger centripetal acceleration?
The person at the equator
If the speed of an object undergoing uniform circular motion is doubled, what must happen to the radius of the motion, if the period remains constant?
The radius must double
What is the chance of a light car safely rounding an unbanked curve on an icy road as compared to that of a heavy car: worse, the same, or better? Assume that both cars have the same speed and are equipped with identical tires.
The same
If an object is moving in uniform circular motion, its period is given by which one of the following quantities?
The time interval for the object to make one revolution
A model airplane is following a circular path with a speed of 4.4 m/s. If the radius of the circle is 2.1 m, what is the period for the airplane's motion?
The time it takes the airplane to complete the circular loop can be found using the equationv=2πrTSolve for period T.4.4ms=2π×2.1mT4.4T=13.2T=3.0s
What occurs when the speed is constant?
The vectors have the same magnitude.
Would a change in the earth's mass affect (a) the banking of airplanes as they turn, (b) the banking of roadbeds, (c) the speeds with which satellites are put into circular orbits, and (d) the performance of the loop-the-loop motorcycle stunt?
Yes to all of them
The speedometer of your car shows that you are traveling at a constant speed of 35 m/s. Is it possible that your car is accelerating?
Yes, if you are going around a circle.
What is the formula for centripetal acceleration?
ac=v^2/r
What is the term for an object moving toward a center called?
centripetal acceleration
A stuntwoman jumps from a high bridge. Initially (before air resistance becomes significant), the stuntwoman is in a state of free fall. While in free fall, the stuntwoman's apparent weight is approximately equal to her actual weight.
false
In the formula below, "T" represents total energy.v=2πrT
false
A stone is tied to a string and whirled at constant speed in a horizontal circle. The speed is then doubled without changing the length of the string. Afterward, the magnitude of the acceleration of the stone is
four times as greatUsing the centripetal acceleration equation, the acceleration for the first scenario is:ac=v2rIf velocity is doubled and the string stays the same length,ac=(2v)2rac=4v2racceleration in the second scenario must be 4 times the acceleration in the first scenario4ac=4v2rac=v2r
What do greater speeds, and or tighter turns require?
greater centripetal forces
An iron ball weighing 9.8 N is being swung in a vertical circle at the end of a 1.4-m string. What is the tension force at the 3 o'clock position, if the ball moves at 2.2 m/s?
sum of forces x=T=Fc w=mg T=mv^2/r T=3.5N
What is the chance of a light car safely rounding an unbanked curve on an icy road as compared to that of a heavy car? Assume that both cars have the same speed and are equipped with identical tires.
the same
A particle at the edge of a disk with a diameter of 46 mm makes 850 revolutions per minute. What is the velocity of the particle?
v=2.0
The Tower is an amusement park ride that takes one minute to complete a revolution when the circular car is at its maximum height. The car has a diameter of 9.75 m. What is the speed of a person as they look at the sites from one of the ride's many windows?
v=2pir/T
A children's roller coaster has a horizontal, circular loop of radius 4.00 m. Cars enter the loop with a speed of 11.5 m/s. How long does it take for a car to complete the circular loop?
v=2pir/T T=2.19
What is apparent weightlessness?
weightlessness is when the force of Gravitational attraction is zero, where acceleration due to gravity is equal to zero. Apparent weightlessness is where gravity act so weight equals mg but the apparent weight(normal force) is zero because the object is accelerating in free fall where the acceleration equals g.
A car moves at a constant speed along a straight line as it approaches a circular turn. In which of the following parts of the motion is the car in equilibrium?
As it moves along the straight line toward the circular turn and as it moves away from the turn along a straight line. In both of these cases, the speed and direction of motion are constant. Thus, the velocity vector does not change, and there is no acceleration.
What is seen at 2 and 4 of the cycle in a motorcycle stunt?
At points 2 and 4 on either side, only FN2 and FN4 provide the centripetal force. The weight is tangent to the circle at points 2 and 4 and has no component pointing toward the center.
One end of a 0.50-m long string is fixed; the other end is attached to a 1.2-kg stone. The stone swings in a vertical circle, passing the bottom point at 5.0 m/s. The tension force of the string at this point is about
At the bottom point of the vertical orbit, three forces act upon the stone: T is the tension force, mg is the weight of the stone, and Fc is the centripetal force.The sum of the forces acting on the stone in the y direction can be expressed by:ΣFy=T-mg=FcSolve the expression for tension.T=Fc+mgT=mv2r+mgCalculate the tension force.T=(1.2kg)(5.0ms)20.5m+(1.2kg)(9.8ms2)T=60+12=72N
The iron ball shown is being swung in a vertical circle at the end of a string, moving at 3.0 m/s. What must the length of the string be such that the ball can go through its top position without having the string go slack?
At the top point of the vertical orbit the tension force T, the weight of the ball mg, and the centripetal force Fc are all directed downward. The sum of these forces acting in the y direction can be expressed by: ΣFy=-T-mg=-Fc In this scenario, the tension force at the top position is equal to 0 N. We are left with T=Fc-mg=0 mv2/r=mg v2r=g Calculate the length of the string (the radius).(3.0ms)2/r=9.8ms2 9=9.8r 0.92m=r
The iron ball shown is being swung in a vertical circle at the end of a string, moving at 3.0 m/s. What must the length of the string be such that the ball can go through its top position without having the string go slack?
At the top point of the vertical orbit the tension force T, the weight of the ball mg, and the centripetal force Fc are all directed downward.The sum of these forces acting in the y direction can be expressed by:ΣFy=-T-mg=-FcIn this scenario, the tension force at the top position is equal to 0 N. We are left withT=Fc-mg=0mv2r=mgv2r=gCalculate the length of the string (the radius).(3.0ms)2r=9.8ms29=9.8r0.92m=r
A physics student of mass 54 kg rides a Ferris wheel around in a vertical circle of radius 12 m at a constant speed of 7.1 m/s. What is the magnitude of the normal force on her from the seat when she goes through the highest point of the circular path
At the top point of the vertical orbit, the sum of the forces acting in the y direction can be expressed by: ΣFtop=FN(top)- mg=-FcFN(top)=-Fc+mgCalculate the magnitude of the normal force.FN(top)=-mv2r+mgFN(top)=-(54kg)(7.1ms)212m+(54kg)(9.8ms2)FN(top)=300N
One end of a 1.0-m string is fixed; the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the top point at 4.0 m/s. The tension force of the string at this point is about
At the top point of the vertical orbit, three forces act upon the stone, all directed downward. T is the tension force, mg is the weight of the stone, and Fc is the centripetal force.The sum of the forces acting on the stone in the y direction can be expressed by:ΣFy=-T-mg=-FcS olve the expression for tension.T=Fc-mgT=mv2r-mgCalculate the tension force.T=(2.0kg)(4.0ms)21.0m-(2.0kg)(9.8ms2)T=32-20=12N
Passengers at the rim of a rotating space station feel as if they were on the surface of the Earth. If the speed of passengers at the rim is 33.3 m/s , what is the distance between the rim and the center of the station?
Because of the rotational motion, any object located on the rim of this space station experiences a centripetal force directed toward the axis.The force produces a centripetal acceleration equal to g, making passengers feel as if they were on the surface of the Earth.Calculate the radius. Ac=g=v^2/r r=113
Which of the following statements about centripetal acceleration is true? (a) An object moving at a constant velocity cannot have a centripetal acceleration. (b) An object moving at a constant speed may have a centripetal acceleration.
Both are correct
What is a better way of describing uniform circular motion?
By specifying the period of the motion, rather than the speed.
A stone is tied to a string and whirled around in a circle at a constant speed. Is the string more likely to break when the circle is horizontal or when it is vertical? Assume that the constant speed is the same in each case
Vertical
It takes a toy car 7.0 s to go around half a circle with a radius of 2.0 m. If the speed of the car is constant, what is the magnitude of the instantaneous acceleration of the car during this time?
0.41s you have to double the time
A rotating space station simulates artificial gravity by means of centripetal acceleration at the rim. If the station rotates once every 33.5 s, and the distance from the center to the rim is 125 m, then what is the apparent weight of a 58.1 -kg passenger at the rim?
1) Calcualte the velocity of the passenger 2) Calculate weight mv^2/r 255 N
A 0.60-kg stone is attached to a string and swung in a circle of radius 0.60 m on a horizontal and frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the string on the stone is
1) Convert rev/min to seconds 2) Use formula Fc=mv^2/r Fc= 0.60 *9.4^2/0.60 88N
A car rounds a 60-m radius curve at a constant speed of 22 m/s. A ball of mass 1.0 kg is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the vertical is
1) Find centripetal force with formula Fc=mv^2/r 2) Calculate force of gravity Fg=mg 3) angle of x direction is inverse tangent
The apparent weight of passengers at the rim of a rotating space station is 70.0 % of their actual weight at the surface of the Earth. If the rim of the station is 86.3 m from its center, what is the speed of passengers at the rim?Type your answer here m/s
1) calculate velocity Ac=0.700*g=v^2/r 24.3 m/s
An airplane flying at a speed of 250 km/h pulls out of a vertical dive by turning upward along a circular path. What is the smallest radius of the circle such that the acceleration of the plane does not exceed 4.00 g, where g = 9.80 m/s2?
1) convert km to m 2) use formula ac=v^2/r (4.00)(9.80)= v^2(insert converted form /r
An model airplane is following a circular path with a speed v = 6.2 m/s. If the radius of the circle is 1.7 m, what is the period for the airplane's motion?
1.7
A roller coaster has a horizontal, circular loop of radius 4.75 m. Cars enter the loop with a speed of 14.5 m/s. How long does it take for a car to complete the circular loop?
2.06
A newly completed highway has a curve with a radius of 136 m and is banked at an angle of 23.2 degrees. What is the maximum speed that a minivan can have and still follow the curve safely under very icy conditions?
23.9 m/s
Passengers at the rim of a rotating space station feel as if they were on the surface of the Earth. If the rim of the station is 63.2 m from its center, what is the speed of passengers at the rim?
24.8 m/s
In uniform circular motion at constant speed, the particle travels the circumference of the circle in time defined by
2pir/v
One end of a 1.5-m long string is fixed; the other end is attached to a 2.0-kg bucket of water. The bucket swings in a vertical circle, passing the bottom point at a speed of 4.0 m/s. The tension force of the string at this point is closest to
31 At the bottom point of the vertical orbit, three forces act upon the bucket: T is the tension force, mg is the weight of the bucket, and Fc is the centripetal force.The sum of the forces acting in the y direction can be expressed by:ΣFy=T-mg=FcSolve the expression for tension.T=Fc+mgT=mv2r+mgCalculate the tension force.T=(2.0kg)(4.0ms)21.5m+(2.0kg)(9.8ms2)T=21+20=41N
A particle at the edge of a disk with a diameter of 54 cm travels at 1.3 m/s. How many revolutions does the particle make in one minute?
46
A car is traveling in uniform circular motion on a section of road whose radius is r (see the drawing.) The road is slippery and the car is just on the verge of sliding. If the car's speed were doubled, then what would have to be the smallest radius in order that the car does not slide?
4r
A car rounds a 20 m radius curve at 10 m/s. The magnitude of its acceleration in m/s2 is
5
A 90.0 -kg passenger stands at the rim of a rotating space station and feels as if he were on the surface of the Earth. What is the normal force exerted on the feet of the passenger?
882 90.0*9.8
An airplane makes a gradual 120 ° turn while flying at a constant speed of 175 m/s. The process takes half a minute to complete. For this turn, the magnitude of the average centripetal acceleration of the plane is
A 120o turn constitutes 1/3 of a revolution, and is completed in 30 seconds. Calculate the time it takes to make 1 full revolution.13T=30sT=90sCalculate the radius of the path.v=2πrT175ms=2πr90s15750=2πr2507m=rCalculate the centripetal acceleration.ac=v2rac=(175ms)22507mac=12.2ms2
Where does an object in uniform circular motion accelerate towards?
Accelerates toward the center of the circle at every moment.
Which of the following statements about centripetal acceleration is true? More than one statement or no statements may be true.
An object moving at a constant velocity cannot have a centripetal acceleration. An object moving at a constant speed may have a centripetal acceleration.
Uniform circular motion, in which an object moves on a circular path at constant speed, is an example of motion where the acceleration is equal to zero.
False
A person riding a Ferris wheel is strapped into her seat by a seat belt. The wheel is spun so that the centripetal acceleration is g. Select the correct combination of forces that act on her when she is at the top. Here, Fg = force of gravity, down; Fb = seat belt force, down; and Fs = seat force, up.
Fg=mg, Fb=0, Fs=0
A highway engineer wishes to design a roadway curve that has a bank angle of 9.72 degrees. The curve will enable vehicles to follow the curve at a maximum speed of 20.4 m/s, even in the absence of friction. What is the radius of the curve?
Formula for banked curves is tan(theta)=v^2/rg 248
A geosynchronous satellite orbits the Earth once every 24 hours. What is the altitude above Earth's surface needed for a satellite to be geosynchronous?
Formula for orbital motion is T=2pir^3/2/square root GM 1) Convert time to seconds 2) Calculate total radius (mass of earth is 5.97*10^24) 3) Find altitude= subtracting radius from earth from total radius B) 3.6*10^4
What does GPS stand for and what does it do?
Global Positioning system, which can be used to determine the position of an object to within 15 m or less.
How can turns relate to different centripetal accelerations?
Going around tight turns (smaller r) and gentle turns (larger r) at the same speed entails different centripetal accelerations.
What kind of characteristics require steeply banked curves, also known as larger values of theta?
Greater speeds and smaller radii
What must be known in order for the normal force to be calculated at the 4 points?
If the speed at each of the four places is known, along with the mass and the radius, the normal forces can be determined.
A truck is traveling at 6.7 m/s due north as it exits a highway. The truck exits to the right, following a road curved such that the truck follows a circular path for 27 seconds, at which time it is directed due west. Assuming the truck's speed remained constant, what is the radius of the circular path?
In order for the truck's direction to change from north to west, the truck must travel three quarters the circumference of its path.Calculate the time it takes for the truck to travel the circumference of its path.34T=27sT=36sCalculate the radius of the truck's path.v=2πrT6.7ms=2πr36s241=2πr 38m=r
What is uniform circular motion?
Is the motion of an object traveling at a constant (uniform) speed on a circular path. Emphasizes that the speed, or the magnitude of the velocity vector, is constant. The direction of the vector is not constant.
What is period T?
Is the time required to travel once around the circle-that is, to make one complete revolution.
Two satellites are placed in orbit, one about Mars and the other about Jupiter, such that the orbital speeds are the same. Mars has the smaller mass. What is true about the radius of the orbit of the satellite that orbits Mars?
It is less than the radius of the orbit of the satellite orbiting Jupiter.
The speedometer of your car shows that you are traveling at a constant speed of 35 m/s. Is it possible that your car is accelerating?
It is possible
Two satellites are placed in orbit, one about Mars and the other about Jupiter, such that the orbital speeds are the same. Mars has the smaller mass. Is the radius of the satellite in orbit about Mars less than, greater than, or equal to the radius of the satellite orbiting Jupiter?
Less than
What is centripetal force?
Magnitude: the centripetal force is the name given to the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of Fc=mv^2/r Labels the pointing toward the center of the circular path, and this net force is the vector sum of all the force components of a single force such as tension.
Other things being equal, which would be easier? To drive at high speed around an unbanked horizontal curve on the moon To drive at high speed around an unbanked horizontal curve on the earth Neither would be easier because there's no difference
Since the magnitude of the acceleration due to gravity is greater on the earth, then it'd be easier to drive at high speed there.
A circular airport luggage carousel has a radius of 4.5 m. A suitcase on the carousel is moving at 0.91 m/s. How many revolutions does the suitcase make in the 4.5 minutes that it is on the carousel before its owner claims it?
Step One:Calculate the period of one revolution.v=2πrT0.91ms=2π×4.5mT0.91T=28.3T=31.1srev Step Two:Calculate how many revolutions the luggage made, by dividing the time spent on the carousel by the period.Be sure to convert to seconds.4.5min(60s1min)31.1srev=8.7rev
What is the centripetal acceleration of a person standing at the equator? Take the radius of Earth to be 6400 km.
The Earth rotates at a speed of about 460 meters per second, as does the person standing at the equator.Convert the radius of the Earth to meters.6400km(1000m1km)=6400000mCalculate the person's acceleration.ac=v2rac=(460ms)26400000mac=0.033ms2
What is centripetal acceleration?
The acceleration that occurs in circular motion
Where does the direction point in terms of the centripetal force?
The centripetal force always points toward the center of the circle and continually changes direction as the object moves.
The earth exerts the necessary centripetal force on an orbiting satellite to keep it moving in a circle at constant speed. Which statement best explains why the speed of the satellite does not change although there is a net force exerted on it?
The centripetal force is always perpendicular to the velocity
What force allows for a car to move at a steady speed around an unbanked curve?
The centripetal force keeping the car on the curve comes from the static friction between the road and the tires. It is static rather than friction because the tires are not slipping with respect to the radial direction.
What accounts for a smaller value of r and the greater the orbital speed would be?
The closeness of the satellite to the earth
Incorrect answer iconYour answer is incorrect. If it takes a satellite 96 minutes to make one revolution around the Earth (rEarth = 6370 km) and its acceleration is 8.0 m/s2, at what height above the Equator is it orbiting?
The satellite is located at some radius R above the Equator. Its total radius r isr=R+6370km.We can use the equations for uniform circular motion velocity and centripetal acceleration to calculate the satellite's total radius.Step One:Convert the period of motion to seconds.T=96min(60s1min)=5760sStep Two:Solve the centripetal acceleration equation for velocity.ac=v2racr=vStep Three:Substitute acr for velocity into the uniform circular motion equation and solve for the total radius r.v=2πrTacr=2πrT(8.0ms2)r=2πr5760s8r=4π2r2331776002.65×108=39.5r6710000m=rStep Four:Calculate the satellite's distance above the Equator.6710000m=R+6370000m340000m=RR=340km
A space shuttle is in orbit around the earth at an altitude of 200 miles. Which one of the following statements best explains why the astronauts experience "weightlessness"?
The spaceship is in free fall, and its floor cannot press upwards on the astronauts.The astronauts and the space-craft "fall" with the same acceleration toward the center of the Earth and cannot push against one another, thus why they feel "weightless".
An object is moving on a circular path of radius π meters at a constant speed of 4.0 m/s. The time required for one revolution is
The time it takes the object to complete the circular loop can be found using the equation v=2πrT Solve for period T. T=pi^2/2s
A toy train follows a circular track of radius 1.9 m. The train completes ten laps around the track in 4.9 minutes. Find the total distance traveled by the train as it completes the ten laps.
The train completes 10 laps around a track of radius 1.9 meters.The distance traveled in one lap is the circumference of the track, so the distance traveled over 10 laps is 10 times the circumference.d=10×2πrd=10×2π(1.9m)d=119m≈120m
A toy train follows a circular track of radius 1.9 m. The train completes ten laps around the track in 5.3 minutes. Find the average speed of the train as it completes the ten laps
The train completes 10 laps around a track of radius 1.9 meters.The period of the motion is the time it takes to complete one lap.Find the period of motion for one lap by dividing 5.3 minutes by 10. (Convert to seconds).T=5.3min10laps(60s1min)=31.8 seconds per one lapCalculate the average speed of the train.v=2πrTv=2π×1.9m31.8sv=0.38ms
A car travels at a constant speed around a circular track. Which one of the following statements about this car is true?
The velocity of the car is changing
How is it that direction of the vector is not constant under uniform circular motion?
The velocity vector changes direction as the plane moves around the circle, any change in the acceleration is occuring.
What is the speed of a satellite?
There is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius.
What is the acceleration like in a large circle?
Uniform circular motion along the arc of an infinitely large circle entails no acceleration, because it is just like motion at a constant speed along a straight line.
For a biological sample in a centrifuge of radius 1.0 m to have a centripetal acceleration of 25g's, its speed must be (where one g is taken as 10 m/s2 )
Use the centripetal acceleration formula to find the speed of the sample.ac=v2r25×10ms2=v21.0m250=v2 16ms=v
A carnival ride called "The Gravitron" has a radius of 4.5 m, and riders experience a centripetal acceleration of 3g's. Its speed must be (where g is taken as 10 m/s2 )
Use the centripetal acceleration formula to find the speed of the sample.ac=v2r3×10ms2=v24.5m135=v2 12ms=v
In a circus, a man hangs upside down from a trapeze, legs bent over the bar and arms downward, holding his partner. Is it harder for the man to hold his partner (a) when the partner hangs straight down and is stationary or (b) when the partner is swinging through the straight-down position?
When the partner is swinging through the straight-down position because when the two are swinging, the partner is moving on a circular arc, and therefore, has a centripetal acceleration. The man's arms must support the partner's weight and must simultaneously exert an additional pull to provide the centripetal force that produces this acceleration. Because of the additional pull, it is harder for the man to hold his partner while swinging.
The acceleration due to gravity on the moon is one-sixth that on earth. (a) Is the true weight of a person on the moon less than, greater than, or equal to the true weight of the same person on earth? (b) Is the apparent weight of a person in orbit about the moon less than, greater than or equal to the apparent weight of the same person in orbit about the earth?
a) less than ; (b) equal to
Which of these would be affected by a change in the earth's mass? the banking of airplanes as they turn the banking of roadbeds the speeds with which satellites are put into circular orbits the performance of the loop-the-loop motorcycle stunt
all
A penny is placed on a rotating turntable. Where on the turntable does the penny require the largest centripetal force to remain in place?
at the edge of the turntable
An astronaut in an orbiting space-craft feels "weightless" because she
has the same acceleration as the space-craft.The astronaut and the space-craft "fall" with the same acceleration toward the center of the Earth and cannot push against one another, thus why she feels "weightless".
The car in the drawing is moving clockwise around a circular section of road at a constant speed. What are the directions of its velocity and acceleration at positions 1 and 2?
position 1: velocity south, acceleration west. position 2: velocity west, acceleration north
A stone is tied to a string and whirled around in a circle at a constant speed. Is the string more likely to break when the circle is horizontal or when it is vertical? Assume that the constant speed is the same in each case.
vertical
