P201 Exam 3

A wheel rotates with a constant angular acceleration of 3.80 rad/s2. Assume the angular speed of the wheel is 2.35 rad/s at ti = 0. (c) What angular displacement (in revolutions) results while the angular speed found in part (b) doubles?

(wf²-wi²)=2aΔθ solve for Δθ

A wheel rotates with a constant angular acceleration of 3.80 rad/s2. Find the angle through which the wheel rotates between t = 2.00 s and t = 3.30 s.

(Δθf= (ω)t+½at²)-(Δθi= (ω)t+½at²)

x = (0.325 m) cos (1.05t) (c) What are the position, velocity, and acceleration of the object after 1.45 s has elapsed?

***Put calculator in radian*** X=A cos(ωt) V=-Aω sin(ωt) a=-Aω²cos(ωt)

A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 420 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. With what angular speed does the turntable rotate?

0=(m) (r) (v)+(I) (ω) solve for ω

Mars rotates on its axis once every 1.02 days (almost the same as Earth does). (a) Find the distance from Mars at which a satellite would remain in one spot over the Martian surface. (Use 6.42 1023 kg for the mass of Mars.)

1.Convert the number of days to seconds r³=GMT² ---- 4π²

x = (0.325 m) cos (1.05t) Find A, F, and T

A=0.325 F=ω/2π ω=1.05 T=1/F

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 61,000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period.

Convert from miles to ft by multiplying by 5280 ft θ=s/r

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 61,000 miles. (b) How many revolutions of the tire are equivalent to your answer in (a)?

Convert from radians to revolutions by dividing radian by 0.159

Use the worked example above to help you solve this problem. A 0.475 kg object connected to a light spring with a spring constant of 18.0 N/m oscillates on a frictionless horizontal surface. (a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm.

E=½kA² ½(m)(v²max)=E solve for vmax A=length

A jet traveling at a speed of 1.90 102 m/s executes a vertical loop with a radius of 6.50 102 m. (See Figure (b).) Find the magnitude of the force of the seat on a 70.0-kg pilot at the following positions. (a) at the top, and bottom

F-mg=force at top F+mg=force at bottom F=mv²/r

A bicycle wheel has a diameter of 63.4 cm and a mass of 1.81 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 121 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.95-cm-diameter sprocket in order to give the wheel an acceleration of 4.48 rad/s2?

F= (I) (a)+(Fr) (r₁) ...------------ ..........(r₂) I=Mr₁²

When four people with a combined mass of 290 kg sit down in a 2000-kg car, they find that their weight compresses the springs an additional 0.70 cm. (b) The four people get out of the car and bounce it up and down. What is the frequency of the car's vibration?

F=1/2π√k/m

The International Space Station has a mass of 4.19 ✕ 105 kg and orbits at a radius of 6.79 ✕ 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 92.0 kg astronaut living inside the station.(a) the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.)

F=G (Me)(Mss) ......------- ..........rss²

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.45 m, rotating with an angular speed of 3.55 rad/s. (b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?

Fc=m(ac)

A sample of blood is placed in a centrifuge of radius 13.0 cm. The mass of a red blood cell is 3.0 ✕ 10−16 kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 ✕ 10−11 N. At how many revolutions per second should the centrifuge be operated?

Fc=mrw² solve for w then multiply by 0.159 for conversion

A woman of mass m = 57.7 kg sits on the left end of a seesaw—a plank of length L = 3.59 m, pivoted in the middle as shown in the figure. (b) Find the normal force exerted by the pivot if the plank has a mass of mpl = 10.2 kg.

Fn=(Mm+Mw+mpl)g

Suppose a wedge is placed 1.50 m from the hinges on the other side of the door. What minimum force must the wedge exert so that the force applied in part (a) won't open the door?

Fw(-r)=-Tf solve for Fw

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars.

GM= (2π ²/T) (r³)

(c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm.

KE=½mv² PE= ½kx²

A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 16.0 s. (a) How tall is the tower?

L=gt² --- 4π²

(a) where L is the length of the pendulum and g is the acceleration due to gravity at the pendulum's location. Thus, if a pendulum has a period of T = 1.5 s on Earth where gEarth = 9.8 m/s2, its length is

L=gt² ---- 4π

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 202 m, and the car completes the turn in 35.0 s. (b) What is the magnitude and direction of the acceleration when the car is at point B?

Mag. of acceleration =v²/r r= s ----- π/2 direction 145

A dentist's drill starts from rest. After 4.40 s of constant angular acceleration it turns at a rate of 2.25 ✕ 104 rev/min. (a) Find the drill's angular acceleration

Multiply rate by 6.281 then multiply time by 60 then divide rate by time

The International Space Station has a mass of 4.19 ✕ 105 kg and orbits at a radius of 6.79 ✕ 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 92.0 kg astronaut living inside the station. (b) the space station's gravitational potential energy (in J)

PE=-G (Me)(Mss) ............------- ...............rss

A space station shaped like a giant wheel has a radius of 139 m and a moment of inertia of 4.98 ✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What apparent acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.

Population initially (m)(r²)+I Population finally (m)(r²)+I divide the two

A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 16.0 s. (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2, what is the period there?

T=2π√L/a

A dental bracket exerts a horizontal force of 93.8 N on a tooth at point B in the figure. What is the torque on the root of the tooth about point A?

T=fd d=(L) cosθ

A man ties one end of a strong rope 8.21 m long to the bumper of his truck, 0.507 m from the ground, and the other end to a vertical tree trunk at a height of 2.90 m. He uses the truck to create a tension of 7.89 10^2 N in the rope. Compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point.

T=t(cosθ)(bigger h) Cosθ= √L²-(bigger h-smaller h)²/L

The fishing pole in the figure below makes an angle of 20.0° with the horizontal. What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force F = 110 N at an angle 37.0° below the horizontal? The force is applied at a point L = 1.84 m from the angler's hands.

T=|Fsinθ(L)|

A man applies a force of F = 3.00 102 N at an angle of 60.0° to a door, x = 2.10 m from the hinges. Find the torque on the door, choosing the position of the hinges as the axis of rotation.

Tf=r(Fsinθ)

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in the figure below. The length of the arc ABC is 202 m, and the car completes the turn in 35.0 s. (a) Determine the car's speed.

V=s/t

x = (0.325 m) cos (1.05t) (b) Find the maximum magnitude of the velocity and acceleration.

Vmax=aω Amax=aω² a=amplitude

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. (c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.

Vt=rw

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. find the tangential speed at the rim at this time.

Vt=rw

the weight (in N) of an 92.0 kg astronaut living inside the station

W=m (GMe/rss²)

A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 420 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. How much work is done

W=½(m)(v²)+½(I)(ω²)

A solid, frictionless cylinder reel of mass M = 2.86 kg and radius R = 0.360 m is used to draw water from a well (see Figure (a)). A bucket of mass m = 2.08 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.) (a) Find the tension T in the cord and acceleration a of the bucket.

a=-mg/(m+½M) T=-½ Ma

(a). Find the amplitude, wavelength, speed, and period of the wave if it has a frequency of 7.60 Hz. In Figure (a), Δx = 42.0 cm and Δy = 15.0 cm.

a=∆y λ=∆x V=ƒλ T=1/ƒ

A block-spring system consists of a spring with constant k = 405 N/m attached to a 2.50 kg block on a frictionless surface. The block is pulled 4.60 cm from equilibrium and released from rest. For the resulting oscillation, find the amplitude, angular frequency, frequency, and period. What is the maximum value of the block's velocity and acceleration?

a=∆y 4.60→0.046 angular frequency= √k/m frequency= w/2π period= 2π√m/k vmax=√ka²/m amax= ka/m

A race car accelerates uniformly from a speed of 41.0 m/s to a speed of 59.5 m/s in 5.00 s while traveling clockwise around a circular track of radius 3.90 102 m. When the car reaches a speed of 50.0 m/s, find the following. (d) the magnitude of the total acceleration (centripetal)

a=√at²+ac²

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.45 m, rotating with an angular speed of 3.55 rad/s. (a) What is the child's centripetal acceleration?

ac = w²r

A 57.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 21.0 m. (a) The child moves in a circular path of radius r = 10.5 m with a constant angular velocity of ω = 4.00 rev/min. The centripetal acceleration is..

ac=rw² w=rate times 6.281 divided by 60

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. (a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?

angular acceleration=w/t

A race car accelerates uniformly from a speed of 41.0 m/s to a speed of 59.5 m/s in 5.00 s while traveling clockwise around a circular track of radius 3.90 102 m. When the car reaches a speed of 50.0 m/s, find the following. (a) the magnitude of the centripetal acceleration

centripetal acceleration=v²/r

Using a small pendulum of length 0.170 m, a geophysicist counts 75.0 complete swings in a time of 60.0 s. What is the value of g in this location?

g=4π²L ------ T²

When four people with a combined mass of 290 kg sit down in a 2000-kg car, they find that their weight compresses the springs an additional 0.70 cm. (a) What is the effective force constant of the springs?

k=mg/∆x m= people

(c) Therefore, to have a period T = 1.5 s when suspended from a spring with a force constant k = 10 N/m, the required mass is

m=kT² ---- 4π²

from rad to rev

multiply by 0.159

from rev to rad

multiply by 6.281

A dentist's drill starts from rest. After 4.40 s of constant angular acceleration it turns at a rate of 2.25 ✕ 104 rev/min. (b) Determine the angle (in radians) through which the drill rotates during this period.

multiply rate by 6.281 and divide that by 60 then divide the whole answer by 2 then multiply that answer by time θ=wt

A 57.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 21.0 m. (b) At the lowest point of the ride, the forces acting on the child are a normal force exerted by the seat and the gravitational force. These forces are shown in the diagram below.

n=m(g+ac)

A 57.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 21.0 m. (c) At the highest point of the ride, the forces are as shown in the diagram below

n=m(g-ac)

What does w mean

speed

A race car accelerates uniformly from a speed of 41.0 m/s to a speed of 59.5 m/s in 5.00 s while traveling clockwise around a circular track of radius 3.90 102 m. When the car reaches a speed of 50.0 m/s, find the following. (c) the magnitude of the tangential acceleration

tangential acceleration= vf-vi/Δt

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. (d) What is the magnitude of the tangential acceleration of the microbe at the given time?

tangential acceleration=ra

At what maximum speed can a car negotiate a turn on a wet road with coefficient of static friction 0.205 without sliding out of control? The radius of the turn is 23.5 m.

v²=μs*rg

A wheel rotates with a constant angular acceleration of 3.80 rad/s2. Assume the angular speed of the wheel is 2.35 rad/s at ti = 0. (b)What is the angular speed of the wheel at t = 2.00 s?

w=(wi)+at

A wheel rotates with a constant angular acceleration of 3.80 rad/s2. Find the angular speed when t = 3.30 s

w=(wi)+at

A race car accelerates uniformly from a speed of 41.0 m/s to a speed of 59.5 m/s in 5.00 s while traveling clockwise around a circular track of radius 3.90 102 m. When the car reaches a speed of 50.0 m/s, find the following. (b) the angular speed (centripetal)

w=v/r

A woman of mass m = 57.7 kg sits on the left end of a seesaw—a plank of length L = 3.59 m, pivoted in the middle as shown in the figure. (a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M = 69.1 kg sit if the system (seesaw plus man and woman) is to be balanced?

x=Mw(L/2) ---------- Mm

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.45 m, rotating with an angular speed of 3.55 rad/s. (c) What minimum coefficient of static friction is required?

µs= Fc/mg

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. (b) Through what angle does the disc turn while coming up to speed?

Δθ= (ω)t+½at²

A compact disc rotates from rest up to an angular speed of 34.3 rad/s in a time of 0.925 s. what is the angular displacement of the disc 0.250 s after it begins to rotate?

Δθ= (ω)t+½at²

A wheel rotates with a constant angular acceleration of 3.80 rad/s2. Assume the angular speed of the wheel is 2.35 rad/s at ti = 0. (a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions.

Δθ= (ω)t+½at² from radians to revolutions multiply by 0.159

A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 5.58 104 Hz, and if the speed of sound in air is 343 m/s, what is the smallest insect a bat can detect?

λ=v/f convert to mm

A car travels at a constant speed of 33.0 mi/h (14.7 m/s) on a level circular turn of radius 48.0 m, as shown in the bird's-eye view in figure a. What minimum coefficient of static friction, μs, between the tires and the roadway will allow the car to make the circular turn without sliding?

μs=v²/rg

A solid, frictionless cylinder reel of mass M = 2.86 kg and radius R = 0.360 m is used to draw water from a well (see Figure (a)). A bucket of mass m = 2.08 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.) (b) If the bucket starts from rest at the top of the well and falls for 3.30 s before hitting the water, how far does it fall?

∆y= Vot+½at² Vot=0