Physics Final
A long pendulum extends from the ceiling of a tall tower almost to the floor. The period of the pendulum is 15.5 s. How tall is the tower?
59.6 m
If your body has a density of 995 kg/m3, what fraction of you will be submerged when floating gently in: (a) freshwater? (b) salt water, which has a density of 1027 kg/m3?
99.5% submerged; 96.9% submerged
An older model car accelerates from 0 to speed v in 10 s. A newer, more powerful sports car of the same mass accelerates from 0 to 2v in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars.
sports car 4x the older model
A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.20 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
F= 25N
A bullet with a mass of 5.0 g leaves the muzzle of a rifle with a speed of 320 m/s. What force (assumed to be constant) is exerted on the bullet while it is traveling down the 0.82-m long barrel of the rifle?
F= 312N
High-speed stroboscopic photographs shows that the head of a 200-g golf club is traveling at 55 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision the club head travels (in the same direction) at 40 m/s. Find the speed of the golf ball just after impact.
v2f = 65.2 m/s
Gayle runs at a speed of 4.00 m/s and dives on a sled, initially at rest on a frictionless, snowcovered hill. After she descends a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back, and they continue down the hill together. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 50.0-kg, the sled has a mass of 5.00-kg, and her brother has a mass of 30.0-kg.
v= 15.6 m/s
A 12.0 kg bullet is fired horizontally into a 100 kg wooden block that is initially at rest on a frictionless horizontal surface and connected to spring having a spring constant 150 N/m. The bullet becomes imbedded in the block. If the bullet-block system compresses the spring by a maximum of 80 cm, what was the speed of the bullet at impact with the block?
v= 273 m/s
A 2000 kg car moving east at 10.0 m/s collides with a 3000 kg car moving north. The cars stick together and move as a unit at an angle of 40.0° north of east and a speed of 5.22 m/s. Find the speed of the 3000 kg car before the collision.
vbi= 5.59 m/s
The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark estimate the time it takes the nerve impulse to travel to your brain.
~ 0.02 s
What is the tangential acceleration of a bug on a rim of a 0.254 m diameter disk if the disk accelerates uniformly to an angular speed of 8.17 rad/s in 3.00s? (b) When the disk is at its final speed, what is the tangential velocity of the bug? One second after the bug starts from rest, what are its (c) tangential acceleration, (d) centripetal acceleration, and (e) total acceleration?
(a) 0.346 m/s2 (b) 1.04 m/s (c) 0.346 m/s2 (d) 0.943 m/s2 (e) 1.00 m/s2 at 20.1° forward with respect to the direction (right) ac
A 0.250 -kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring force constant of 4.60 N/m located at the end of the track. (a) What is the springs maximum compression if the track is frictionless? (b) If the track is not frictionless, would the springs maximum compression be greater than, less than, or equal to the value obtained it part (a)?
(a) 0.350 m (b) less than 0.350 m because mechanical energy is lost due to the friction between the block and track
A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have a radius of 0.330 m? (b) What is the angular speed of the wheels when the car has traveled half the total distance?
(a) 116 rev (b) 62.1 rad/s
A mechanic pushes a 2.50 X 103 -kg car from rest to a speed of v., doing 5,000 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find (a) v and (b) the horizontal force exerted on the car
(a) 2.00 m/s (b) 200 N
A 7.80-g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. (a)Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the fictional is constant, determine how much time elapse between the m moment the bullet enters the tree and the moment it stops moving.
(a) 2.34 X 104 N (b) 1.91 X 10-4 s
A 0.20-kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Taking y=0 at the top of the edge of the well, what is the gravitational potential energy of the stone-Earth system (a) before the stone is released and (b) when it reaches the bottom of the well. (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
(a) 2.5 J (b) -9.8 J (c) -12.3 J
Objects with masses of 200 kg and 500 kg are separated by 0.400 m. (a) Find the net gravitational force exerted by these objects on a 50.0 kg object placed midway between them. (b) At which position (other than the infinitely remote ones) can the 50.0 kg object be placed so as to experience a net force of zero?
(a) 2.50*10-5 N toward the 500 kg object (b) between the two objects and around 0.245 m from the 500 kg object
A skier of mass 70 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him up a 30° slope (assumed frictionless) at a constant speed of 2.0 m/s? (b) What power must a motor have to perform this task?
(a) 20600 J (b) 686 W
Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is µk=0.436. Determine (a) the work done by the force of gravity, (b) the work done by the force between block and incline, and (c) the work done by the normal force. (d) Qualitatively, how would the answers change if a shorter ramp at a steeper angle were used to span the same vertical height?
(a) 61.3 J (b) -46.3 J (c) 0 (d) work done by gravity and normal force does not change, work done by friction decreases
A fan blade rotates at an angular speed of 0.05 rad/s; its speed is then increased to 3 rad/s at an angular acceleration of 0.60 rad/s2 . (a) Find the angle through which it rotates before reaching this final speed. (b) In general, if both the initial and final angular speed are doubled at the same angular acceleration, by what factor is the angular displacement changed?
(a) 7.5 rad (b) The angular displacement increases by a factor of 4
A car tire has a radius of 0.26 m. a) How far (path length) does a point on the circumference travel if the wheel is rotated through angles of 30 rad? b) If the car travels 80000 km before wearing out the tires, how many revolutions do the tires make, neglecting backing up and any change in radius due to wear?
(a) 7.8 m (b) 4.89*107 rev
A sledge loaded with bricks has a total mass of 18.0 kg and is pulled at a constant speed by a rope inclined at 20.0° m on a horizontal surface. The sledge moves a distance of 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and the surface is 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sledge?
(a) 79.4 N (b) 1.49 kJ 1493 J
When a 2.50-kg object is hung vertically on certain light spring described by Hooke's law, the spring stretches 2.76 cm. (a) What is the force constant of the spring? (b) If the 2.50-kg object is removed, how far will the spring stretch if a 1.25-kg block is hung on it? (c) How much work must an external agent do to stretch the same spring 8.00 cm from its upstretched position?
(a) 888 N/m (b) 1.38 cm (c) 2.84 J
A worker pushing a 35.0-kg wooden crate at a constant speed for 12.0 m along wood floor does 350 J of work by applying a constant horizontal force magnitude of F0 on the crate. (a) Determine the value of F0. (b) If the worker now applies a force greater that F0, describe the subsequent motion of the crate. (c) Describe what would happen to the crate if the applied force is less than F0.
(a) Fo= 29 N (b) crate will accelerate (c) crate would decelerate to a stop
A projectile of mass m is fired horizontally with an initial speed of vo from a height of h above a flat, desert surface. Neglecting air friction, at the instant before the projectile hits the ground, find the following in terms of m, vo, h and g: (a) the work done by the force of gravity on the projectile, (b) the change in kinetic energy of the projectile since it was fired, and (c) the final kinetic energy of the projectile. (d) Are any of the answers changed if the initial angle is changed?
(a) wg= mgh (b) w= Δke= mgh (c) √2gh + v1 2 = vp 2 (d) No
What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?
0.2 Hz, 0.5 Hz, 0.3 Hz
Tarzan swings on a 30.0-m long vine initially inclined at an angle of 37.0° with the vertical. What is the speed at the bottom of the swing (a) if he starts from rest? (b) if he pushes off with a speed of 4.00 m/s?
. (a) 10.9 m/s (b) 11.6 m/s
A 50.0 kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. (a) What is the child's centripetal acceleration? (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? (c) What is the minimum coefficient of static friction is required? Is the required answer you found reasonable? In other words, is she likely to say on the merry-goround?
. (a) 18.0 m/s2 (b) 900 N (c) 1.84; this large coefficient is unrealistic, and she will not be able to stay on the merry-go- round
A truck covers 40.0 m in 8.50 s while uniformly slowing down to a final velocity of 2.80 m/s. (a) Find the truck's original speed. (b) Find the truck's acceleration.
. a) 6.62 m/s b) -0.45 m/s2
Assuming bicycle tires are perfectly flexible and support the weight of bicycle and rider by pressure alone, calculate the total area of the tires in contact with the ground. The bicycle plus rider has a mass of 80.0 kg, and the gauge pressure in the tires is 3.50×10^5 Pa
0.00224 m^2 = 22.4 cm^2
Some people have considered placing rotating cylinders about 16093 m long and 8047 m in diameter in space to be used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?
0.049 rad/s
A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?
0.198 kg, 1.98 x 10^-4 m^3, 2727 kg/m^3
If a curve with a radius of 88 m is perfectly banked for a car traveling 75 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95 km/h?
0.216
The position of an object connected to a spring varies with time according to the expression 𝑥 = (5𝑐𝑚)sin(8𝜋𝑡). a) Find the period of this motion, b) the frequency of the motion, c) the amplitude of the motion, d) the first time after t=0 that the object reaches the position x = 2.6 cm.
0.25s, 4Hz, 5 cm, 0.0217 s
When poked by a spear, an operatic soprano lets out a 1200-Hz shriek. What is its wavelength if the speed of sound is 345 m/s?
0.288 m
A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?
0.459 m
A wave of amplitude 0.3 m interferes with a second wave of amplitude 0.2 m traveling in the same direction. What are a) the largest and b) the smallest resultant amplitudes that can occur?
0.5 m, 0.1 m
What depth of mercury creates a pressure of 1.00 atm?
0.76 m
A pendulum of length 0.9927 m in Tokyo has a period of 1 second, while a pendulum in Cambridge must have a length of 0.9942 m in order for it to have a period of 1 second. a) Why do the pendulums need to have different lengths to have the same period? b) What is the ratio of the free-fall acceleration at these locations?
1.0015
A 0.05 kg Super Ball travelling at 25 m/s bounces off a brick wall and rebounds at 22 m/s. A high speed camera records this event. If the ball is in contact with the wall for 0.0035 s, what is the magnitude of the average acceleration of the ball during this time interval?
1.34 x 104 m/s2
The tub of a washing machine goes into its spin-dry cycle, starting from rest and then reaching an angular speed of 10π rad/s in 8.0 s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 12.0 s. Through how many radians does the tub turn during the entire 20.0 s interval? Assume constant angular acceleration while it is starting and stopping.
100π rad ≈ 314 rad
What sound intensity level in dB is produced by earphones that create an intensity of 4.00×10−2W/m2?
106 dB
What pressure is exerted on the bottom of a 0.500-m-wide by 0.900-m-long gas tank that can hold 50.0 kg of gasoline by the weight of the gasoline in it when it is full?
1088 Pa
What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the slave cylinder? The master cylinder has a 2.00-cm diameter and the slave has a 24.0-cm diameter.
136 N
(a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.400 kgm^2. (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia if his angular velocity decreases to 1.25 rev/s. (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.00 rev/s. What average torque was exerted if this takes 15.0 s?
15.1 kgm^2, 1.92 kgm^2, -0.503 Nm
A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.
2.3 rad/s
Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
2.65 rad/s or 25.3 rpm
Suppose you exert a force of 180 N tangential to a 0.280-m-radius, 75.0-kg grindstone (a solid disk). (a)What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?
2.94 kgm^2, 17.14 rad/s^2, 17.04 rad/s^2
A flywheel (I=50kg-m2) starting from rest acquires an angular velocity of 200.0 rad/s while subject to a constant torque from a motor for 5 s. (a) What is the angular acceleration of the flywheel? (b) What is the magnitude of the torque?
2000 Nm
A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?
22.6 m/s
Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.
23.3 N
. A jet airplane in level flight has a mass of 8.66 x 104 kg and the two wings have an estimated total area of 90 m2 . (a) What is the pressure difference between the lower and upper surfaces of the wings? (b) If the speed of air under the wings is 225 m/s, what is the speed of air over the wings? Assume air has a density of 1.29 kg/m3 .
255 m/s
The aqueous humor in a person's eye is exerting a force of 0.300 N on the 1.10-cm^2 area of the cornea. (a) What pressure is this in mm Hg? (b) Is this value within the normal range for pressures in the eye?
2727 Pa = 20.45 mmHg
A skier starts from rest at the top of a hill that is inclined 10.5° with respect to the horizontal. The hill side is 200 m long and the coefficient of friction between snow and skies is 0.0750. At the bottom of the hill, the snow is level and the coefficient is unchanged. How long does the skier glide along the horizontal portion of the snow before coming to rest?
289 m
A twin-sized air mattress used for camping has dimensions of 100 cm by 200 cm by 15 cm when blown up. The weight of the mattress is 2 kg. How heavy a person could the air mattress hold if it is placed in freshwater?
2920.4 N
As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of 1.50cm^2 and the woman's mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)
3.59 x 10^6 Pa
A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that of Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at each of the three locations.
3. a) 2.27 kg b) Fm= 3.71N or 0.83lb c) Fj= 58.7N or 13.2lb
What is the intensity in watts per meter squared of 85.0-dB sound?
3.16 x 10-4 W/m2
Water towers store water above the level of consumers for times of heavy use, eliminating the need for high-speed pumps. How high above a user must the water level be to create a gauge pressure of 3.00×105N/m2size 12{3 "." "00" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } } {}?
30.6 m
A sample of blood is placed in a centrifuge of radius 15.0 cm. The mass of a red blood cell is 3.0* 10-16 kg, and the magnitude of the force acting on it settles out of the plasma is 4.0*10-11 N. At how many rad per second should the centrifuge be operated?
300π rad/s ≈ 942 rad/s
What frequency sound has a 0.10-m wavelength when the speed of sound is 340 m/s?
3400 Hz
Suppose you have a coffee mug with a circular cross section and vertical sides (uniform radius). What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.50 cm? Assume coffee has the same density as water.
4 cm
A submarine is stranded on the bottom of the ocean with its hatch 25.0 m below the surface. Calculate the force needed to open the hatch from the inside, given it is circular and 0.450 m in diameter. Air pressure inside the submarine is 1.00 atm.
40000 N
(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges? There is only one pair of hinges.
46.75 Nm
A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. (b) Repeat the calculation for the same ball if it slides up the hill without rolling.
5.44 m, 3.27 m
A bat can detect small objects approximately equal to one wavelength of the sound the bat makes. A bat emits a chirp at a frequency of 60000 Hz. What is the smallest insect a bat can detect? The speed of sound in air is 343 m/s.
5.72 mm
A satellite has a mass of 100 kg and is located at 2.00*106 m above the surface of the Earth. What is the magnitude of the gravitational force on the satellite?
568 N
A cube of wood having an edge dimension of 20 cm and a density of 650 kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) What mass of lead should be placed on top of the cube so that the top of the cube will be just level with the water surface?
7 cm, 2.8 kg
What is the final velocity of a hoop that rolls without slipping down a 5.00-m-high hill, starting from rest?
7 m/s
A synchronous satellite, which always remains above the same point on a planet's equator, is put in circular orbit around Jupiter to study that planet's famous red spot. Jupiter rotates once every 9.84 h. Mass of Jupiter = 1.9 x 1027 kg, radius of Jupiter = 6.99 x 107 m.
8.92*107 m
(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?
878 Hz, 735 Hz
An outfielder throws a 0.150-kg baseball at a speed of 40.0 m/s and an incline angle of 30.0°. What is the kinetic energy of the ball at the highest point of its motion?
90 J
(a) What is the decibel level of a sound that is twice as intense as a 90.0-dB sound? (b) What is the decibel level of a sound that is one-fifth as intense as a 90.0-dB sound?
93 dB, 83 dB
A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses to friction.
A2/A1 = 100; d2/d1 = 10
Tarzan (m = 85 kg) tries to cross a river by swinging from a vine. The vine is 10 m long, and his speed at the bottom of the swing is 8 m/s. The vine has a breaking strength of 1000 N. Does Tarzan make it across the river without the vine breaking?
T= 1377 N; He does not make it
The distance between two telephone poles is 50.0 m. When a bird with a mass of 1.0 kg lands on the telephone wire halfway between the two poles, the wire sags 0.200 m. (a) Draw a free-body diagram of the bird. (b) How much tension does the bird produce in the wire? Ignore the weight of the wire
T= 612.5N
A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. (a) After 2.00 s, find the speed of the mailbag. (b) At this same time, how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is instead rising steadily at 1.50 m/s?
a) -21.1 m/s b) 19.6 m c) -18.1 m/s, 19.6 m
. A tennis player tosses a tennis ball straight up and then catches it after 2.00 s at the same height as the point of release. (a) What is the acceleration of the ball while it is in flight? (b) What is the velocity of the ball when it reaches its maximum height? (c) Find the initial velocity of the ball. (d) Find the maximum height the ball reaches.
a) -9.8 m/s2 b) 0 m/s c) 9.8 m/s d) 4.9 m
A billiard ball moving at 5.00 m/s sticks a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s at an angle of 30° with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the second ball after the collision. (b) Was the collision inelastic or elastic?
a) 2.5 m/s @ 60° below + x-axis b) elastic collision
. A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of -5.00 m/s2 as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is 0.800 km long?
a) 20 s b) 1000 m, no
A ball thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to return to its original throwing height after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?
a) 31.9 m b) 2.55 s c) 2.55 s d) -25 m/s
The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat, including its crew, has a mass of 270 kg, what are the magnitude and direction of its acceleration?
a) 429.5N b) a= 1.59 m/s2 @ 65° N of E c) θ= 65°
A 6.0 kg object undergoes an acceleration of 2.0 m/s2 . (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.0 kg object, what accelration is produced?
a) F= 12N b) a= 3 m/s2
A man claims he can safely hold onto a 12.0-kg child in a head-on collision with a relative speed of 120-mi/h lasting for 10 s as long as he has his seat belt on. (a) Find the magnitude of the average force needed to hold on to the child. (b) Based on the result to part (a), is the man's claim valid?
a) F= 6437 N or 1448 lbs b) No
A 0.280-kg volleyball approaches a player horizontally with a speed of 15.0 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s. (a) What impulse is delivered to the ball by the player? (b) If the players fist is in contact with the ball for 0.0600 s, find the magnitude of the average force exerted on the player's fist?
a) I= -10.4 kg*m/s b) |F|= 173 N
A tennis player receives a shot with the ball (0.0600-kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a) what is the impulse delivered to the ball by the racket? (b) what work does the racket do on the ball?
a) I= -5.4 kg*m/s (negative depends on your coordinate system) b) Wby rachet= -27 J
An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. (a) When the elevator is accelerating upward, is T or w larger? (b) When the elevator is moving at a constant velocity upward, which is larger, T or w? (c) When the elevator is moving upward, but the acceleration is downward, which is larger, T or w? (d) Let the elevator have a mass of 1500 kg and an upward acceleration of 2.5 m/s2 . Find T. Is your answer consistent with the answer to part (a)? (e) The elevator of part (d) now moves with a constant upward velocity of 10 m/s. Find T. Is your answer consistent with your answer to part (b)? (f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.50 m/s2 . Find T. Is your answer consistent with your answer to part (c)?
a) T b) they are the same c) w d) T= 18450N e) a=0,50 T=w f) T= 12450N
A hockey puck struck by a hockey stick is given an initial speed vo in the positive x-direction. The coefficient of kinetic friction between the ice and the puck is µk. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance d that the puck slides. The answer should be in terms of the variables vo, µk, and g only
a) ax= μkg b) Δx= 𝑣0^2/2𝜇𝑘g
A dockworker loading crates on a ship finds that a crate with a mass of 20 kg, initially at rest on a horizontal surface, requires a horizontal force of 75 N to set it in motion. However, after the crate is in motion, a horizontal force of 60 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between the crate and the floor.
a) us= 0.38 b) uk= 0.31
A 65.0-kg person throws a 0.045-kg snowball forward with a ground speed of 30.0 m/s. A second, person with a mass of 60.0-kg, catches the snowball. Both people are on skates. The first person is initially on skates with a speed of 2.50 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard friction between the skates and the ice.
a) vaf= 2.48 m/s b) vbf= 0.022 m/s
A railroad car of mass 2.00 X 104 kg moving at 3.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the collision? (b) How much kinetic energy is lost in the coupling?
a) vf= 1.8 m/s b) ΔKE= - 2.16* 10 4 J
An attacker at the base of a castle wall that is 3.65 m high throws a rock straight up with an initial speed of 7.40 m/s at a height of 1.55 m above the ground. (a) Will the rock reach the top of the wall? (b) If so, what is the rock's speed at the top? If not, what initial speed must the rock have to reach the top? (c) Find the change in the speed of a rock thrown straight down from the top of the wall with an initial speed of 7.40 m/s, moving between the same two points. (d) Does the change in speed of the downward-moving rock equal the magnitude of the speed change of the rock moving upward between the same elevations? Explain physically why or why not.
a) yes b) 3.69 m/s c) 2.4 m/s d) No, explain
A car starts from rest and travels for t1 seconds with a uniform acceleration a1. The driver then applies the brakes, causing a uniform acceleration a2. The brakes are then applied for t2 seconds. (a) How fast is the car going just before the beginning of the braking period? (b) How far does the car go before the driver begins to brake? (c) Using the answers to parts (a) and (b) as the initial velocity and position for the motion of the car during braking, what total distance does the car travel? Answers are in terms of a1, a2, t1, and t2.
a) 𝑣1𝑓 = 𝑎1𝑡1 b) 𝑥1 = 1 2 𝑎1𝑡1/2 c) 𝑥 = 1/2 𝑎1𝑡1 2 + 𝑎1𝑡1𝑡2 + 1/2 𝑎2𝑡2 2
Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?
eagle 1 hears 4.23 x 103 Hz, eagle two hears 3.56 x 103 Hz
A 0.030 kg bullet is fired vertically at 200 m/s into a 0.15 kg baseball that is initially at rest. How high does the combined bullet and baseball rise after the collision, assuming that the bullet embeds itself into the baseball?
h= 56.7 m
If a pendulum is taken from the earth to the moon, how will its period change? Increase, decrease, remain the same?
increase