Exam three Flashcards by Khadeeja Ali

for these conservative force find the potential energy U=1/4x^4+1/3y^3+1/2z^2

F=-x^3i-y^2j-zk

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The object starts at point A with y = 0, where the spring is
at its natural length. Find the maximum stretch of the
spring when the object reaches point C
*Fspring and FG = mg⃗ are conservative forces.
*Energy is conserve

Object A–> all the on top compressed fully
Object C–> fully stretched out

h=2mg/k

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A particle of mass is hung from the ceiling by a massless
string of length 1 m. The particle is released from rest, when
the angle between the string and the downward vertical
direction is 30∘. What is its speed when it reaches the lowest
point of its arc?
*Only gravity does work
*Gravity is a conservative force
*Mechanical Energy is conserved:
*KA + UA = KB + UB
EA = EB

1.62

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*A boy throws a ball of mass
0.25 Kg straight upward
with an initial speed of 20
m/s. When the ball returns
to the boy, its speed is 17
m/s. How much work does
air resistance do on the ball
during its flight?
*3 J
*7.5 J
*13.9 J
*25 J
*32 J

-13.9 J

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A small block of mass slides without
friction around the loop-the-loop apparatus
shown below. (a) If the block starts from
rest at A, what is its speed at B? (b) What
is the force of the track on the block at B?

Height for A is 4R
Height for b is R

Don’t solve just leave G alone

(a) square root 6gR
(b)5mg

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*In the movie, a spring expands quickly and sends the coyote into a rock.
If the spring extended 5 m and sent the coyote of mass 20 kg to a speed
of 15 m/s, (a) what is the spring constant of this spring? (b) If the
coyote were sent vertically into the air with the energy given to him by
the spring, how high could he go if there were no non-conservative
forces

(a)180
(b)11.5

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A 5 × 105 kg subway train is brought to a stop from a speed of 0.5 m/s in 0.4
m by a large spring bumper at the end of its track. What is the spring constant
k of the spring?
* 1 N/m
* 3.4 × 102 N/m
* 5.2 × 104 N/m
* 7.8 × 105 N/m
* 9.2 × 106 N/m

7.8 × 105 N/m

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The massless spring of a spring gun has a force constant
k = 1200 N/m. When the gun is aimed vertically, a 0.015 K
projectile is shot to a height of 5 m above the end of the
expanded spring. How much was the spring compressed
initially

x=0.035 m

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*In the Hunger Games movie, Katniss Everdeen fires a 0.02-kg
arrow from ground level to pierce an apple up on a stage. The
spring constant of the bow is 330 N/m and she pulls the arrow
back a distance of 0.55 m. The apple on the stage is 5.00 m
higher than the launching point of the arrow. At what speed
does the arrow (a) leave the bow? (b) strike the apple?
* va = 10.6 m/s; vb = 15.0 m/s
* va = 20.1 m/s; vb = 15.3 m/s
* va = 40.7 m/s; vb = 35.2 m/s
* va = 70.6 m/s; vb = 70.0 m/s
* va = 80.3 m/s; vb = 62.5 m/

va = 70.6 m/s; vb = 70.0 m/s

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A disc of mass m = 0.05 Kg slides with zero initial velocity down an
inclined plane of height = 0.1 m and angle = 30∘; having traversed
the distance = 0.5 m along the horizontal plane, the disc stops. Find
the work performed by friction forces over the whole distance,
assuming the friction coefficient k = 0.15 for both inclined and
horizontal plane

-0.04948

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TOPIC:potential energy of a system

A camera weighing 10 N falls from a small drone hovering 20m
overhead and enters free fall. What is the gravitational potential energy change of the camera from the drone to the ground if you take a reference point of (a) the ground being zero gravitational potential energy? (b) The drone being zero gravitational potential energy? What is the gravitational potential energy of the camera (c) before it falls from the drone and (d) after the camera lands on the ground if the reference point of zero gravitational potential energy is taken to be a second person looking out of a building 30m
from the ground?

a.−200J;b.−200J;c.−100J;d.−300J

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TOPIC:potential energy of a system

A cat’s crinkle ball toy of mass 15g
is thrown straight up with an initial speed of 3m/s
. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball’s rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak? (d) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height? (e) What if the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand? (f) What is the maximum height the ball reaches?

a.0.068J;b.−0.068J;c.0.068J;d.0.068J;e.−0.068J;f.46cm

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Topic: Conservative and nonconservative forces

A particle of mass 2.0kg
moves under the influence of the force F(x)=(−5x2+7x)N.
If its speed at x=−4.0m
is v=20.0m/s,
what is its speed at x=4.0m?

14m/s

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Topic: Conservative and nonconservative forces

A force F(x)=(−5.0x2+7.0x)N
acts on a particle. How much work does the force do on the particle as it moves from x=2.0m
to x=5.0m?

−120J

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topic: conservative energy

A boy throws a ball of mass 0.25kg
straight upward with an initial speed of 20m/s
When the ball returns to the boy, its speed is 17m/s
How much much work does air resistance do on the ball during its flight?

14J

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topic: conservative energy
Ignoring details associated with friction, extra forces exerted by arm and leg muscles, and other factors, we can consider a pole vault as the conversion of an athlete’s running kinetic energy to gravitational potential energy. If an athlete is to lift their body 4.8 m during a vault, what speed must they have when they plant the pole?

9.7m/s

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topic: conservative energy

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of  150N  . If the mass of the arrow is  50g   and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?

39m/s

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topic: conservative energy

A sled of mass 70 kg starts from rest and slides down a  10°   incline  80m   long. It then travels for 20 m horizontally before starting back up an  8°   incline. It travels 80 m along this incline before coming to rest. What is the magnitude of the net work done on the sled by friction?

1900 J

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topic: conservative energy

A baseball of mass 0.25 kg is hit at home plate with a speed of 40 m/s. When it lands in a seat in the left-field bleachers a horizontal distance 120 m from home plate, it is moving at 30 m/s. If the ball lands 20 m above the spot where it was hit, how much work is done on it by air resistance?

–39 J

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topic: conservative energy

The massless spring of a spring gun has a force constant k=12N/cm.
When the gun is aimed vertically, a 15-g projectile is shot to a height of 5.0 m above the end of the expanded spring. (See below.) How much was the spring compressed initially?

answer in cm

3.5 cm

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topic: sources of energy

In the reality television show “Amazing Race”, a contestant is firing 3.0-kg watermelons from a slingshot to hit targets down the field. The slingshot is pulled back 2.0 m and the watermelon is considered to be at ground level. The launch point is 0.75 m from the ground and the targets are 10 m horizontally away. Calculate the spring constant of the slingshot.

490 N/m

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topic: sources of energy

In the Hunger Games movie, Katniss Everdeen fires a 0.0200-kg arrow from ground level to pierce an apple up on a stage. The spring constant of the bow is 330 N/m and she pulls the arrow back a distance of 0.55 m. The apple on the stage is 5.00 m higher than the launching point of the arrow. At what speed does the arrow (a) leave the bow? (b) strike the apple?

a. 70.6 m/s; b. 69.9 m/s

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topic: sources of energy

In a Coyote/Road Runner cartoon clip, a spring expands quickly and sends the coyote into a rock. If the spring extended 5 m and sent the coyote of mass 20 kg to a speed of 15 m/s, (a) what is the spring constant of this spring? (b) If the coyote were sent vertically into the air with the energy given to him by the spring, how high could he go if there were no non-conservative forces?

a. 180 N/m; b. 11 m

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topic: sources of energy

In the movie Monty Python and the Holy Grail a cow is catapulted from the top of a castle wall over to the people down below. The gravitational potential energy is set to zero at ground level. The cow is launched from a spring of spring constant 1.1×104N/m
that is expanded 0.5 m from equilibrium. If the castle is 9.1 m tall and the mass of the cow is 110 kg, (a) what is the gravitational potential energy of the cow at the top of the castle? (b) What is the elastic spring energy of the cow before the catapult is released? (c) What is the speed of the cow right before it lands on the ground?

a. 9.8×103J
; b. 1.4×103J
; c. 14 m/s

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topic: sources of energy (a) How high a hill can a car coast up (engines disengaged) if work done by friction is negligible and its initial speed is 110 km/h? (b) If, in actuality, a 750-kg car with an initial speed of 110 km/h is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy was generated by friction? (c) What is the average force of friction if the hill has a slope of 2.5° above the horizontal?

a. 47.6 m; b. 1.88×105J ; c. 373 N

topic: sources of energy A pogo stick has a spring with a spring constant of 2.5×104N/m, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?

.45

Find the force corresponding to the potential energy U(x)= a/x +b/x2

=-a/x^2+2b/x^3

A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance

-189.6

A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m high rise as shown. Find her final speed at the top, given that the coe cient of friction between her skis and the snow is 0.80.

7.47

What is the average momentum of a 91.0 kg sprinter who runs the 100. m dash in 11.6 s?

784

A cruise ship with a mass of 1.5 x10^7 kg strikes a pier at a speed of 1.25 m/s. It comes to rest after traveling 5 m (into the pier) damaging the ship and the pier. Calculate the average force exerted on the pier.

2,343,750

An object with mass m = 5 kg moves with an initial velocity vi=2 . After it bounces back from the wall, it has a velocity vf=-0.3 . Neglect gravitation. What is the impulse the wall exerts on the object when they interact? J=-11.5N J=1.5N J=11.5N J=-10N J=10N

-11.5

Two hockey players approach each other head-on, each traveling at the same speed . They collide and get tangled together, falling down and moving off at a speed of v0/6. What is ratio of their masses (assuming m1>m2) m1/m2=7/5 m1/m2=2/1 m1/m2=3/2 m1/m2=9/8 m1/m2=5/4

m1/m2=7/5

Two carts on a straight track collide head on. The first cart was moving at 3.6 m/s in the positive x direction and the second was moving at 2.4 m/s in the opposite direction. After the collision, the second car continues moving in its initial direction of motion at 0.24 m/s. If the mass of the second car is 5.0 times that of the first, what is the final velocity of the first car? -7.2 m/s -3.6 m/s -1.8 m/s 1.8 m/s -14.4 m/s

-7.2

Two particles with equal mass m collides with each other elastically. Before the collision, the first particle has a velocity v1 going towards the positive-x axis. The second particle has a velocity -v2 (i.e., it is going towards the negative-x axis). What are their velocity after the collisions? v1=-v2; v2=v1 v1=-v1; v2=v2 v1=0; v2=0 v1=0; v2=v2 v1=-v1; v2=0

v1=-v2; v2=v1

Which has a larger magnitude of momentum: a 3000-kg elephant moving at 5 km/h or a 60-kg cheetah moving at 112 km/h? (A) Elephant (B) Cheetah (C) They are equal (D)Not enough information

(A) Elephant

A meteor with mass 5 × 108 kg hit the earth with a speed 1 × 104 m/s. The impact time lasts for 2s. * (a)What is the force the meteor exerts on earth? * (b)How large is the acceleration of earth? (mearth = 6 × 1027 Kg)

(a)-2.5x10^12 (b)4.2x10^-14

A car travels at 30 m/s collides with a building and comes to a stop. The driver has a mass of 80 kg. The seat belt and air bags slow his velocity and make him come to a stop in 2.5 s. Without them, his collision time would be 0.2 s when he hits the wheel. What is the averaged forces the driver feels in these two cases

-960;-12000

A Tesla car, m=2 × 103 kg, can accelerate from 0 to 60 miles/hr in 2.3 seconds. * What average force did the impulse engines apply to the car? 1 mile equals 1609 (A)5235 N (B) 23478 N (C) 32456 N (D) 50235 N (E) 87435

(B) 23478 N

Water from a fire hose is directed horizontally against a wall at a rate of 50 kg/s and a speed of 42 m/s. * Calculate the force exerted on the wall, assuming the water’s horizontal momentum is reduced to zero on impact.

-2100N

A car crashed into a large tree and stopped. The car goes from 30 m/s to 0 in 1.5 m. * What impulse is applied to the driver (m = 80 kg) by the seatbelt, assuming he follows the same motion as the car? * What is the average force applied to the driver by the seatbelt? (A) 400 N ; 400 N (B) 800 N ⋅ ; 8000 N (C) 2400 N ⋅ ; 24000 N (D) 3200 N ⋅ ; 1600 N (E) 4800 N ⋅ ; 4800

A bullet of mass 0.2 kg traveling horizontally towards the east with speed 400 m/s. It strikes a block of mass 1.8 kg that is initially at rest on a frictionless table. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. (a) What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact? (b)If it took 3 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?

40;-2.4x10^4

A puffer fish expands to 150% of its mass by taking in water. When the puffer fish is threatened, it releases the water toward the threat to move quickly away. What is the ratio of the speed of the puffer fish forward to the speed of the expelled water backwards?

1/2

* A player is standing on a very slippery icy surface and throws a 1-kg football horizontally at a speed of 6.5 m/s. What is his velocity right after releasing the football? Assume the player’s mass is 65 kg.

1/65 or 0.1

A 100-g firecracker is launched vertically into the air and explodes into two pieces at the peak of its trajectory. If a 80-g piece is projected horizontally to the left at 20 m/s, what is the speed and direction of the other piece?

A great white shark of mass m , coasting through the water in a 1 nearly frictionless way at speed 1, engulfs a tuna of mass m2 = m1/3 traveling in the same direction at speed v2(v2 < v1), swallowing it in one bite. What is the speed of the shark after its tasty meal?

(3/4)(v1+1/3v2)

Three point masses are placed at the corners of a triangle as shown in the figure below. Find the center of mass of the three- mass system (A) (-2.03, 1.00) (B) (-1.23, 0.69) (C) (-4.00, 3.00) (D) (-3.41, 1.50) (E) (-2.00, 1.50

(B) (-1.23, 0.69)

An elephant and a hunter are having a confrontation.A drawing of an elephant, on the left, and hunter, on the right. An x y coordinate system is shown, with positive x to the right and positive y up. The elephant is labeled with m E = 2000.0 k g, and vector v E = 7.50 meters per second times I hat. An arrow above the v E vector points to the right. The hunter is labeled with m hunter = 90.0 k g, and vector v hunter = 7.40 meters per second times I hat. An arrow above the v hunter vector points to the right. Between the hunter and elephant is a dart with a long arrow pointing to the left drawn near it and labeled vector v dart = 600 meters per second times minus I hat, and m dart = 0.0400 k g. (a)Calculate the momentum of the 2000.0-kg elephant charging the hunter at a speed of 7.50 m/s. (b)Calculate the ratio of the elephant’s momentum to the momentum of a 0.0400-kg tranquilizer dart fired at a speed of 600 m/s. (c)What is the momentum of the 90.0-kg hunter running at 7.40 m/s after missing the elephant?

(a)p =15000.0 kg⋅m/s (b)PE/Pdart=625 (c)666

What is the average momentum of a 70.0-kg sprinter who runs the 100-m dash in 9.65 s?

725.2 kg·m/s.

A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment (see the following figure).A drawing of a car on a bridge. The car is labeled as having velocity v sub i equals 20 meters per second i hat to the right. (a)Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. (b)Calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 cm.

(a) a. 1.50×106N (b); b. 1.00×105N

A cruise ship with a mass of 1.00×107kg strikes a pier at a speed of 0.750 m/s. It comes to rest after traveling 6.00 m, damaging the ship, the pier, and the tugboat captain’s finances. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest, assuming a constant force.)

4.69×10^5N

A 0.450-kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. Assume constant acceleration of the hammer-nail pair. (a)Calculate the duration of the impact. (b)What was the average force exerted on the nail?

(a)0.00286s (b)1102.5 N

A hockey puck of mass 150 g is sliding due east on a frictionless table with a speed of 10 m/s. Suddenly, a constant force of magnitude 5 N and direction due north is applied to the puck for 1.5 s. Find the north and east components of the momentum at the end of the 1.5-s interval.

Let the positive x-axis be in the direction of the original momentum. Then px=1.5kg⋅m/s and py=7.5kg⋅m/s

Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1.50×105kg and a velocity of (0.30m/s)iˆ , and the second having a mass of 1.10×105kg and a velocity of −(0.12m/s)iˆ . What is their final velocity?

(0.122m/s)iˆ

The figure below shows a bullet of mass 200 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table.A drawing of a block on a table, and a bullet headed toward it. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. (a)What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact? (b)What is the magnitude and direction of the impulse by the block on the bullet? (c)What is the magnitude and direction of the impulse from the bullet on the block? (d)If it took 3 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?

a. 47 m/s in the bullet to block direction; b. 70.6N⋅s , toward the bullet; c. 70.6N⋅s , toward the block; d. magnitude is 2.35×104N

Explain why a cannon recoils when it fires a shell.

The cannon recoils when it fires a shell due to conservation of momentum. Initially, both the cannon and shell are at rest, so the total momentum is zero. When the cannon fires, it exerts a forward force on the shell, and the shell exerts an equal and opposite force on the cannon, causing it to recoil. To keep the total momentum zero, the cannon moves backward with a velocity opposite to the shell's forward velocity.

In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is much, much less than that of the bumper cars, what are their final speeds?

the speed of the leading bumper car is 6.00 m/s and that of the trailing bumper car is 5.60 m/s

A boy sleds down a hill and onto a frictionless ice-covered lake at 10.0 m/s. In the middle of the lake is a 1000-kg boulder. When the sled crashes into the boulder, he is propelled backwards from the boulder. The collision is an elastic collision. If the boy’s mass is 40.0 kg and the sled’s mass is 2.50 kg, what is the speed of the sled and the boulder after the collision?

The final speed of the sled and boy, v f , is approximately −9.62m/s

A 0.90-kg falcon is diving at 28.0 m/s at a downward angle of 35° . It catches a 0.325-kg pigeon from behind in midair. What is their combined velocity after impact if the pigeon’s initial velocity was 7.00 m/s directed horizontally? Note that vˆ1,i is a unit vector pointing in the direction in which the falcon is initially flying.

22.1 m/s at 32.2° below the horizontal

A proton traveling at 3.0×106m/s scatters elastically from an initially stationary alpha particle and is deflected at an angle of 85° with respect to its initial velocity. Given that the alpha particle has four times the mass of the proton, what percent of its initial kinetic energy does the proton retain after the collision?

11%

Two cars of the same mass approach an extremely icy four-way perpendicular intersection. Car A travels northward at 30 m/s and car B is travelling eastward. They collide and stick together, traveling at 28° north of east. What was the initial velocity of car B?

After calculating, you should find that the initial velocity of Car B is approximately 56.57 m/s.

Exam three Flashcards

(61 cards)