Physics Final Exam

In a region where the electric field is uniform and points in the +x direction the electric potential is -2000 V at x = 8 m and is +400 V at x= 2 m. What is the magnitude of the electric field?

-2000 - 400 / 8-2

Two ice skaters suddenly push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s relative to the ice. What speed does the 60-kg skater acquire relative to the ice. What speed does the 60-kg skater acquire relative to the ice?

.28 m/s 45 ( .375 ) = 60 * x

The three point charges +4.0 *10^-6 , 5.0*10^-6, -9*10^-6 are placed on the x-axis at the points x=0 cm, x=40 cm, and x=120 cm, respectively. What is the x component of the electrostatic force on the -9.0*10^-6 charge due to the other two charges?

.41 N k(4*9)/1.2^2 = -.225 k(5*9)/.8^2 = .632

How fast (in terms of the speed of light) should a moving clock travel if it is to be observed by a stationary observer as running at one half its normal rate?

.866c 1=.5/(sqr1-v^2/c^2)

How fast must a meter stick move, relative to the frame of the observer making the measurement, so it's length will be measured to be .6 m?

.8c

A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position. How much work did gravity do on the bucket during this process?

0 J

An ideal spring has a constant (force constant) of 60 N/m. How much energy does it store when it is stretched by 1.0 cm?

0.003 J cm to m (10^-2) (PE spring = 1/2 ( k ) ( x )^2)

A 0.330-kg volleyball is thrown vertically downward with a speed of .150 m/s in a place where g = 9.81 m/s^2. It takes it 0.0655 s to reach the ground. What is the magnitude of its momentum just before it hits the ground?

0.262 kg * m/s ( v = ( 9.8 m/s^2 * 0.0655 s ) + .15 m/s ) (Mom = m * v)

A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground and bounces. It rebounds with an upward velocity of 1.00 m/s. What is the change of the ball's momentum during the bounce?

0.308 kg * m/s upwards ( Mom = ( m * v ) + ( m * v ) )

Two very small +3.00*10^-6 charges are at the ends of a meter stick. Find the electric potential (relative to infinity) at the center of the meter stick.

1.08 * 10^5 V K(3.0 *10^-6/.5)

What is the minimum energy needed to change the speed of a 1600-kg sport utility vehicle from the 15.0 m/s to 40 m/s?

1.10 MJ or 1100000 J ( w = 1/2 ( m ) ( vf )^2 - 1/2 ( m ) ( vi )^2 )

A piece of plastic has a net charge of + 2.00 * 10^-6 C. How many more protons and electrons does this piece of plastic have? ( e= 1.60 * 10^-19)

1.25 * 10^13 2*10^-6 / 1.6 * 10^-19

A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision?

10 kg * m/s (Mom = m * v) (a^2 + b^2+ c^2)

The potential (relative to infinity) at the midpoint of a square is 3.0 V when a point charge of + Q is located at one of the corners of the Square. What is the potential (relative to infinity) at the center when each of the other corners is also contains a point charge of + Q.

12 V 3*4

A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at 28 m/s at 15° north of east just after the collision, how fast was the car initially traveling?

14 m/s 28 * sin(15) * 2

You do 116 J of work while pulling a frictionless swing, whose chain is 5.10 m long, until the swing makes an angle of 32.0° with the vertical. What is your sister's mass?

15.3 kg ( 5.10 m ) ( 1 - cos 32° ) = .775 m. 116 J = m ( 9.8 m/s² ) ( .775 m ) m = 15.3 kg

A child pulls on a wagon with a force of 75 N. If the wagon moves a total of 42 m in 3.1 min, what is the average power delivered by the child?

17 W min to sec (min*60) (W = f * d) III (P = W / T)

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on earth, Andrea rides on the spaceship that travels away from Earth at a speed of .60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea?

18 years

A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is .35. At what speed will the car begin to skid sideways?

19 m/s Sqr 100 * 9.81 * .35

A small object with a 5.0 *10^-6 C charge is accelerating horizontally on a friction - free surface at .0050 m/s^2 due to only an electric field. If the object has a mass of 2.0 g, what is the magnitude of the electric field?

2.0 N/C E = (m*a) / q

As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes 10.5 y to travel between two planets that are not moving relative to each other. How long does the trip take as measured by someone on the spaceship?

2.79 yrs 10.5 = x/sqr1-(.9c^2/c^2

Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m?

28 m 60 kg * x = 80 kg * 12 ans + 12

When a car of mass 1167 kg accelerates form 10 m/s to some final speed, 4.00 x 10^5 J of work are done. Find this final speed.

28.0 m/s ( w = 1/2 ( m ) ( vf )^2 - 1/2 ( m ) ( vi )^2 )

The force of attraction that -40.0 * 10^-6 point charge exerts on a +108 * 10^-6 Point charge has a magnitude 4.00 N. How far apart are these two charges?

3.12 m 4 = k(40*108) /x^2

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

3.49 rad/s 33.33 rev / 2π rad / 1 min 1 min /1 rev / 60 s

A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center if the merry-go-round, how fast is the child moving?

3.50 m/s 7.18 rev 2π rad 1 min 1 min 1 rev 60 s answ * 4.65

A spaceship carrying a light clock moves at a speed of .960c relative to an observer on earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long did that advance take as measured by the observer on Earth?

3.6 s

What is the distance from the center of the moon to the point between earth and the moon where the gravitational force of Earth are equal? The mass of the earth is 5.97×10^24 kg, the mass of the moon is 7.35×10^22 kg, the center-to-center distance between earth and the moon 3.84×10^8 m, and G = 6.67*10^-11 N * m^2/kg^2.

3.84 * 10^7 m Let x be the distance from the moon to the balance point so (3.84x10^8 - x) is the distance form Earth to this point Using Universal Law of Gravitation we get GM(moon)m/x^2 = GM(Earth)m/(3.94x10^8 - x)^2 Note m and G drops out leaving M(moon)/x^2 = M(Earth)/(3.84x10^8 - x)^2 Expanding yields 7.35x10^22*((3.84x10^8)^2 - 2*3.84x10^8*x +x^2) = 5.97x10^24*x^2 Rearranging yields (5.97x10^24-7.35x10^22)*x^2 + 7.35x10^22*2*3.84x10^8 - 7.35x10^22*(3.84x10^8)^2 = 0 So 5.8965x10^24*x^2 + 5.6448x10^31*x - 1.0838x10^40 = 0 solving we get x = -5.6448x10^31 +-sqrt((5.6448x10^31)^2 - 4*5.8965x10^24*(-1.0838x10^40))/(2*5.896... = 3.84x10^7m from the moon = 38400 km

A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. They clay sticks to the wall. Which of these objects experiences the greater momentum?

The ball.

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping?

The disk (disk = rotational kinetic energy)

If two objects are electrically attracted to each other,

The objects could be electrically neutral.

A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change if the lighter fragment is

The same as the momentum change of the heavier fragment.

A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the momentum change during the collision is correct?

The small car and the truck experience the same magnitude momentum change.

Spaceship is traveling at constant velocity passes by earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

The spaceship frame of reference

Which of the following are basic postulates of special relativity?

The speed of light is the same for all observers The laws of physics are the same in all inertial reference frames

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45 above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below?

The speed will be the same in all cases.

Three cars, car X, car Y and car Z, begin accelerating from rest,at the same time. Car X is more massive than car Y, which is more massive than car Z. The net force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum?

They all have the same amount of momentum.

During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a very long barrel. What was the reason for using a long barrel in these guns?

To allow the force of the expanding gases from the gunpowder to act for a longer time.

If you stood on a planet having a mass four times of that of Earth's mass, and the radius two times that of earths radius, you would weigh

Two times more than you do on earth

You are riding in a spaceship that has no windows, radios, or other means for you to observe a measure what is outside. You wish to determine if the ship stop or is moving at constant velocity. How can you do this?

You should give up because you have taken on an impossible task!

Suppose One twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on earth. Compared to the twin who remained on earth, the astronaut twin is

Younger than the earth twin.

An electron is initially moving to the right when it enters a uniform electric field directed upward, as shown in the figure. Which trajectory will the electron follow in the field?

Z (down)

A hypothetical planet has a mass of one half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the accleration due to gravity at the surface of the earth?

g/8

A square is 1.0 m on the side. Point charges of +4.0*10^-6 are placed in two diagonally opposite corners. In the other two corners are placed charges of +3.0*10^-6 C and -3.0*10^-6 C. What is the potential (relative to infinity) at the midpoint of the square?

h^2=.5^2 *.5^2 v = k ( 4.00 * 10^-6 / .71 )

A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,

her moment of inertia increases and her angular speed decreases.

A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system

is half as much as before.

The zirconium nucleus contains 40 protons, and electron is 1.0 nm from the nucleus. What is the electric force on the electron due to the nucleus?

k(40*1.6*10^-9 * 1.6*10^-9) / 1.0 *10^-9

If you want to double the kinetic energy if a gas molecule, by what factor must you increase its kinetic energy?

√2

What is the minimum energy needed to lift to 1.0-kg rocket to a height of 200 km and to give it a speed to 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance.)

34 MJ or 34000000 km to m (10^3) ( TE = ( m * g * h ) + 1/2 ( m ) ( v )^2 )

Planet Z - 34 has a mass equal to one third that of Earth and a radius equal to one third that earth. With G representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z - 34 is

3g

A tiger is running in a straight line. If we double both the mass and the speed of the tiger, the magnitude of its momentum will increase by what factor?

4

If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy?

4

Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is

4 mom= mass * radius^2

While spinning down from 500 rpm to rest, a flywheel does 3.9 kJ of work. This flywheel is in the shape of a solid uniform disk of radius 1.2 m. What is the mass of this flywheel?

4 kg rot kinetic energy = .5 ( .5 * m * r^2 ) * w^2

A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution?

4.13 s 2π / 1.52

A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball just as it leaves the tee?

40 m/s I = F * t ( 10^-3 ) Mom = m * V

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 555 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

46 N ( w = f ( d ) cos ( θ ) )

If it takes 50 J of energy to move 10 C of charge from point A to point B, what is the magnitude of the potential difference between point A and B?

5.0 V J/C

The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is .40, what would be the maximum safe driving speed for this horizontal curved section of highway?

54 m/s Sqr 740 * .4 * 9.81

An object moves with a constant speed of 30 m/s on a circular track of radius 50 m. What is the accleration of the object?

6.0 m/s Centripetal acc

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides with a stationary seal of mass 200 kg. The seal grabs on to the whale and holds fast. What is the momentum of these two sea creatures just after their collision. You can neglect any drag effects of the water during the collision.

6000 kg * m/s 1000 kg * 6 m/s

Through how many degrees does a 33 rpm turntable rotate in 0.32 s?

63° 33 rev 360° 1 min answ * .32 1 min 1 rev 60 s

How fast must a 6.0-kg cat run to have kinetic energy of 150 J?

7.1 m/s ( w = 1/2 ( m ) ( v )^2 )

An ice skater has a moment of inertia of 5.0 kg * m^2 when her arms are outstretched, and at this time she is spinning at 3.0 rev/s. If she pulls in her arms and decreases her moment of interia to 2.0 kg * m^2 , how fast will she be spinning?

7.5 rev/s ang mom = mom * w

A proton is placed in an electric field of intensity 800 N/C. What are the magnitude and direction of the celebration of the proton due to this field? (e= 1.6 * 10^-19 C, mproton = 1.67 * 10^-27 kg)

7.66*10^9 m/s opposite to the electric field E = (m(a))/q

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied .30 m on the other side of the ticket, that is needed to make the child lift off the ground?

740 N

What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

85.14 rad/s 813 rev / 2π rad / 1 min 1 min / 1 rev / 60 s

A spaceship visit a store that is 4.5 ly from Earth, and the spaceship travels at one half speed of light for the entire trip. How long did the trip take a cording to an observer on earth? How long did the trip take according to an observer on the spaceship?

9.0 yrs, 7.8 yrs a) 4.5(2) b) 9=x/sqr1-(.5c^2/c^2)

What is the charge on 1 kg of protons? (e = 1.60 * 10^-19 C, mproton = 1.67 * 10^-27)

9.6 * 10^7 C 1 proton/ mP answ(e)

How much work would a child do while pulling a 12-kg wagon a distance of 4.3 m with a 22 N force?

95 J (w = f * d)

Charges

A

Charges

B

Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the following statements is true?

Both do zero work.

Charges

C

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

Constant velocity with respect to inertial frame.

Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one?

F

Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed it to 2m and 2M, and the distance is changed to 4r. What is the magnitude of the gravitational force?

F/4

The moon is accelerated toward the earth, so it is gradually getting close to the earth.

False

There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.

False

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements is true about the skater during this process?

Her angular momentum remains constant.

If a satellite moves with constant speed in a perfectly circular orbit around the earth, what is the direction of the acceleration of satellite?

Inward toward the earth

An astronaut is resting on the bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer the sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

Is greater than the angle observed by the astronaut

A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from the ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod

Is repelled by the sphere.

Two point charges, Q1 and Q2, are separated by distance R. If the magnitude of both charges are doubled and their separation is also doubled, what happens to the electrical force that each charge exerts on the other one?

It increases by a factor of four.

A spaceship is traveling to the moon. At what point is it beyond the point of Earth's gravity?

It is never beyond the pull of Earth's gravity.

You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions?

It would have skidded 4 times farther.

A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission last exactly 20 years as measured on earth. Biologically speaking, at the end of the mission, the astronaut's age would be

Less than 50 years.

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

Move at constant velocity with respect to an inertial frame

You are making a circular turn in your car on the horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. Well the car is on ice, it

Moves along the straight-line path in its original direction.

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

No change in the length of your spaceship

If you were in a spaceship traveling close to the speed of light with respect to earth, you would notice that

None of the above effects occur

A negatively-charged plastic rod is brought close to (but does not touch) a neutral metal sphere that is connected to ground. After waiting a few seconds, the ground connection removed (without touching the sphere), and after that the rod is also removed. The sphere is now

Positively charged