b mechanics 2008-answers - mater lakes...the graph above represents position x versus time t for an...

Physics B AP Review Packet: Mechanics Name:________________

3/30/2010 1 Bertrand

Position (x) (unit: m) Location of a particle in space.

Distance (unit: m) The total length of the path traveled by an object. Does not depend upon direction.

Displacement (∆x) (unit: m) Change in position. Depends only on the initial and final positions, not on path. Includes direction. 1. Distance vs Displacement (PAB) A hiker hikes 25 miles due north and then all the way back to the starting point.

a) How far does the hiker hike? Show your work: b) What is the hiker’s displacement? Show your work:

Average Velocity (unit: m/s) vave = �x/�t Average speed (unit: m/s) save = d /�t For motion in a straight line, average speed is the magnitude (abs. value) of the average velocity.

2. Average Speed/Velocity (S-113 #11)

The graph above represents position x versus time t for an object being acted on by a constant force. The average speed during the interval between 1 s and 2 s is most nearly

a. 2 m/s b. 4 m/s c. 5 m/s d. 6 m/s e. 8 m/s

Show your work:

Acceleration (a) (unit: m/s2) Any change in velocity, including speeding up,

slowing down, or turning. If the sign of the velocity and the sign of the

acceleration is the same, the object speeds up. If the sign of the velocity and the sign of the

acceleration are different, the object slows down. Uniformly Accelerated Motion aave = �v/�t

3. Acceleration (A-182 #1) In which of the following situations would an

object be accelerated? I. It moves in a straight line at constant speed. II. It moves with uniform circular motion. III. It travels as a projectile in a gravitational

field with negligible air resistance. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III Explain your answer: Kinematic Equations v = vo + at x = xo + vot + 1/2 at2 v2 = vo

2 + 2a(�x)

4. Kinematic Equations (A-195 #65) A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration of 6 meters per second squared in the negative x direction. The position x of the body at t = 11 seconds is

(A) +99 m (B) +36 m (C) -36 m (D) -75 m (E) -99 m

Show your work:

Physics B AP Review Packet: Mechanics


5. Kinematic Graphs for 1-D motion Stationary particle x vs t v vs t a vs t Particle moving with constant non-zero velocity x vs t v vs t a vs t Particle moving with constant non-zero acceleration x vs t v vs t a vs t

6. Kinematic Graphs (S-199 #1)

The displacement x of an object moving along the x-axis is shown above as a function of time t. The acceleration of this object must be

(A) zero (B) constant but not zero (C) increasing (D) decreasing (E) equal to g

Explain your answer:

7. Kinematic Graphs (S-195 #3)

The graph shows the velocity versus time for an object moving in a straight line. At what time after time = 0 does the abject again pass through its initial position?

(A) Between O and 1 s (B) at 1 s (C) Between 1 and 2 s (D) at 2 s (E) Between 2 and 3 s

Show your work: Free Fall An object falls accelerated by gravity g = 9.8 m/s2 downward.

a = -g if up is positive. acceleration is down when ball is thrown up

EVERYWHERE in the balls flight.

8. Free Fall (A-182 #5) An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet?

(A) l .5 m/s2 (B) 3.0 m/s2 (C) 6.0 m/s2 (D) 10.0 m/s2 (E) 12.0 m/s2

Show your work: Projectile Motion Something is fired, thrown, shot, or hurled near the earth’s surface. Horizontal velocity is constant. Vertical velocity is accelerated. Air resistance is ignored. Trajectory of Projectile Parabolic path of a projectile RANGE is how far it travels horizontally. MAXIMUM HEIGHT occurs halfway through

range, if fired over level ground. Acceleration is DOWN at 9.8 m/s2 everywhere. Instantaneous velocity is tangent to the path. The vertical velocity changes while the

horizontal velocity remains constant.

9. Kinematic Graphs for 2D Projectiles x-component of motion x vs t v vs t a vs t



y-component of motion x vs t v vs t a vs t

10. Projectile Motion (A-182 #64, #65)

a) How do the speeds of the ball at the three points compare?

(A) vP < vQ< vR (B) vR < vQ < vP (C) vQ < vR < vP (D) vQ < vP = vR (E) vP = vR < vQ

Explain your choice:

b) Which of the following diagrams best shows the direction of the acceleration of the ball at point P ? Explain your choice:

11. Graphs of Projectiles (A-177 #63)

A projectile is fired with initial velocity v0 at an

angle θ with the horizontal and follows the trajectory shown above. Which of the following pairs of graphs best represents the vertical components of the velocity and acceleration, v and a, respectively, of the projectile as functions of time t ?

Explain your reasoning:

Working 2-D Motion Problems Resolve vectors into components. Work as one-dimensional problems.

Horizontal Component of Velocity Not accelerated by gravity (or anything) Follows equation x = Vo,xt

12. Horizontal Component (A-177 #9) A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v ?

(A) d (B) 2d (C) 2d (D) 4d (E) It cannot be determined unless the height of the cliff is known.

Show your work or explain your reasoning:

Vertical Component of Velocity Accelerated by gravity (9.8 m/s2 down) Use kinematic equations for accelerated motion.



13. Vertical Component (S-199 #5) A 2-kilogram block rests at the edge of a platform that is 10 meters above level ground. The block is launched horizontally from the edge of the platform with an initial speed of 3 meters per second. Air resistance is negligible. The time it will take for the block to reach the ground is

(A) 0.3 s (B) 1.0 s (C) 1.4 s (D) 2.0 s (E) 3.0 s

Show your work:

14. Vertical Component (A-187 #59)

A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is υ 0 . How much time does it take the rock to travel from the edge of the building to the ground?

(A) hυ 0

(B) h υ 0

(C) h gυ0

(D) 2h g (E) 2h g

Show your work: �

Force (F) (unit: N) A force is a push or pull on an object. Forces cause an objects to accelerate. Newton’s First Law (Law of Inertia) A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by an external force.

Equilibrium A body with no net force on it is in equilibrium. Bodies in static equilibrium are stationary; bodies in translational equilibrium are moving.

15. Newton’s 1st Law (A-187 #7 - mod) Three forces act on an object. If the object is in translational equilibrium, which of the following must be true? I. The vector sum of the three forces must equal

zero. II. The magnitudes of the three forces must be equal. III. One force must be the equilibrant of the other two.

(A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

Explain your reasoning

16. Newton’s 1st Law (A-187 #44 - mod)

The sum of the forces on the object is zero in which of the cases?

(A) II only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

Explain your reasoning

17. Newton’s 1st Law (S-195 #5)

A ball of mass m is suspended from two strings of unequal length as shown above. The tensions T1 and T2 in the strings must satisfy which of the following relations?

(A) T1= T2 (B) T1>T2 (C) T1<T2 (D) T1+T2=mg (E) T1-T2 = mg




18. Newton’s 1st Law (A-177 #58) When an object of weight W is suspended from the center of a massless string as shown above, the tension at any point in the string is (A) 2W cosθ (B) W cosθ

2 Show your work:

(C) W cosθ (D) W

2cosθ

(E) Wcosθ

Newton’s Second Law ΣF = ma

Procedure for Second Law Problems Step 1: Draw the problem Step 2: Free Body Diagram Step 3: Set up equations

ΣF = ma ΣFx = max ΣFy = may Step 4: Substitute known values Step 5: Solve

19. Second Law (A-173 #11)

When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension in the string between the blocks is

(A) 2F (B) F Show your work:

(C) 2

3F

(D) 1

2F

(E) 1

3F

20. Second Law (A-182 #2) A ball falls straight down through the air under the influence of gravity. There is a retarding force F on the ball with magnitude given by F = bv, where v is the speed of the ball and b is a positive constant. The magnitude of the acceleration a of the ball at any time is equal to which of the following?

(A) g b− Show your work:

(B) gbvm

−

(C) gbvm

+

(D) gb

(E) bvm

21. Second Law (A-182 #45)

A block of mass 3m can move without friction on a horizontal table. This block is attached to another block of mass m by a cord that passes over a frictionless pulley, as shown above. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?

(A) Zero (B) g/4 (C) g/3 (D) 2g/3 (E) g

Show your work:

Newton’s Third Law For every action there exists an equal and opposite reaction. If A exerts a force F on B, then B exerts a force of -F on A. Weight (W) (N) W = mg (near the surface of the earth)

Normal Force Force that prevents objects from penetrating each other Reaction to other forces Commonly a reaction to gravity



22. Normal Force Flat (A-177 #4)

A block of weight W is pulled along a horizontal surface at constant speed v by a force F. which acts at an angle of θ with the horizontal, as shown above. The normal force exerted on the block by the surface has magnitude

(A) W - Fcos θ (B) W - Fsin θ (C) W (D) W + Fsin θ (E) W + Fcos θ

Show your work

23. Normal Force Ramp (A-271 #62)

A plane 5 meters in length is inclined at an angle of 37°, as shown above. A block of weight 20 newtons is placed at the top of the plane and allowed to slide down. The magnitude of the normal force exerted on the block by the plane is most nearly

(A) l0 N (B) 12N (C) l6 N (D) 20 N (E) 33 N

Show your work

24. Elevators and Normal Force (PAB) A 50-kg middle school student stands on a scale in an elevator that is moving downward, but slowing with an acceleration of magnitude 2.0 m/s2. What does the scale read (in N)?

(A) 300 (B) 400 (C) 500 (D) 600 (E) 700

Show your work Friction (f) (unit: N) The force that opposes a sliding motion. Static friction exists before sliding occurs. Kinetic friction exists after sliding occurs. In general Kinetic friction <= Static friction

fs ≤ µsN (for static friction) Static friction increases as the force trying to push an object increases, until it reaches its maximum value. fk = µkN (for kinetic friction)

25. Friction on Flat Surface (S-195 #61)

A push broom of mass m is pushed across a rough horizontal floor by a force of magnitude T directed at angle θ as shown above. The coefficient of friction between the broom and the floor is µ. The frictional force on the broom has magnitude

(A) µ(mg +Tsinθ) (B) µ(mg -Tsinθ) (C) µ(mg +Tcosθ) (D) µ(mg -Tcosθ) (E) µmg

Show your work

26. Friction on Ramp(S-195 #6-#7) Questions 6-7

A 2-kilogram block slides down a 30° incline as shown above with an acceleration of 2 meters per second squared.

(a) Which of the following diagrams best represents the gravitational force W, the frictional force f, and the normal force N that act on the block?



Explain your Reasoning: (b) The magnitude of the frictional force along the plane is most nearly (A) 2.5 N (B) 5N (C) 6 N (D) 10 N (E) 16 N Show your work: Uniform Circular Motion An object moves at uniform speed in a circle of constant radius. Acceleration in Uniform Circular Motion Turns object; doesn’t speed it up or slow it down. Acceleration points toward center of the circle. Called centripetal acceleration. Centripetal Acceleration ac = v2/r Force in Uniform Circular Motion Any force responsible for uniform circular motion is called a centripetal force. Centripetal force can arise from one force, or a combination of sources. ΣF = mac = m v2 / r Since speed of object remains constant, kinetic

energy remains constant, and work is zero. Friction, tension, normal force, gravity and the magnetic force are common forces that can act centripetally to cause uniform circular motion.

27. Centripetal Force (A-184 #46) A car initially travels north and then turns to the left along a circular curve. This causes a package on the seat of the car to slide toward the right side of the car. Which of the following is true of the net force on the package while it is sliding? (A) The force is directed away from the center of the circle. (B) The force is directed north. (C) There is not enough force directed north to keep the

package from sliding. (D) There is not enough force tangential to the car's path to

keep the package from sliding. (E) There is not enough force directed toward the center of

the circle to keep the package from sliding. Explain your reasoning:

28. Centripetal Force (A-355 #2) The horizontal turntable shown below rotates at a constant rate. As viewed from above, a coin on the turntable moves counterclockwise in a circle as shown. Which of the following vectors best represents the direction of the frictional force exerted on the coin by the turntable when the coin is in the position shown?

Explain your reasoning: Universal Law of Gravity Fg = Gm1m2/r

2

Most orbit problems can be solved by setting the gravitational force equal to the centripetal force.

Gm1m2 / r2 = m1v

2 / r

29. Orbit (A-266 #61) A satellite of mass M moves in a circular orbit of radius R at a constant speed v. Which of the following must be true? I. The net force on the satellite is equal to mv2/R and

is directed toward the center of the orbit. II. The net work done on the satellite by gravity in one

revolution is zero. III. The angular momentum of the satellite is a

constant. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III




30. Orbit (S-226 #67) A satellite of mass m and speed v moves in a stable, circular orbit around a planet of mass M. What is the radius of the satellite's orbit?

a. mv

GM b.

mMGv

c. 2v

GM

d. v

GmM e.

2v

GmM

Show your work:

31. Law of Gravity, Weight (S-226 #10) A new planet is discovered that has twice the Earth's mass and twice the Earth's radius. On the surface of this new planet, a person who weighs 500 N on Earth would experience a gravitational force of

a. 125 N b. 250 N c. 500 N d. 1000 N e. 2000 N

Show your work:

32. Gravity, Acceleration (A-182 #48) The planet Mars has mass 6.4 x 1023 kilograms and radius 3.4 x 106 meters. The acceleration of an object in free-fall near the surface of Mars is most nearly (A) zero (B) l.0 m/s2 (C) 1.9 m/s2 (D) 3.7 m/s2 (E) 9.8 m/s2 Show your work: Torque (� ) (Nm) Torque is a “twist” caused by a force in combination with a “moment arm”. τ = F r sin θ

33. Torque (A-187 #68)

A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force F is applied at the other end, at an angle θ to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque? (A) L sinθ Show your work: (B) Lcosθ (C) L (D) L tanθ (E) 2 L Rotational Equilibrium If counterclockwise torques equal the clockwise torques, the system is balanced and no rotation occurs. Στcw = Στccw

34. Rotational Equilibrium (A-271 #57)

Two objects, of masses 6 and 8 kilograms, are hung from the ends of a stick that is 70 centimeters long and has marks every l0 centimeters, as shown above. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord? (A) A (B) B (C) C (D) D (E) E Show your work:

35. Rotational Equilibrium (A-173 #13)

A 5-meter uniform plank of mass 100 kilograms rests on the top of a building with 2 meters extended over the edge as shown above. How far can a 50-kilogram person venture past the edge of the building on the plank before the plank just begins to tip?



12ms

2

A)

1

2m B) 1 m

C)

2

3m D) 2 m

E) It is impossible to make the plank tip since the person would have to be more than 2 meters from the edge of the building. Show your work:

36. Rotational Equil (S-115 #3-#33) A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N. a) What is the tension in the left chain?

a. 250 N b. 375 N c. 500 N d. 625 N e. 875 N

Show your work:

b) How far from the left end of the board is the person sitting? a. 0.4 m b. 1.5 m c. 2 m d. 2.5 m e. 3 m

Show your work:

ADVANCE TOPIC: ANGULAR MOMENTUM The tendency of a spinning body to remain spinning. L = I ω

L: angular momentum (kg m2/s) I: rotational inertia (MR2 for a particle) ω: angular speed (radians/second)

Angular momentum, like linear momentum, is conserved. Unless there is an external torque on the system, there can be no change in angular momentum

37. Angular Momentum (A-187 #6) A 2 kg object moves in a circle of radius 4 m at a constant speed of 3 m/s. A net force of 4.5 N acts on the object. What is the angular momentum of the object with respect to an axis

perpendicular to the circle and through its center? Show your work: (A) 9

N mkg⋅

(B)

(C) 135.kg m

s

2

2

⋅

(D) 18N mkg⋅

(E) 24kg m

s

2⋅

38. Angular Momentum (A-173 #14)

An asteroid moves in an elliptic orbit with the Sun at one focus as shown above. Which of the following quantities increases as the asteroid moves from point P in its orbit to point Q? (A) Speed (B) Angular momentum (C) Total energy (D) Kinetic energy (E) Potential energy Show your work or explain your reasoning:

Periodic Motion Repeats itself over a fixed and reproducible

period of time. Oscillators undergo periodic motion. Simple Harmonic Motion (SHM) Periodic motion described by sine or cosine function. Springs and pendulums are Simple Harmonic

Oscillators (SHOs) that obey Hooke’s Law. Restoring Force (Hooke’s Law) F = -kx (negative sign indicates force is restoring) Restoring force is greatest at maximum

displacement and zero at equilibrium Equilibrium The midpoint of the oscillation of a simple

harmonic oscillator. Position of minimum potential energy and

maximum kinetic energy.


3/30/2010 10 Bertrand

Amplitude (A) (unit: m) How far the oscillating mass is from equilibrium

at its maximum displacement. Period (T) (unit: s) The length of time it takes for one cycle of

periodic motion to complete itself. Frequency (f) (unit: Hz or s-1) How fast the oscillation is occurring. f = 1/T

39. Simple Harmonic Motion (A-271 #43)

A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram above. At what time t does the particle achieve its maximum positive acceleration? (A) 1s (B) 2s (C) 3s (D) 4s (E) None of the above; the acceleration is constant Explain your reasoning:

40. Hooke’s Law (A-271 #3) An ideal spring obeys Hooke's law, F = - kx. A mass of 0.50 kilogram hung vertically from this spring stretches the spring 0.075 meter. The value or the force constant for the spring is most nearly (A) 0.33 N/m (B) 0.66 N/m (C) 6.6 N/m (D) 33 N/m (E) 66 N/m Show your work:

Period of a spring T = 2π√m/k Potential Energy of a Spring Us = ½ k x2 Pendulum The pendulum can be thought of as an oscillator. The displacement needs to be small for it to work properly. Pendulum Forces: Gravity and tension�

Period of a pendulum T = 2π√l/g Potential Energy of a Pendulum Ug = mgh

41. Period of Pendulum (A-177 #8) The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10.0 m Show your work:

42. Period: Spring, Pendulum (A-088 #44) An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring, also with period T. If the masses of both objects are doubled, what are the new values for the periods? Pendulum Spring (A) T

2 2T

(B) T 2T (C) 2T T (D) 2T T (E) 2T T 2 Explain your reasoning:

Work (W) (Unit: Joule, J) The scalar bridge between force and energy. W = F ∆x cos θ Counterintuitive Results There is no work if there is no displacement. Forces perpendicular to displacement don’t work. By doing positive work on an object, a force or

collection of forces increases its mechanical energy in some way.

The two forms of mechanical energy are called potential and kinetic energy.

43.


3/30/2010 11 Bertrand

43. Work (A-088 #6) A horizontal force F is used to pull a 5-kilogran block across a floor at a constant speed of 3 meters per second. The frictional force between the block and the floor is 10 newtons. The work done by the force F in 1 minute is most nearly (A) 0 J (B) 30 J (C) 600 J (D) 1,350 J (E) 1,800 J Show your work: Kinetic Energy (K) (unit: Joule, J) Energy due to motion K = ½ m v2

44. Kinetic Energy (A-177 #3)

Which of the following quantities is a scalar that is always positive or zero? (A) Power (B) Work (C) Kinetic energy (D) Linear momentum (F) Angular momentum State your reasoning: The Work-Energy Theorem Wnet = ∆K Net work – work due to ALL forces -- is used in this theorem. When net work is positive, the kinetic energy of the object will increase, when negative, the kinetic energy will decrease. Work and graphs The area under the curve of a graph of force vs displacement gives the work done by the force in performing the displacement. Power (P) (unit: Watt, W which is a J/s) The rate of which work is done. When we run upstairs, t is small so P is big. When we walk upstairs, t is large so P is small. P = W/t P = F V

45. Power (S-115 #68)

A constant force of 900 N pushes a 100 kg mass up the inclined plane shown above at a uniform speed of 4 m/s. The power developed by the 900 N force is most nearly a. 400 W b. 800 W c. 900 W d. 1000 W e. 3600 W Show your work: How We Buy Energy… The kilowatt-hour is a commonly used unit by the electrical power company. Power companies charge you by the kilowatt-hour (kWh), but this not power, it is really energy consumed. 1 kW = 1000 W 1 h = 3600 s 1 kWh = 1000J/s • 3600s = 3.6 x 106J

46. Power (A-187 #5) Units of power include which of the following?

I. Watt II. Joule per second III. Kilowatt-hour

(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

State your reasoning:

47. Power (A-187 #9) A child pushes horizontally on a box of mass m which moves with constant speed υ across a horizontal floor. The coefficient of friction between the box and the floor is µ. At what rate does the child do work on the box? (Α) µmgυ (Β) mgυ (C) υ/µmg (D) µmg/υ (E) µmυ2 Show your work:


3/30/2010 12 Bertrand

Force Types Conservative forces:

Work is path independent. Work along a closed path is zero. Work done against conservative forces increases potential energy; work done by them decreases it. Ex: gravity, springs

Non-conservative forces: Work is path dependent. Work along a closed path is NOT zero. Work may be related to a change in total energy (including thermal energy). Ex: friction, drag

Potential energy Energy of position or configuration. Examples:

Gravitational, Spring, Electrical energies Potential energy is related to work done by CONSERVATIVE FORCES only. ∆Ug = -Wg (gravity)

∆Ug = -Ws (spring) Gravitational potential energy close to earth’s surface. Wg = -mgh (close to earth’s surface) ∆U = -Wg = mgh Note: we calculate changes in potential energy only using this method. We assign the potential energy to be zero at some certain point, usually the surface of the earth.

48. Work, gravity (A-182 #63)

A plane 5 meters in length is inclined at an angle of 37°, as shown above. A block of weight 20 newtons is placed at the top of the plane and allowed to slide down. The work done on the block by the gravitational force during the 5-meter slide down the plane is most nearly

(A) 20 J (B) 60 J (C) 80 (D) 100 J (E) l30 J

Show your work:

Gravitational potential energy changes far from earth’s surface. Ug = -GMem/r (close to earth’s surface) Ug has been defined to be zero when an object is

infinitely far from the earth, and it gets increasingly negative as an object approaches the earth.

Note: This literal definition is impractical in most problems, but this is the equation that must be used to calculate ∆∆∆∆U when you a very far from the earth’s surface.

49. Escape Velocity (PAB)

Use conservation of energy to derive an expression for the escape velocity of a rocket of mass m from the surface of a planet of mass M and radius R. Assume the planet has no atmosphere. (A)

Gmr

(B) Gm

r

(C) 2GM

r

(D) 2GmM

r

(E) None of the above Show your work: Spring potential energy Us = ½ kx2 Us is zero when a spring is in its equilibrium

position (neither compressed nor extended) Law of Conservation of Mechanical Energy The total mechanical energy of a system remains constant, provided only conservative forces act upon the system. U + K = Constant U1 + K1 = U2 + K2 ∆U + ∆K = 0 ∆U = -∆K

50. Springs (A-088 #11,#12)

A block oscillates without friction on the end of a spring as shown above. The minimum and maximum lengths of the spring as it oscillates are, respectively, xmin and xmax The graphs below can represent quantities associated with the


3/30/2010 13 Bertrand

oscillation as functions of the length x of the spring.

(a) Which graph can represent the total mechanical energy of the block-spring system as a function of x ? (A) A (B) B (C) C (D) D (E) E Explain your reasoning:

(b) Which graph can represent the kinetic energy of the block as a function of x ? (A) A (B) B (C) C (D) D (E) E Explain your reasoning:

.

51. Conservation of Energy (A-098 #38)

A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3.0 kg block is then replaced by a 4.0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4.0 kg block fall before its direction is reversed? (A) 9 cm (B) 18 cm (C) 24 cm (D) 32 cm (E) 48 cm

Show your work:

52. Cons. of Energy (A-098 #60)

A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is υ 0 .What is the kinetic energy of the rock just before it hits the ground? (A) mgh (B) 1

2 02mυ (C) 1

2 02m mghυ −

(D) 12 0

2m mghυ + (E) mgh m− 12 0

2υ

Show your work:

53. Cons. of Energy (A-182 #47) A block of mass m slides on a horizontal frictionless table with an initial speed v 0 . It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed from its natural length? (A) v

g0

2

2 Show your work:

(B) mgk

(C) mk

v0

(D) mk

v0

(E) km

v0


3/30/2010 14 Bertrand

54. Cons. of Energy (A-355 #51,52)

A ball swings freely back and forth in an arc from point I to point IV, as shown above. Point II is the lowest point in the path, III is located 0.5 meter above II, and IV is l meter above II. Air resistance is negligible. a) If the potential energy is zero at point II,

where will the kinetic and potential energies of the ball be equal? (A) At point II (B) At some point between II and III (C) At point III (D) At some point between III and IV (E) At point IV

State your reasoning: b) The speed of the ball at point II is most nearly

(A) 3.0 m/s (B) 4.5 m/s (C) 9.8 m/s (D) l4 m/s (E) 20 m/s

Show your work: Conservation of Energy and Dissipative Forces. Dissipative forces cause loss of mechanical

energy by producing heat. Wnc = ∆U + ∆K

55. Cons.of Energy (A-093 #4)

The figure above shows a rough semicircular track whose ends are at a vertical height h. A

block placed at point P at one end of the track is released from rest and slides past the bottom of the track. Which of the following is true of the height to which the block rises on the other side of the track? (A) It is equal to h/2 π . (B) It is equal to h/4. (C) It is equal to h/2. (D) It is equal to h. (E) It is between zero and h; the exact height

depends on how much energy is lost to friction.

Explain your reasoning: Momentum (P) (unit: kg m/s or N s) How hard it is to stop a moving object. For one particle

p = mv For a system of multiple particles

P = Σpi = Σmivi Momentum is a vector!

56. Momentum (A-098 #43)

The magnitude of the momentum of the object is increasing in which of the cases?

(A) II only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

Explain your reasoning: Impulse (J) (units: N s or kg m/s) The product of an external force and time, which

results in a change in momentum J = F t J = ∆P


3/30/2010 15 Bertrand

57. Impulse (A-262 #56) Two planets have the same size, but different masses, and no atmospheres. Which of the following would be the same for objects with equal mass on the surfaces of the two planets? I. The rate at which each would fall freely II. The amount of mass each would balance on

an equal-arm balance III. The amount of momentum each would

acquire when given a certain impulse (A) I only (B) III only (C) I and II only (D) II and II1 only (E) I, II, and III


58. Impulse (A-187 #57)

A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leaves the kicker's foot with a speed of 5.0 m/s in a direction 60° above the horizontal. The magnitude of the impulse imparted by the ball to the foot is most nearly (A) 1 N s⋅

(B) 3 N s⋅ Show your work:

(C) 2 N s⋅

(D) 23

N s⋅

(E) 4 N s⋅ Law of Conservation of Momentum If the resultant external force on a system is zero, then the momentum of the system will remain constant. The sum of the momentums before a collision is

equal to the sum of the momentums after a collision.

ΣPb = ΣPa

59. Cons. of Momentum (A-093 #11)

Two objects having the same mass travel toward each other on a flat surface. each with a speed of 1.0 meter per second relative to the surface. The objects collide head-on and are reported to rebound after the collision. each with a speed of

2.0 meters per second relative to the surface. Which of the following assessments of this report is most accurate? (A) Momentum was not conserved; therefore the report is false. (B) If potential energy was released to the objects during the collision, the report could be true. (C) If the objects had different masses, the report could be true. (D) If the surface was inclined, the report could be true. (E) If there was no friction between the objects and the surface, the report could be true. Explain your reasoning:

Collisions Follow Newton’s Third Law (forces exerted on

colliding bodies are equal magnitude) During a collision, external forces are ignored. The time frame of the collision is very short. The forces are impulsive forces (high force, short duration). Collision Types Elastic: P is conserved, K is conserved Inelastic: P is conserved, K is NOT conserved Perfectly Inelastic means the bodies stick together

60. Collisions (A-093 #10) Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface? (A) The collision is elastic. (B) All of the initial kinetic energy of the less-massive

object is lost. (C) The momentum of the objects that are stuck

together has a smaller magnitude than the initial momentum of the less-massive object.

(D) The speed of the objects that are stuck together will be less than the initial speed of the less-massive object.

(E) The direction of motion of the objects that are stuck together depends on whether the hit is a head-on collision.



3/30/2010 16 Bertrand

61. Collisions (A-093 #11) Two objects having the same mass travel toward each other on a flat surface, each with a speed of 10 meter per second relative to the surface. The objects collide head-on and are reported to rebound after the collision, each with a speed of 20 meters per second relative to the surface. Which of the following assessments of this report is most accurate? (A) Momentum was not conserved, therefore the report is false. (B) If potential energy was released to the objects during the collision, the report could be true. (C) If the objects had different masses, the report could be true. (D) If the surface was inclined, the report could be true. (E) If there was no friction between the objects and the surface, the report could be true. Explain your reasoning:

62. Collision (A-004 #63)

The two blocks of masses M and 2M shown above initially travel at the same speed v but in opposite directions. They collide and stick together. How much mechanical energy is lost to other forms of energy during the collision?

a. Zero b. 2

21

Mv c. 2

43

Mv d.

2

34

Mv e. 2

23

Mv

Show your work:

63. Momentum Change (S-199 #7)

A tennis ball of mass m rebounds from a racquet with the same speed v as it had initially, as shown above. The magnitude of the momentum change of the ball is

(A) 0 (B) mv (C) 2mv (D) 2mv sin θ (E) 2mv cos θ

Show your work:

64. Collision (A-276 #41)

Two objects of mass 0.2 kg and 0.1 kg, respectively, move parallel to the x-axis, as shown above. The 0.2 kg object overtakes and collides with the 0.1 kg object. Immediately after the collision, the y-component of the velocity of the 0.2 kg object is 1 m/s upward. What is the y-component of the velocity of the 0.1 kg object immediately after the collision?

(A) 2 m/s downward (B) 0.5 m/s downward (C) 0 m/s (D) 0.5 m/s upward (E) 2 m/s upward

Show your work:

Explosion Mathematically, handled just like an ordinary

perfectly inelastic collision. Momentum is conserved, kinetic energy is not.

65. Explosion (A-098 #67)

A stationary object explodes, breaking into three pieces of masses m, m, and 3m. The two pieces of mass m move off at right angles to each other with the same magnitude of momentum mV, as shown in the diagram


3/30/2010 17 Bertrand

above. What are the magnitude and direction of the velocity of the piece having mass 3m?

�Show your work:

<<ADVANCED TOPIC>> Center of Mass

Where all the mass can be considered to exist For uniform objects, the center of mass resides at geometric center.

For collection of points, use these equations xcm = Σ mixi / Σmi ycm= Σ miyi / Σmi zcm= Σ mizi / Σmi

where xcm, ycm, and zcm are the coordinates of the center of mass, and Σmi is the total mass of the system.

66. Center of Mass (A-098 #63) Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true? (A) The kinetic energies of the two people are equal. (B) The speeds of the two people are equal. (C) The momenta of the two people are of equal

magnitude. (D) The center of mass of the two-person system

moves in the direction of the less massive person. (E) The less massive person has a smaller initial

acceleration than the more massive person. Explain your reasoning:

67. Center of Mass (A-182 #8)

The two spheres pictured above have equal densities and are subject only to their mutual gravitational attraction. Which of the following quantities must have the same magnitude for both spheres?

(A) Acceleration (B) Velocity (C) Kinetic energy (D) Displacement from the center of mass (E) Gravitational force


b mechanics 2008-answers - mater lakes...the graph above represents position x versus time t for an...

Documents