READING QUIZ

1. Newton’s second law can be written in mathematical form as F = ma. Within the summation of forces, F, ________ are(is) not included.

A) external forces B) weight

C) internal forces D) All of the above.

2. The equation of motion for a system of n-particles can be written as Fi = miai = maG, where aG indicates _______.

A) summation of each particle’s acceleration

B) acceleration of the center of mass of the system

C) acceleration of the largest particle

D) None of the above.

CONCEPT QUIZ

1. The block (mass = m) is moving upward with a speed v. Draw the FBD if the kinetic friction coefficient is k.

A) B) C) D) None of the above.

mg

kmg

N

mg

N

kN

N

mg

kN

v

CONCEPT QUIZ (continued)

2. Packaging for oranges is tested using a machine that exerts ay = 20 m/s2 and ax = 3 m/s2, simultaneously. Select the correct FBD and kinetic diagram for this condition.

A) B)

C) D)

= •

may

max

W

Ry

Rx

= • max

W

Ry

Rx

= •

may

max

W

Ry

= •

may

Ry

y

x

CHECK YOUR UNDERSTANDING QUIZ

1. If the cable has a tension of 3 N, determine the acceleration of block B.

A) 4.26 m/s2 B) 4.26 m/s2

C) 8.31 m/s2 D) 8.31 m/s2

10 kg

4 kg

k=0.4

2. Determine the acceleration of the block.

A) 2.20 m/s2 B) 3.17 m/s2

C) 11.0 m/s2 D) 4.26 m/s2 5 kg

60 N

•30

READING QUIZ

2. The positive n direction of the normal and tangential coordinates is ____________.

A) normal to the tangential component B) always directed toward the center of curvature

C) normal to the bi-normal component D) All of the above.

1. The “normal” component of the equation of motion is written as Fn=man, where Fn is referred to as the _______.

A) impulse B) centripetal force

C) tangential force D) inertia force

ATTENTION QUIZ

1. The tangential acceleration of an object

A) represents the rate of change of the velocity vector’s direction.

B) represents the rate of change in the magnitude of the velocity.

C) is a function of the radius of curvature.

D) Both B and C.

2. The block has a mass of 20 kg and a speed of v = 30 m/s at the instant it is at its lowest point. Determine the tension in the cord at this instant.

A) 1596 N B) 1796 N

C) 1996 N D) 2196 N

10 m

v = 30m/s

CONCEPT QUIZ

1. When a pilot flies an airplane in a vertical loop of constant radius r at constant speed v, his apparent weight is maximum at

A) Point A B) Point B (top of the loop)

C) Point C D) Point D (bottom of the loop)

r A

B

C

D

READING QUIZ

1. What is the work done by the force F?

A) F s B) –F s

C) Zero D) None of the above.

s

s1 s2

F

2. If a particle is moved from 1 to 2, the work done on the particle by the force, FR will be

A) B)

C) D)

2

1

s

tsF ds 2

1

s

tsF ds

2

1

s

nsF ds

2

1

s

nsF ds

CONCEPT QUIZ

1. A spring with an un-stretched length of 5 in expands from a length of 2 in to a length of 4 in. The work done on the spring is _________ in·lb .

A) -[0.5 k(4 in)2 - 0.5 k(2 in)2] B) 0.5 k (2 in)2

C) -[0.5 k(3 in)2 - 0.5 k(1 in)2] D) 0.5 k(3 in)2 - 0.5 k(1 in)2

2. If a spring force is F = 5 s3 N/m and the spring is compressed by s = 0.5 m, the work done on a particle attached to the spring will be

A) 0.625 N · m B) – 0.625 N · m

C) 0.0781 N · m D) – 0.0781 N · m

ATTENTION QUIZ

1. What is the work done by the normal force N if a 10 lb box is moved from A to B ?

A) - 1.24 lb · ft B) 0 lb · ft

C) 1.24 lb · ft D) 2.48 lb · ft

2. Two blocks are initially at rest. How many equations would be needed to determine the velocity of block A after block B moves 4 m horizontally on the smooth surface?

A) One B) Two

C) Three D) Four

2 kg

2 kg

READING QUIZ

1. The formula definition of power is ___________.

A) dU / dt B) F v

C) F dr/dt D) All of the above.

2. Kinetic energy results from _______.

A) displacement B) velocity

C) gravity D) friction

CONCEPT QUIZ

2. A twin engine jet aircraft is climbing at a 10 degree angle at 260 ft/s. The thrust developed by a jet engine is 1000 lb. The power developed by the aircraft is

A) (1000 lb)(260 ft/s) B) (2000 lb)(260 ft/s) cos

C) (1000 lb)(260 ft/s) cos D) (2000 lb)(260 ft/s)

1. A motor pulls a 10 lb block up a smooth incline at a constant velocity of 4 ft/s. Find the power supplied by the motor.

A) 8.4 ft·lb/s B) 20 ft·lb/s

C) 34.6 ft·lb/s D) 40 ft·lb/s

30º

READING QUIZ

1. The potential energy of a spring is ________

A) always negative. B) always positive.

C) positive or negative. D) equal to ks.

2. When the potential energy of a conservative system increases, the kinetic energy _________

A) always decreases. B) always increases.

C) could decrease or D) does not change. increase.

CONCEPT QUIZ

2. Recall that the work of a spring is U1-2 = -½ k(s22 – s1

2) and can be either positive or negative. The potential energy of a spring is V = ½ ks2. Its value is __________

A) always negative. B) either positive or negative.

C) always positive. D) an imaginary number!

1. If the work done by a conservative force on a particle as it moves between two positions is –10 ft·lb, the change in its potential energy is _______

A) 0 ft·lb. B) -10 ft·lb.

C) +10 ft·lb. D) None of the above.

ATTENTION QUIZ

1. The principle of conservation of energy is usually ______ to apply than the principle of work & energy.

A) harder B) easier

C) the same amount of work D) It is a mystery!

2. If the pendulum is released from the horizontal position, the velocity of its bob in the vertical position is _____

A) 3.8 m/s. B) 6.9 m/s.

C) 14.7 m/s. D) 21 m/s.

READING QUIZ

1. The linear impulse and momentum equation is obtained by integrating the ______ with respect to time.

A) friction force B) equation of motion

C) kinetic energy D) potential energy

2. Which parameter is not involved in the linear impulse and momentum equation?

A) Velocity B) Displacement

C) Time D) Force

CHECK YOUR UNDERSTANDING QUIZ

1. Calculate the impulse due to the force.

A) 20 kg·m/s B) 10 kg·m/s

C) 5 N·s D) 15 N·s

F

10 N

t2 s

2. A constant force F is applied for 2 s to change the particle’s velocity from v1 to v2. Determine the force F if the particle’s mass is 2 kg.

A) (17.3 j) N B) (–10 i +17.3 j) N

C) (20 i +17.3 j) N D) ( 10 i +17.3 j) N

v2=20 m/s

v1=10 m/s60

Force curve

READING QUIZ

1. The internal impulses acting on a system of particles always __________

A) equal the external impulses. B) sum to zero.

C) equal the impulse of weight. D) None of the above.

2. If an impulse-momentum analysis is considered during the very short time of interaction, as shown in the picture, weight is a/an __________

A) impulsive force.

B) explosive force.

C) non-impulsive force.

D) internal force.

CONCEPT QUIZ

2) A drill rod is used with a air hammer for making holes in hard rock so explosives can be placed in them. How many impulsive forces act on the drill rod during the drilling?

A) None B) One

C) Two D) Three

1) Over the short time span of a tennis ball hitting the racket during a player’s serve, the ball’s weight can be considered _____________

A) nonimpulsive.

B) impulsive.

C) not subject to Newton’s second law.

D) Both A and C.

ATTENTION QUIZ

2. The 200-g baseball has a horizontal velocity of 30 m/s when it is struck by the bat, B, weighing 900-g, moving at 47 m/s. During the impact with the bat, how many impulses of importance are used to find the final velocity of the ball?

A) Zero B) One

C) Two D) Three

1. The 20 g bullet is fired horizontally at 1200 m/s into the 300 g block resting on a smooth surface. If the bullet becomes embedded in the block, what is the velocity of the block immediately after impact.

A) 1125 m/s B) 80 m/s

C) 1200 m/s D) 75 m/s

1200 m/s

BAT

vball

vbat

READING QUIZ

1. When the motion of one or both of the particles is at an angle to the line of impact, the impact is said to be ________

A) central impact. B) oblique impact.

C) major impact. D) None of the above.

2. The ratio of the restitution impulse to the deformation impulse is called _________

A) impulse ratio. B) restitution coefficient.

C) energy ratio. D) mechanical efficiency.

CONCEPT QUIZ

2. Under what condition is the energy lost during a collision maximum?

A) e = 1.0 B) e = 0.0

C) e = -1.0 D) Collision is non-elastic.

1. Two balls impact with a coefficient of restitution of 0.79. Can one of the balls leave the impact with a kinetic energy greater than before the impact?

A) Yes B) No

C) Impossible to tell D) Don’t pick this one!

ATTENTION QUIZ

2. A particle strikes the smooth surface with a velocity of 30 m/s. If e = 0.8, (vx) 2 is _____ after the collision.

A) zero B) equal to (vx) 1

C) less than (vx) 1 D) greater than (vx)

1

v30 m/s x

y

30

1. Block B (1 kg) is moving on the smooth surface at 10 m/s when it squarely strikes block A (3 kg), which is at rest. If the velocity of block A after the collision is 4 m/s to the right, (vB)2 is

A) 2 m/s B) 7 m/s

C) 7 m/s D) 2 m/sB A

vB=10 m/s

READING QUIZ

1. Select the correct expression for the angular momentum of a particle about a point.

A) r × v B) r × (m v)

C) v × r D) (m v) × r

2. The sum of the moments of all external forces acting on a particle is equal to

A) angular momentum of the particle.

B) linear momentum of the particle.

C) time rate of change of angular momentum.

D) time rate of change of linear momentum.

CONCEPT QUIZ

1. If a particle moves in the x - y plane, its angular momentum vector is in the

A) x direction. B) y direction.

C) z direction. D) x - y direction.

2. If there are no external impulses acting on a particle

A) only linear momentum is conserved.B) only angular momentum is conserved.C) both linear momentum and angular momentum are conserved.D) neither linear momentum nor angular momentum are

conserved.

ATTENTION QUIZ1. A ball is traveling on a smooth surface in a 3 ft radius circle

with a speed of 6 ft/s. If the attached cord is pulled down with a constant speed of 2 ft/s, which of the following principles can be applied to solve for the velocity of the ball when r = 2 ft?

A) Conservation of energy

B) Conservation of angular momentum

C) Conservation of linear momentum

D) Conservation of mass

2. If a particle moves in the z - y plane, its angular momentum vector is in the

A) x direction. B) y direction.

C) z direction. D) z - y direction.

READING QUIZ

1. If a rigid body is in translation only, the velocity at points A and B on the rigid body _______ .

A) are usually different B) are always the same C) depend on their position D) depend on their relative position

2. If a rigid body is rotating with a constant angular velocity about a fixed axis, the velocity vector at point P is _______.

A) rp B) rp

C) drp/dt D) All of the above.

ATTENTION QUIZ

1. The fan blades suddenly experience an angular acceleration of 2 rad/s2. If the blades are rotating with an initial angular velocity of 4 rad/s, determine the speed of point P when the blades have turned 2 revolutions

(when rad/s).

A) 14.2 ft/s B) 17.7 ft/s

C) 23.1 ft/s D) 26.7 ft/s

2. Determine the magnitude of the acceleration at P when the blades have turned the 2 revolutions.

A) 0 ft/s2 B) 3.5 ft/s2

C) 115.95 ft/s2 D) 116 ft/s2

ATTENTION QUIZ

2. If vA=10 m/s and aA=10 m/s, determine the angular acceleration, when = 30.

A) 0 rad/s2 B) -50.2 rad/s2

C) -112 rad/s2 D) -173 rad/s2

1. The sliders shown below are confined to move in the horizontal and vertical slots. If vA=10 m/s, determine the connecting bar’s angular velocity when = 30.

A) 10 rad/s B) 10 rad/s

C) 8.7 rad/s D) 8.7 rad/s

CHECK YOUR UNDERSTANDING QUIZ

1. If the disk is moving with a velocity at point O of 15 ft/s and = 2 rad/s, determine the velocity at A.

A) 0 ft/s B) 4 ft/s

C) 15 ft/s D) 11 ft/s

2. If the velocity at A is zero, then determine the angular velocity, .

A) 30 rad/s B) 0 rad/s

C) 7.5 rad/s D) 15 rad/s

2 ft V=15 ft/s

A

O

ATTENTION QUIZ

1. Which equation could be used to findthe velocity of the center of the gear, C,if the velocity vA is known?

A) vB = vA + gear × rB/A B) vA = vC + gear × rA/C

C) vB = vC + gear × rC/B D) vA = vC + gear × rC/A

vA

2. If the bar’s velocity at A is 3 m/s, what “base” point (first term on the RHS of the velocity equation) would be best used to simplify finding the bar’s angular velocity when = 60º?

A) A B) B

C) C D) No difference.

A

4 m

B

C

READING QUIZ

1. If applicable, the method of instantaneous center can be used to determine the __________ of any point on a rigid body.

A) velocity B) acceleration

C) velocity and acceleration D) force

2. The velocity of any point on a rigid body is __________ to the relative position vector extending from the IC to the point.

A) always parallel B) always perpendicular

C) in the opposite direction D) in the same direction

ATTENTION QUIZ

1. The wheel shown has a radius of 15 in and rotates clockwise at a rate of = 3 rad/s. What is vB?

A) 5 in/s B) 15 in/s

C) 0 in/s D) 45 in/s

2. Point A on the rod has a velocity of 8 m/s to the right. Where is the IC for the rod?

A) Point A.

B) Point B.

C) Point C.

D) Point D.

• C

D •

CONCEPT QUIZ

2. What are the tangential and normal components of the relative acceleration of point B with respect to G.

A) - 2r i −r j B) - r i + 2r j

C) 2r i −r j D) Zero.

1. If a ball rolls without slipping, select the tangential and normal components of the relative acceleration of point A with respect to G.

A) r i + 2r j B) - r i + 2r j

C) 2r i − r j D) Zero.

ATTENTION QUIZ

1. Two bodies contact one another without slipping. If the tangential component of the acceleration of point A on gear B is 100 ft/sec2, determine the tangential component of the acceleration of point A’ on gear C.

A) 50 ft/sec2 B) 100 ft/sec2

C) 200 ft/sec2 D) None of above.

2. If the tangential component of the acceleration of point A on gear B is 100 ft/sec2, determine the angular acceleration of gear B.A) 50 rad/sec2 B) 100 rad/sec2

C) 200 rad/sec2 D) None of above.

READING QUIZ

1. Mass moment of inertia is a measure of the resistance of a body to _____________.

A) translational motion B) deformation

C) angular acceleration D) impulsive motion

2. Mass moment of inertia is always ____________.

A) a negative quantity

B) a positive quantity

C) an integer value

D) zero about an axis perpendicular to the plane of motion

ATTENTION QUIZ

2. If the mass of body A and B are equal but kA = 2kB, then ____________.

A) IA = 2IB B) IA = (1/2)IB

C) IA = 4IB D) IA = (1/4)IB

1. The mass moment of inertia of any body about its center of mass is always ____________.

A) maximum B) minimum

C) zero D) None of the above

READING QUIZ

1. When a rigid body undergoes translational motion due to external forces, the translational equations of motion (EOM) can be expressed for _____________.

A) the center of rotation B) the center of mass

C) any arbitrary point D) All of the above

2. The rotational EOM about the mass center of the rigid body indicates that the sum of moments due to the external loads equals _____________.

A) IG B) m aG

C) IG + m aG D) None of the above.

CONCEPT QUIZ

A

B1. A 2 lb disk is attached to a uniform 6 lb rod AB with a frictionless collar at B. If the disk rolls without slipping, select the correct FBD.

6 lb

2 lb

Na

Nb

Fs

8 lb

Na

Nb

6 lb2 lb

Na

NbA) B) C)

Fs

CONCEPT QUIZ

A

B2. A 2 lb disk is attached to a uniform 6 lb rod AB with a frictionless collar at B. If the disk rolls with slipping, select the correct FBD.

6 lb2 lb

Na

Nb

k Na

8 lb

Na

NbA) B) C)

6 lb2 lb

Na

Nb

s NaFk

READING QUIZ

1. In rotational motion, the normal component of acceleration at the body’s center of gravity (G) is always __________.

A) zero

B) tangent to the path of motion of G

C) directed from G toward the center of rotation

D) directed from the center of rotation toward G

2. If a rigid body rotates about point O, the sum of the moments of the external forces acting on the body about point O equals?

A) IG B) IO

C) m aG D) m aO

CONCEPT QUIZ

2. In the above problem, when = 90°, the horizontal component of the reaction at pin O is __________.

A) zero B) m g

C) m (l/2) 2 D) None of the above

1. If a rigid bar of length l (above) is released from rest in the horizontal position ( = 0), the magnitude of its angular acceleration is at maximum when

A) = 0 B) = 90

C) = 180 D) = 0 and 180

1. A drum of mass m is set into motion in two ways: (a) by a constant 40 N force, and, (b) by a block of weight 40 N. If a and b represent the angular acceleration of the drum in each case, select the true statement.

A) a > b B) a < b

C) a = b D) None of the above

2. In case (b) above, what is the tension T in the cable?

A) T = 40 N B) T < 40 N

C) T > 40 N D) None of the above

ATTENTION QUIZ(a) (b)m m

T

10 lb 10 lb

READING QUIZ

1. If a disk rolls on a rough surface without slipping, the acceleration af the center of gravity (G) will _________ and the friction force will be __________.

A) not be equal to r; less thansN

B) be equal to r;equal tokN

C) be equal to rless than sN

D) None of the above

2. If a rigid body experiences general plane motion, the sum of the moments of external forces acting on the body about any point P is equal to __________.

A) IP B) IP maP

C) m aG D) IG rGP × maP

CONCEPT QUIZ

2. For the situation above, the moment equation about G is?

A) 0.75 (FfA) - 0.2(30) = - (80)(0.32)

B) -0.2(30) = - (80)(0.32)C) 0.75 (FfA) - 0.2(30) = - (80)(0.32) + 80aG

D) None of the above

1. An 80 kg spool (kG = 0.3 m) is on a rough surface and a cable exerts a 30 N load to the right. The friction force at A acts to the __________ and the aG

should be directed to the __________ .

A) right, left B) left, right

C) right, right D) left, left

30N

A

0.2m

0.75m

G•

ATTENTION QUIZ

2. Select the equation that best represents the “no-slip” assumption.

A) Ff = s N B) Ff = k N

C) aG = r D) None of the above

1. A slender 100 kg beam is suspended by a cable. The moment equation about point A is?

A) 2

B) 2

C) 2 + (100 aGx)(2)

D) None of the above

4m

10 N

3m

A

READING QUIZ

1. Kinetic energy due to rotation of the body is defined as

A) (1/2) m (vG)2. B) (1/2) m (vG)2 + (1/2) IG

2.

C) (1/2) IG 2. D) IG 2.2. When calculating work done by forces, the work of an

internal force does not have to be considered because ____________.

A) internal forces do not exist

B) the forces act in equal but opposite collinear pairs

C) the body is at rest initially

D) the body can deform

CONCEPT QUIZ

1. If a rigid body rotates about its center of gravity, its translational kinetic energy is ___________ at all times.

A) constant

B) zero

C) equal to its rotational kinetic energy

D) Cannot be determined

m

L•

2. A rigid bar of mass m and length L is released from rest in the horizontal position. What is the rod’s angular velocity when it has rotated through 90°?

A) g/3L B) 3g/L

C) 12g/L D) g/L

ATTENTION QUIZ

1. A disk and a sphere, each of mass m and radius r, are released from rest. After 2 full turns, which body has a larger angular velocity? Assume roll without slip.

A) Sphere B) Disk

C) The two are equal. D) Cannot be determined.

r

2. A slender bar of mass m and length L is released from rest in a horizontal position. The work done by its weight when it has rotated through 90° is?

A) m g (/2) B) m g L

C) m g (L/2) D) -m g (L/2)

m

L•

READING QUIZ

1. Elastic potential energy is defined as ___________.

A) + (1/2) k (s)2 B) - (1/2) k (s)2

C) + (1/2) k (v)2 D) None of the above

2. The kinetic energy of a rigid body consists of the kinetic energy due to ___________.

A) translational motion and rotational motion

B) only rotational motion

C) only translational motion

D) the deformation of the body

UNDERSTANDING QUIZ

2. Determine the kinetic energy of the disk at this instant.

A) (½)(20)(3)2 B) ½(20)(0.52)(10)2

C) Answer A + Answer B D) None of the above

1. At the instant shown, the spring isundeformed. Determine the change inpotential energy if the 20 kg disk(kG = 0.5 m) rolls 2 revolutionswithout slipping.

A) ½(200)(1.2)2 + (20)9.81(1.2 sin 30°)

B) - ½(200) (1.2)2 - (20)9.81(1.2 sin 30°)

C) ½(200)(1.2)2 - (20)9.81(1.2 sin 30°)

D) ½(200)(1.2)2

datum

3 m/s

ATTENTION QUIZ

1. Blocks A and B are released from rest and the disk turns 2 revolutions. The V2 of the system includes a term for ______________.A) only the 40 kg block

B) only the 80 kg block C) the disk and both blocks

D) only the two blocks

1m

40 kg

80 kg

datum

2. A slender bar is released from rest while in the horizontal position. The kinetic energy (T2) of the bar when it has rotated through 90° is?

A) ½ m (vG2)2 B) ½ IG (2)2

C) ½ k (s1)2 - W (L/2) D) ½ m (vG2)2 + ½ IG (2)2

m

L•

READING QUIZ

1. The angular momentum of a rotating two-dimensional rigid body about its center of mass G is ___________.

A) m vG B) IG vG

C) m D) IG

2. If a rigid body rotates about a fixed axis passing through its center of mass, the body’s linear momentum is __________.

A) a constant B) zero

C) m vG D) IG

CONCEPT QUIZ

A) larger than B) less than

C) the same as D) None of the above

1. If a slab is rotating about its center of mass G, its angular momentum about any arbitrary point P is __________ its angular momentum computed about G (i.e., IG ).

2. The linear momentum of the slab in question 1 is __________.

A) constant B) zero

C) increasing linearly D) decreasing linearly with time with time

ATTENTION QUIZ

1. If a slender bar rotates about end A, its angular momentum with respect to A is?

A) (1/12) m l2 B) (1/6) m l2

C) (1/3) m l2 D) m l2

Gl

A

2. As in the principle of work and energy, if a force does no work, it does not need to be shown on the impulse and momentum diagram/equation.

A) False B) True

C) Depends on the case D) No clue!

READING QUIZ

1. If there are no external impulses acting on a body _____________.

A) only linear momentum is conserved

B) only angular momentum is conserved

C) both linear momentum and angular momentum are conserved

D) neither linear momentum nor angular momentum are conserved

2. If a rigid body rotates about a fixed axis passing through its center of mass, the body’s linear momentum is __________.

A) constant B) zero

C) m vG D) IG

CONCEPT QUIZ

2. For the rod in question 1, the angular momentum about A of the rod and bullet just after impact will be ___________.

A) m vb + M(0.5)2 B) m(0.5)22 + M(0.5)22

C) m(0.5)22 + M(0.5)22 D) zero

+ (1/12) M 2

1. A slender rod (mass = M) is at rest. If a bullet (mass = m) is fired with a velocity of vb, the angularmomentum of the bullet about A justbefore impact is ___________.

A) 0.5 m vb2 B) m vb

C) 0.5 m vb D) zero

G

1.0

A0.5

m

ATTENTION QUIZ

2. The angular momentum of a body about a point A that is the fixed axis of rotation but not the mass center (G) is _____________.

A) IA B) IG

C) rG (m vG) + IG D) Both A & C

1. Using conservation of linear and angular momentum requires that _____________.

A) all linear impulses sum to zero

B) all angular impulses sum to zero

C) both linear and angular impulses sum to zero

D) None of the above