AEM 264 - Dynamics Final Exam study Questions
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
A) + (1/2) k (s)^2
A particle has an initial velocity of 3 ft/s to the left at s0 = 0 ft. Determine its position when t = 3 s if the acceleration is 2 ft/s2 to the right. A) 0.0 ft B) 6.0 ft to the left C)18.0 ft to the right D)9.0 ft to the right
A) 0.0 ft -3(3) + (1/2)(2)(3)^2 = 0
For the situation above, the moment equation about G is? A) 0.75 (FfA) - 0.2(30) = - (80)(0.32)a B) -0.2(30) = - (80)(0.32)a C) 0.75 (FfA) - 0.2(30) = - (80)(0.32)a + 80aG D) None of the above
A) 0.75 (FfA) - 0.2(30) = - (80)(0.32)a (Positive has been set to be CCW)
Two particles, A and B, are moving in the directions shown. What should be the angle q so that vB/A is minimum? Particle A is moving in the x-direction at 3 ft/s Particle B is moving at angle θ at 4 ft/s. A) 0° B) 180° C)90° D)270°
A) 0°
. Determine the speed of block B. Pully system, one cable, two pullies. A is moving at 2 m/s. block at B is hanging below the second pully, cable wraps under the second pully and connects to the bottom of the upper one. The other end of the cable wraps around pully at c, the end is point A, moving downward at 2 m/s A) 1 m/s B) 2 m/s C) 4 m/s D)None of the above.
A) 1 m/s
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 θ = 30°. A) 10 rad/s counter clockwise B) 10 rad/s clockwise C) 8.7 rad/s clockwise D) 8.7 rad/s counter clockwise
A) 10 rad/s counter clockwise
The fan blades suddenly experience an angular acceleration of 2 rad/s^2. 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 w = 8.14 rad/s). A) 14.2 ft/s B) 17.7 ft/s C) 23.1 ft/s D) 26.7 ft/s
A) 14.2 ft/s (using v=rw and the angular velocity provided)
Determine the acceleration of the block. A block hangs on a cable that is fixed on one end and strung through a pully on the other. The end of the cable strung through the pully is pulled down with a force of 60 N. The angle between the cable and the ceiling at the pully is 30 degrees. The block weighs 5 kg. A) 2.20 m/s^2 up B) 3.17 m/s^2 up C) 11.0 m/s^2 up D) 4.26 m/s^2 up
A) 2.20 m/s^2 up
If a particle has moved from A to B along the circular path in 4s, what is the average velocity of the particle? (r=5m) A) 2.5 i m/s B) 2.5 i +1.25 j m/s C) 1.25 p i m/s D) 1.25 pj m/s
A) 2.5 i m/s
If the pendulum is released from the horizontal position, the velocity of its bob in the vertical position is _____ Pendulum has a string with a length of 0.75 m and a ball attached to the end. A) 3.8 m/s. B) 6.9 m/s. C) 14.7 m/s. D) 21 m/s.
A) 3.8 m/s.
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 θ = 60º? A B and C form a right triangle on an L bracket. C is 90 degrees. A cable extends from A to B and is 4 m. A is moving in the negative x direction. A) A B) B C) C D) No difference.
A) A
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 (a) B) IP (a) + m(aP) C) m (aG) D) IG (a) + r_GP × m(aP)
A) IP (a)
The rotational EoM about the mass center of the rigid body indicates that the sum of moments due to the external loads equals _____________. A) I_G (a~) B) m (aG) C) I_G (a~) + m (aG) D) None of the above.
A) I_G (a~)
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.
A) Sphere (body with smaller MMI will have a larger angular velocity)
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!
A) Yes (Nothing was said about the masses of the balls!)
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 aa and ab represent the angular acceleration of the drum in each case, select the true statement. A) aa > ab B) aa < ab C) aa = ab D) None of the above
A) aa > ab
In general plane motion, if the rigid body is represented by a slab, the slab rotates A) about an axis perpendicular to the plane. B) about an axis parallel to the plane. C) about an axis lying in the plane. D) None of the above.
A) about an axis perpendicular to the plane.
When the potential energy of a conservative system increases, the kinetic energy _________ A) always decreases. B) always increases. C) could decrease or increase D) does not change.
A) always decreases (Conservation of Energy Principal)
When a relative-motion analysis involving two sets of coordinate axes is used, the x' - y' coordinate system will A) be attached to the selected point for analysis. B) rotate with the body. C) not be allowed to translate with respect to the fixed frame. D) None of the above.
A) be attached to the selected point for analysis.
A projectile is given an initial velocity vo at an angle f above the horizontal. The velocity of the projectile when it hits the slope is ____________ the initial velocity vo. (the horizontal is θ above the x-axis from the origin [/] ) A) less than B) equal to C) greater than D) None of the above.
A) less than
The power supplied by a machine will always be _________ the power supplied to the machine. A) less than B) equal to C) greater than D) A or B
A) less than
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.
A) nonimpulsive.
If the motion of one particle is dependent on that of another particle, each coordinate axis system for the particles _______ A) should be directed along the path of motion. B) can be directed anywhere. C) should have the same origin. D) None of the above.
A) should be directed along the path of motion.
In curvilinear motion, the direction of the instantaneous acceleration is always A) tangent to the hodograph. B) perpendicular to the hodograph. C) tangent to the path. D)perpendicular to the path.
A) tangent to the hodograph.
The velocity of B relative to A is defined as A) vB - vA B) vA - vB C) vB + vA D) vA + vB
A) vB - vA
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
A) velocity
If a rigid body is rotating with a constant angular velocity about a fixed axis, the velocity vector at point P is _______. A) w x rp B) r x w C)dr/dt D) All of the above.
A) w x rp (should be w x r, not r x w)
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.
A) x direction.
The radial component of velocity of a particle moving in a circular path is always A) zero. B) constant. C) greater than its transverse component. D) less than its transverse component.
A) zero.
. 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 w^2. C) (1/2) IG w^2. D) IG w^2.
B) (1/2) m (vG)^2 + (1/2) IG w^2.
Determine the velocity of plane A with respect to plane B. Plane A is traveling at 600 km/h at an angle of 30 degrees clockwise from the negative x-axis. Plane B is moving towards plane A at 700 km/h along the negative axis. A) (400 i + 520 j ) km/hr B) (1220 i - 300 j ) km/hr C) (-181 i - 300 j ) km/hr D) (-1220 i + 300 j ) km/hr
B) (1220 i - 300 j ) km/hr
The time of flight of a projectile, fired over level ground, with initial velocity Vo at angle θ, is equal to? A) (vo sin θ)/g B) (2vo sin θ)/g C) (vo cos θ)/g D) (2vo cos θ)/g
B) (2vo sin θ)/g
Determine the velocity vector of block A when block B is moving downward with a speed of 10 m/s. A) (8i + 6j) m/s B) (4i + 3j) m/s C) (-8i - 6j) m/s D) (3i + 4j) m/s
B) (4i + 3j) m/s
The position of a particle is given as r = (4t^2 i - 2x j) m. Determine the particle's acceleration. A) (4 i +8 j ) m/s2 B) (8 i -16 j ) m/s2 C) (8 i ) m/s2 D) (8 j ) m/s2
B) (8 i -16 j ) m/s2
Jet engines on the 100 Mg VTOL aircraft exert a constant vertical force of 981 kN as it hovers. Determine the net impulse on the aircraft over t = 10 s. A) -981 kN·s B) 0 kN·s C) 981 kN·s D) 9810 kN·s
B) 0 kN·s (impulse of thrust - impulse of weight)
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
B) 0 lb · ft
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
B) 10 kg·m/s
A particle is moving with an initial velocity of v = 12 ft/s and constant acceleration of 3.78 ft/s2 in the same direction as the velocity. Determine the distance the particle has traveled when the velocity reaches 30 ft/s. A) 50 ft B) 100 ft C)150 ft D)200 ft
B) 100 ft
A 100 lb cabinet is placed on a smooth surface. If a force of a 100 lb is applied for 2 s, determine the net impulse on the cabinet during this time interval. A) 0 lb·s B) 100 lb·s C)200 lb·s D)300 lb·s
B) 100 lb·s (impulse of F - impulse of W sin30)
Graph shows a t-a graph, linearlly: at t=0, a = 10 m/s^2 and at t = 20 s, a = 0 m/s^2 If a particle starts from rest and accelerates according to the graph shown, the particle's velocity at t = 20 s is_______. At what time does the particle stop moving? A) 200 m/s B) 100 m/s C) 0 D) 20 m/s A) 10 s B) 20 s C) 30 s D) 40 s
B) 100 m/s D) 40 s
1.For the path defined by r = θ^2 , the angle ψ at θ = 0.5 rad is A) 10º B) 14º C) 26º D) 75º
B) 14º
The position, s, is given as a function of angular position, θ, as s = 10 sin 2θ. The velocity, v, is A) 20 (a) sin (2θ) B) 20 a cos(2θ) - 40 w^2 sin(2θ) C) 20 a (cos 2θ) D) 20 a (sin 2θ)
B) 20 a cos(2θ) - 40 w^2 sin(2θ)
A motor pulls a 10 lb block up a smooth incline (of 30 degrees) 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
B) 20 ft·lb/s
v-t graph: linear graph, 0-0 --> t=6s, v=75 m/s If a car has the velocity curve described above, determine the time t necessary for the car to travel 100 meters. A) 8 s B) 4 s C) 10 s D) 6 s
B) 4 s
If a particle moving in a circular path of radius 5 m has a velocity function v = 4t^2 m/s, what is the magnitude of its total acceleration at t = 1 s? A) 8 m/s B) 8.6 m/s C) 3.2 m/s D) 11.2 m/s
B) 8.6 m/s
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
B) Conservation of angular momentum (Conservation of angular momentum about the vertical axis)
Which parameter is not involved in the linear impulse and momentum equation? A) Velocity B) Displacement C)Time D) Force
B) Displacement
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 which of the following? A) IG (a) B) IO (a) C) m aG D) m aO
B) IO (a)
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
B) One (an argument of scale can be applied to drop the ball due to its much smaller weight/ momentum)
In case (b), 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
B) T < 40 N
. In dynamics, the friction force acting on a moving object is always ________ A) in the direction of its motion. B) a kinetic friction. C) a static friction. D) zero.
B) a kinetic friction.
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
B) a positive quantity
The equation of motion for a system of n-particles can be written as ΣFi = Σ 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.
B) acceleration of the center of mass of the system
The slope of a v-t graph at any instant represents instantaneous A) velocity. B) acceleration. C) position. D) jerk.
B) acceleration.
When particles are interconnected by a cable, the motions of the particles are ______ A) always independent. B) always dependent. C) not always dependent. D) None of the above.
B) always dependent
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
B) always perpendicular
. The potential energy of a spring is ________ A) always negative. B) always positive. C) positive or negative. D) equal to ks.
B) always positive.
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
B) are always the same
The "normal" component of the equation of motion is written as ΣFn=man, where ΣFn is referred to as the _______. A) impulse B) centripetal force C) tangential force D) inertia force
B) centripetal force
The directions of the tangential acceleration and velocity are always A) perpendicular to each other. B) collinear. C) in the same direction. D) in opposite directions.
B) collinear.
The horizontal component of velocity remains _________ during a free-flight motion. A) zero B) constant C) at 9.81 m/s^2 D) at 32.2 ft/s^2
B) constant
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. (D merely means that e is less than 1.0)
B) e = 0.0
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!
B) easier
Internal forces are not included in an equation of motion analysis because the internal forces are_____ A) equal to zero. B) equal and opposite and do not affect the calculations. C) negligibly small. D) not important.
B) equal and opposite and do not affect the calculations.
A particle strikes the smooth surface with a velocity of 30 m/s. at an angle 30 degrees counterclockwise from the positive y-axis. 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
B) equal to (vx) 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
B) equation of motion
The magnitude of the normal acceleration is A) proportional to radius of curvature. B) inversely proportional to radius of curvature. C) sometimes negative. D) zero when velocity is constant.
B) inversely proportional to radius of curvature.
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
B) left, right
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.
B) linear momentum of the particle
The mass moment of inertia of a thin ring of mass m and radius R about the z axis is ___________ . A) (1/2) m R^2 B) m R^2 C) (1/4) m R^2 D) 2 m R^2
B) m R^2
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
B) minimum
If r' is zero for a particle, the particle is A) not moving. B) moving in a circular path. C) moving on a straight line. D) moving with constant velocity.
B) moving in a circular path
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.
B) oblique impact.
In dynamics, a particle is assumed to have: A) both translation and rotational motions B) only a mass C) a mass but the size and shape cannot be neglected D) no mass or size or shape, it is just a point
B) only a mass
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
B) r × (m v)
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.
B) represents the rate of change in the magnitude of the velocity.
The ratio of the restitution impulse to the deformation impulse is called _________ A) impulse ratio. B) restitution coefficient. C) energy ratio. D) mechanical efficiency
B) restitution coefficient.
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) sqrt (g/3L ) B) sqrt (3g/L) C) sqrt (12g/L) D) sqrt (g/L)
B) sqrt (3g/L)
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.
B) sum to zero.
2. When the forces acting on a particle are resolved into cylindrical components, friction forces always act in the __________ direction. A) radial B) tangential C) transverse D) None of the above.
B) tangential
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
B) the center of mass
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
B) the forces act in equal but opposite collinear pairs
The normal component of acceleration represents A) the time rate of change in the magnitude of the velocity. B) the time rate of change in the direction of the velocity. C) magnitude of the velocity. D)direction of the total acceleration.
B) the time rate of change in the direction of the velocity.
Since two-dimensional vector addition forms a triangle, there can be at most _________ unknowns (either magnitudes and/or directions of the vectors). A) one B) two C)three D)four
B) two
Which equation could be used to find the velocity of the center of the gear, C, if the velocity vA is known? A) vB = vA + wgear × rB/A B) vA = vC + wgear × rA/C C) vB = vC + wgear × rC/B D) vA = vC + wgear × rC/A
B) vA = vC + wgear × rA/C
Two blocks are interconnected by a cable with a pully between them. The blocks are on slopes of opposite direction. Which of the following is correct? A) (vx)A= - (vx)B B) vA= - vB C) (vy)A= - (vy)B D) All of the above.
B) vA= - vB
Kinetic energy results from _______. A) displacement B) velocity C) gravity D) friction
B) velocity
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.
C is the correct FBD
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.
C is the correct FBD
A disk is rotating at 4 rad/s. If it is subjected to a constant angular acceleration of 2 rad/s^2, determine the acceleration at B. A) (4 i + 32 j) ft/s^2 B) (4 i - 32 j) ft/s^2 C) (- 4 i + 32 j) ft/s^2 D) (- 4 i -32 j) ft/s^2
C) (- 4 i + 32 j) ft/s^2
A 10 lb particle has forces of F1= (3i + 5j) lb and F2= (-7i + 9j) lb acting on it. Determine the acceleration of the particle. A) (-0.4 i + 1.4 j) ft/s^2 B) (-4 i + 14 j) ft/s^2 C) (-12.9 i + 45 j) ft/s^2 D) (13 i + 4 j) ft/s^2
C) (-12.9 i + 45 j) ft/s^2
The mass moment of inertia of a rod of mass m and length L about a transverse axis located at its end is _________ . A) (1/12) m L^2 B) (1/6) m L^2 C) (1/3) m L^2 D) m L^2
C) (1/3) m L^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. V1 is moving in the negative x direction at 10 m/s. V2 is moving 20 m/s at a direction 60 degrees counterclockwise from the positive x direction. 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
C) (20 i +17.3 j) N
Determine the relative velocity of particle B with respect to particle A. Particle A is moving at 60 km/h at 30 degrees counter clockwise from the positive x-axis. Particle B is moving in the positive x direction at 100 km/h. A) (48i + 30j) km/h B) (- 48i + 30j ) km/h C) (48i - 30j ) km/h D) (- 48i- 30j) km/h
C) (48i - 30j ) km/h
A spring with an unstretched 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
C) -[0.5 k(3 in)2 - 0.5 k(1 in)2]
A 20 lb block is moving along a smooth surface. If the normal force on the surface at A is 10 lb, the velocity is ________. Ball moves up a curved hill, the change in vertical distance is 7 ft. A) 7.6 ft/s B) 9.6 ft/s C) 10.6 ft/s D) 12.6 ft/s
C) 10.6 ft/s
Determine the speed of block B when block A is moving down at 6 ft/s while block C is moving down at 18 ft/s . A) 24 ft/s B) 3 ft/s C) 12 ft/s D) 9 ft/s
C) 12 ft/s
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. The cord is 10 m long. A) 1596 N B) 1796 N C) 1996 N D) 2196 N
C) 1996 N
If s = 10 sin 2θ, the acceleration, a, is A) 20 cos (2θ) B) 20 sin(2θ) C) 20 w (cos 2θ) D) 20 w (sin 2θ)
C) 20 w (cos 2θ
In a projectile motion problem, what is the maximum number of unknowns that can be solved? A) 1 B) 2 C) 3 D) 4
C) 3
A slender 100 kg beam is suspended by a cable. The moment equation about point A is? A) 3(10) = 1/12(100)(4^2) a B) 3(10) = 1/3(100)(4^2) a C) 3(10) = 1/12(100)(4^2) a + (100 aGx)(2) D) None of the above
C) 3(10) = 1/12(100)(4^2) a + (100 aGx)(2)
If the position of a particle is defined by r = [(1.5t^2 + 1) i + (4t - 1) j ] (m), its speed at t = 1 s is ________. A) 2 m/s B) 3 m/s C) 5 m/s D) 7 m/s
C) 5 m/s
Determine the tension in the cable when the 400 kg box is moving upward with a 4 m/s^2 acceleration. A) 2265 N B) 3365 N C) 5524 N D) 6543 N
C) 5524 N
A car is traveling on a level road at 88 ft/s. The power being supplied to the wheels is 52,800 ft·lb/s. Find the combined friction force on the tires. A) 8.82 lb B) 400 lb C) 600 lb D)4.64 x 106lb
C) 600 lb
If the velocity at A is zero, then determine the angular velocity, w. A) 30 rad/s B) 0 rad/s C) 7.5 rad/s D) 15 rad/s
C) 7.5 rad/s
1. The downward acceleration of an object in free-flight motion is A) zero. B) increasing with time. C) 9.81 m/s^2. D) 9.81 ft/s^2.
C) 9.81 m/s^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
C) Answer A + Answer B
2.If needing to solve a problem involving the pilot's weight at Point C, select the approach that would be best. On the circle, point C is where '9' is on the clock. A) Equations of Motion: Cylindrical Coordinates B) Equations of Motion: Normal & Tangential Coordinates C) Equations of Motion: Polar Coordinates D) No real difference - all are bad. E) Toss up between B and C.
C) Equations of Motion: Polar Coordinates
If the mass of body A and B are equal but kA = 2kB, then ____________. A) IA = (2)IB B) IA = (1/2)IB C) IA = (4)IB D) IA = (1/4)IB
C) IA = (4)IB
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) Point C.
How many independent scalar equations of motion can be applied to box A? A) One B) Two C) Three D)Four
C) Three
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 cable connected to block B extends over a pully, down to another pull, back up and over another pully adjacent to the first one, and then to a wall. Block B weighs 2 kg, and A weighs 2 kg. A) One B) Two C) Three D) Four
C) Three (Work & Energy, length of cord equation, velocity of blocks equation)
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
C) Two (The impact on the top of the rod and the reaction at the end in the hard rock. This assumes the weight of the rod itself is small in comparision to the other two forces.)
What is the work done by the force F? A) F s B) -F s C) Zero D) None of the above.
C) Zero
Select the equation that best represents the "no-slip" assumption. A) Ff = μs N B) Ff = μk N C) aG = r a D) None of the above
C) aG = r a
Recall that the work of a spring is U(1-2) = -½ k(s2^2 - s1^2) and can be either -positive or negative. The potential energy of a spring is V = ½ ks^2. Its value is __________ A) always negative. B) either positive or negative. C) always positive. D) an imaginary number!
C) always positive.
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
C) angular acceleration
In a polar coordinate system, the velocity vector can be written as v = (v_r)(u_r) + (v_θ)(u_θ) = (r')(u_r) + (rθ')(u_q) The term θ' is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration
C) angular velocity.
If a disk rolls on a rough surface without slipping, the acceleration of the center of gravity (G) will _________ and the friction force will be __________. A) not be equal to (a)r; less than μsN B) be equal to (a) r; equal to μkN C) be equal to (a) r; less than μsN D)None of the above
C) be equal to (a) r; less than μsN
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.
C) both linear momentum and angular momentum are conserved.
If a particle is connected to a spring, the elastic spring force is expressed by F = ks . The "s" in this equation is the A) spring constant. B) un-deformed length of the spring. C) difference between deformed length and un-deformed length. D)deformed length of the spring.
C) difference between deformed length and un-deformed length.
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
C) directed from G toward the center of rotation
Newton's second law can be written in mathematical form as ΣF = ma. Within the summation of forces, ΣF, ________ are(is) not included. A) external forces B) weight C) internal forces D) All of the above.
C) internal forces
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 (pi/2) B) m g L C) m g (L/2) D) -m g (L/2)
C) m g (L/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.
C) non-impulsive force (it is non-impulsive since the weight of the tennis ball will have a negligible effect on the change in momentum)
The average speed is defined as __________. A) Dr/Dt B) Ds/Dt C) sT/Dt D) None of the above.
C) sT/Dt (total distance/change in time)
A body subjected to general plane motion undergoes a/an A) translation. B) rotation. C) simultaneous translation and rotation. D) out-of-plane movement.
C) simultaneous translation and rotation.
1.The normal force which the path exerts on a particle is always perpendicular to the _________ A) radial line. B) transverse direction. C) tangent to the path. D) None of the above.
C) tangent to the path.
In curvilinear motion, the direction of the instantaneous velocity is always A) tangent to the hodograph. B) perpendicular to the hodograph. C) tangent to the path. D)perpendicular to the path.
C) tangent to the path.
When the velocities of two points on a body are equal in magnitude and parallel but in opposite directions, the IC is located at A) infinity. B) one of the two points. C) the midpoint of the line connecting the two points. D) None of the above.
C) the midpoint of the line connecting the two points.
The kinetic energy of a rigid body consists of the kinetic energy due to ___________. A) only translational motion B) only rotational motion C) translational motion and rotational motion D) the deformation of the body
C) translational motion and rotational motion
Displacement of a particle over a given time interval equals the area under the ___ graph during that time. A) a-t B) a-s C) v-t C) s-t
C) v-t
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.
C) z direction.
If a rigid body rotates about its center of gravity, its translational kinetic energy is ___________ at all times. A) constant B) equal to its rotational kinetic energy C) zero D)Cannot be determined
C) zero
If a particle moves along a curve with a constant speed, then its tangential component of acceleration is A) positive. B) negative. C) zero. D) constant.
C) zero.
At the instant shown, the spring is undeformed. Determine the change in potential energy if the 20 kg disk (kG = 0.5 m) rolls 2 revolutions without slipping. A spring is along an incline at 30 degrees, attached to the end of the spring is a disk with a radius of 0.3 m. The disk travels at 3 m/s down the incline. A) ½(200)(1.2pi)^2 + (20)9.81(1.2pi sin 30°) B) - ½(200) (1.2pi)^2 - (20)9.81(1.2pi sin 30°) C) ½(200)(1.2pi)^2 - (20)9.81(1.2pi sin 30°) D) ½(200)(1.2pi)^2
C) ½(200)(1.2pi)^2 - (20)9.81(1.2pi sin 30°)
If a particle moves in a circular path with constant velocity, its radial acceleration is A) zero B) r '' C) − rθ' ^2. D) 2r'θ'
C) − rθ' ^2.
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.
C)+10 ft·lb.
A particle traveling in a circular path of radius 300 m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4 m/s^2. What is the magnitude of its total acceleration at this instant? A) 3 m/s^2 B) 4 m/s^2 C) 5 m/s^2 D) -5 m/s^2
C)5 m/s^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 10 C) (1000 lb)(260 ft/s) cos 10 D) (2000 lb)(260 ft/s)
D) (2000 lb)(260 ft/s)
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
D) - 0.0781 N · m
If vA=10 m/s and aA=10 m/s, determine the angular acceleration, a, when θ = 30°. A) 0 rad/s^2 B) -50.2 rad/s^2 C) -112 rad/s^2 D) -183 rad/s^2
D) -183 rad/s^2
A particle has an initial velocity of 30 ft/s to the left. If it then passes through the same location 5 seconds later with a velocity of 50 ft/s to the right, the average velocity of the particle during the 5 s time interval is _______. A) 10 ft/s to the right B) 40 ft/s to the right C) 16 m/s to the right D) 0 ft/s
D) 0 ft/
A particle moves along a horizontal path with its velocity varying with time as listed below. The average acceleration of the particle is _________. At t=2s the particle is moving 3 m/s to the right, at t=7s the particle is moving 5 m/s to the left. A) 0.4 m/s2 to the right B) 0.4 m/s2 to the left C)1.6 m/s2® to the right D)1.6 m/s2 to the left
D) 1.6 m/s2 to the left. (-5-3)/(7-2) = -8/5
If the disk is moving with a velocity at point O (center point) of 15 ft/s and w = 2 rad/s, determine the velocity at A. radius of the circle is 2 ft. Point A is where the disk makes contact with the ground. A) 0 ft/s B) 4 ft/s C) 15 ft/s D) 11 ft/s
D) 11 ft/s
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
D) 116 ft/s2 (Answer B is tangential acc. & C is the normal acc.)
If r = θ^2 and θ = 2t, find the magnitude of r ̇ and θ ̈ when t = 2 seconds. A) 4 cm/sec, 2 rad/sec^2 B) 4 cm/sec, 0 rad/sec^2 C) 8 cm/sec, 16 rad/sec^2 D) 16 cm/sec, 0 rad/sec^2
D) 16 cm/sec, 0 rad/sec^2
The path of a particle is defined by y = 0.5x2. If the component of its velocity along the x-axis at x = 2 m is vx = 1 m/s, its velocity component along the y-axis at this position is ____. A) 0.25 m/s B) 0.5 m/s C) 1 m/s D) 2 m/s
D) 2 m/s
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 to the right B) 7 m/s to the left C) 7 m/s to the right D) 2 m/s to the left
D) 2 m/s to the left
If theta equals 90° and A and B start moving from the same point, what is the magnitude of rB/A at t = 5 s? A is moving in the positive x-direction at 3 ft/s B is moving at 4m/s at angle theta, counterclockwise from the positive x axis. A) 20 ft B) 15 ft C) 18 ft D) 25 ft
D) 25 ft
The wheel shown has a radius of 15 in and rotates clockwise at a rate of w = 3 rad/s. What is vB? A) 5 in/s B) 15 in/s C) 0 in/s D) 45 in/s
D) 45 in/s
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
D) 75 m/s
If the cable has a tension of 3 N, determine the acceleration of block B. Block A, 10 kg, is on a level surface moving in the positive x direction, at the corner of the level plane there is a pully. The cable attached to block A, extends over the pully down to a second pully and back up to a fixed end on a 'ceiling'. on the second pully, hangs block b which weighs 4 kg. the coefficient of friction is o.4 A) 4.26 m/s^2 up B) 4.26 m/s^2 down C) 8.31 m/s^2 up D) 8.31 m/s^2 down
D) 8.31 m/s^2 down
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.
D) All of the above.
The radial component of acceleration of a particle moving in a circular path is always A) negative. B) directed toward the center of the path. C) perpendicular to the transverse component of acceleration. D) All of the above.
D) All of the above.
. A 10 kg sack slides down a smooth surface. If the normal force at the flat spot on the surface, A, is 98.1 N (UP) , the radius of curvature is ____. A) 0.2 m B) 0.4 m C) 1.0 m D) None of the above.
D) None of the above
When the direction of velocities of two points on a body are perpendicular to each other, the IC is located at A) infinity. B) one of the two points. C) the midpoint of the line connecting the two points. D) None of the above.
D) None of the above.
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)
D) Point D (bottom of the loop)
As the linkage rotates, box A undergoes ___________. A) general plane motion B) pure rotation C) linear translation D) curvilinear translation
D) curvilinear translation
A Frisbee is thrown and curves to the right. It is experiencing A) rectilinear translation. B) curvilinear translation. C) pure rotation. D) general plane motion.
D) general plane motion.
The speed of a particle in a cylindrical coordinate system is A) r' B) rθ' C) sqrt [(rθ')^2 + (r')^2 ] D) sqrt [(rθ')^2 + (r')^2 + (z')^2]
D) sqrt [(rθ')^2 + (r')^2 + (z')^2]
A particle has an initial velocity vo at angle Φ with respect to the horizontal. The maximum height it can reach is when A) Φ = 30° B) Φ = 45° C) Φ = 60° D) Φ = 90°
D) Φ = 90°
If a rigid bar of length l (above) is released from rest in the horizontal position (θ = 0), the magnitude of its angular acceleration is at maximum when A) θ = 0 B) θ = 90° C) θ = 180° D) θ = 0° and 180°
D) θ = 0° and 180° ( angular accel = [mg (l/2) cos (θ) over [I_G] )
In the relative velocity equation, vB/A is A) the relative velocity of B with respect to A. B) due to the rotational motion. C) w × rB/A . D)All of the above.
D)All of the above.
The formula definition of power is ___________. A) dU / dt B) F · v C)F·dr/dt D)All of the above.
D)All of the above.
A 10 lb block is initially moving down a ramp with a velocity of v. The force F is applied to bring the block to rest. Select the correct FBD.
Forces include: - 10 lb in the negative y direction - normal force in the perpendicular direction of the surface of the incline (i.e. into the block) - frictional force along the incline, in the opposite direction of the block's motion. - force F in whichever direction it is applied in.
The block (mass = m) is moving upward with a speed v. Draw the FBD if the kinetic friction coefficient is mk.
Forces include: - mg in the negative y direction - normal force in the perpendicular direction of the surface of the incline (i.e. into the block) - frictional force along the incline, in the opposite direction of the blocks motion.
Packaging for oranges is tested using a machine that exerts ay = 20 m/s^2 and ax = 3 m/s^2, simultaneously. Select the correct FBD and kinetic diagram for this condition.
Forces on the package: FBD: - W in the negative y direction - Rx in the positive x direction - Ry in the positive y direction Kinetic Diagram: - m(ax) in the positive x direction - m(ay) in the positive y direction.
A velocity-time graph shows a constant positive velocity for x time, then a linearly decreasing velocity until v=0. What does the a-t graph look like for the velocity curve described above?
constant acceleration of 0 for x seconds, and then a jump to a constant negative acceleration for the remaining time. : 0 I-----_____
If a particle is moved from 1 to 2, the work done on the particle by the force, FR will be: Particle is moving along a curved path from s1 to s2. There is a normal and tangential force acting on the particle which create the resulting force FR.
∫_(s_1)^(s_2)〖ΣF_t 〗 ds (sorry idk how else to input the answer)
