Dynamics Concepts

(b) No. Conservation of momentum is satisfied, but the coefficient of restitution equation is not. The coefficient of restitution must be less than 1. (13.4)

A 5 kg ball A strikes a 1 kg ball B that is initially at rest. Is it possible that after the impact A is not moving and B has a speed of 5v? (a) Yes (b) No Explain your answer.

(c) The time required for the bus to travel from A to B is 2 h and from B to C is 100/70 = 1.43 h, so the total time is 3.43 h and the average speed is 200/3.43 = 58 mph. (11.1)

A bus travels the 100 miles between A and B at 50 mi/h and then another 100 miles between B and C at 70 mi/h. The average speed of the bus for the entire 200-mile trip is: a. More than 60 mi/h. b. Equal to 60 mi/h. c. Less than 60 mi/h.

(d) Polar coordinates are most natural for this problem, that is, 2 a = ( r − rθ )er + (rθ + 2r θ)eθ F r o m t h e i n f o r m a t i o n g i v e n , w e k n o w r = 0 , θ = 0 , r = 0 , θ = ω , r = - u . W h e n w e s u b s t i t u t e these values into (1), we will only have a term in the −θ direction. (11.5)

A child walks across merry-go-round A with a constant speed u relative to A. The merry-go-round undergoes fixed axis rotation about its center with a constant angular velocity ω counterclockwise.When the child is at the center of A, as shown, what is the direction of his acceleration when viewed from above. (a) (b) (c) (d) (e) The acceleration is zero.

The ω2r term will be in the negative x-direction and the Coriolis acceleration will be in the negative y-direction. (15.5)

A person walks radially inward on a platform that is rotating counterclockwise about its center. Knowing that the platform has a constant angular velocity v and the person walks with a constant speed u relative to the platform, what is the direction of the acceleration of the person at the instant shown? a. Negative x b. Negative y c. Negative x and positive y d. Positive x and positive y e. Negative x and negative y

(e) (15.3)

Bar BDE is pinned to two links, AB and CD. At the instant shown the angular velocities of link AB, link CD and bar BDE are ωAB, ωCD, and ωBDE, respectively. Which of the following statements concerning the angular speeds of the three objects is true at this instant? (a) ωAB = ωCD = ωBDE (b) ωBDE>ωAB>ωCD (c) ωAB = ωCD > ωBDE (d ) ωAB > ωCD > ωBDE (e) ωCD>ωAB>ωBDE

(b) If you draw a FBD of B, you will see that since it is accelerating downward, the tension in the cable will be less than 40 lb, so the acceleration of A will be less than the acceleration of C. Also, the system on the left has more inertia, so it is harder to accelerate than the system on the right. (12.1)

The two systems shown start from rest. On the left, two 40 lb weights are connected by an inextensible cord, and on the right, a constant 40 lb force pulls on the cord. Neglecting all frictional forces, which of the following statements is true? (a) (b) (c) (d ) (e) Blocks A and C will have the same acceleration Block C will have a larger acceleration than block A Block A will have a larger acceleration than block C Block A will not move None of the above

(a) (15.2)

Three uniform rods, ABC, DCE and FGH are connected as shown. Which of the following statements are true? (a) (b) (c) (d ) (e) ωABC = ωDCE = ωFGH ωDCE > ωABC > ωFGH ωDCE < ωABC < ωFGH ωABC > ωDCE > ωFGH ωFGH = ωDCE < ωABC

a. P1 b. P2 c. P3 d. P4 e. It is the same about all the points.

A 1-m-long uniform slender bar AB has an angular velocity of 12 rad/s and its center of gravity has a velocity of 2 m/s as shown. About which point is the angular momentum of A smallest at this instant?

a. Solid sphere b. Solid cylinder c. Hoop d. They will all travel the same distance. (17.1)

A round object of mass m and radius r is released from rest at the top of a curved surface and rolls without slipping until it leaves the surface with a horizontal velocity as shown. Will a solid sphere, a solid cylinder, or a hoop travel the greatest distance x? a. Solid sphere

(b) (15.1)

Knowing that wheel A rotates with a constant angular velocity and that no slipping occurs between ring C and wheel A and wheel B, which of the following statements concerning the angular speeds are true? (a) ωa = ωb (b) ωa > ωb (c) ωa < ωb (d ) ωa = ωc (e) the contact points between A and C have the same acceleration

(c) The tension will be greater than 1200 lb and the normal force will be greater than 1000 lb. (12.1)

A 1000 lb boulder B is resting on a 200 lb platform A when truck C accelerates to the left with a constant acceleration. Which of the following statements are true (more than one may be true)? (a) (b) (c) (d ) (e) ( f ) The tension in the cord connected to the truck is 200 lb The tension in the cord connected to the truck is 1200 lb The tension in the cord connected to the truck is greater than 1200 lb The normal force between A and B is 1000 lb The normal force between A and B is 1200 lb None of the above

Case 1: (a) Case 2: (a) Case 3: (b)

A cord is attached to a spool when a force P is applied to the cord as shown. Assuming the spool rolls without slipping, what direction does the spool move for each case? Case 1: Case 2: Case 3: (a) left (a) left (a) left (b) right (b) right (b) right (c) It would not move. (c) It would not move. (c) It would not move. * pictures*

(d) This is Newton's 3rd Law. (13.3)

A large insect impacts the front windshield of a sports car traveling down a road. Which of the following statements is true during the collision? (a) Thecarexertsagreaterforceontheinsectthantheinsectexertsonthecar. (b) Theinsectexertsagreaterforceonthecarthanthecarexertsontheinsect. (c) Thecarexertsaforceontheinsect,buttheinsectdoesnotexertaforceonthecar. (d) The car exerts the same force on the insect as the insect exerts on the car. (e) Neitherexertsaforceontheother;theinsectgetssmashedsimplybecauseitgetsinthewayofthecar.

(a) The tangential acceleration is zero since the speed is constant, so there will only be normal acceleration. The normal acceleration will be maximum where the radius of curvature is a minimum, that is at Point A. (11.5)

A racecar travels around the track shown at a constant speed. At which point will the racecar have the largest acceleration? (a) A (b) B (c) C (d) Theaccelerationwillbezeroatallthepoints

(C) The tangential acceleration will be zero since the tires do not slip, but there will be an acceleration component perpendicular to the ground. (!5.4)

A rear wheel drive car starts from rest and accelerates to the left so that the tires do not slip on the road. What is the direction of the acceleration of the point on the tire in contact with the road, that is, Point A? (a)<-- (b) <\ (c)^| (d)|v (e)v/

(a) (15.1)

A rectangular plate swings from arms of equal length as shown below. What is the magnitude of the angular velocity of the plate? (a) 0 rad/s (b) 1 rad/s (c) 2rad/s (d ) 3 rad/s (e) Need to know the location of the center of gravity

a. 0.25v b. 0.5v c. v d. 2v e. 4v (17.1)

A solid steel sphere A of radius r and mass m is released from rest and rolls without slipping down an incline as shown. After travel- ing a distance d, the sphere has a speed v. If a solid steel sphere of radius 2r is released from rest on the same incline, what will its speed be after rolling a distance d?

(b) (12.3)

A uniform crate C with mass mC is being transported to the left by a forklift with a constant speed v1. What is the magnitude of the angular momentum of the crate about Point A, that is, the point of contact between the front tire of the forklift and the ground? (a) 0 (b) mv1d (c) 3mv1 (d) mv1 32 d2

(b) The angular momentum is the moment of the momentum, so simply take the linear momentum, mv1, and multiply it by the perpendicular distance from the line of action of mv1 and Point D. (12.3)

A uniform crate C with mass mC is being transported to the left by a forklift with a constant speed v1. What is the magnitude of the angular momentum of the crate about Point D, that is, the upper left corner of the crate? (a) 0 (b) mv1a (c) mv1b (d)mv a2+b2

(b) In order for A to not maintain contact with the track, the normal force must remain greater than zero, which requires a non-zero speed at the top of the loop. (13.3)

Block A is released from rest and slides down the frictionless ramp to the loop. The maximum height h of the loop is the same as the initial height of the block. Will A make it completely around the loop without losing contact with the track? (a) Yes (b) No (c) need more information

(e) (13.1)

Block A is traveling with a speed v0 on a smooth surface when the surface suddenly becomes rough with a coefficient of friction of μ causing the block to stop after a distance d. If block A were traveling twice as fast, that is, at a speed 2v0, how far will it travel on the rough surface before stopping? (a) d/2 (b) d (c) 2d (d) 2d (e) 4d

(d ) The particle will have velocity components along the tube and perpendicular to the tube. After it leaves, it will travel in a straight line. (12.1)

Marble A is placed in a hollow tube, and the tube is swung in a horizontal plane causing the marble to be thrown out. As viewed from the top, which of the following choices best describes the path of the marble after leaving the tube? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

(c) Draw a FBD and KD at each location and it will be clear that the maximum force will be experiences by the person at Point C. (12.1)

People sit on a Ferris wheel at Points A, B, C and D. The Ferris wheel travels at a constant angular velocity. At the instant shown, which person experiences the largest force from his or her chair (back and seat)? Assume you can neglect the size of the chairs, that is, the people are located the same distance from the axis of rotation. (a) A (b) B (c) C (d) D (e) The force is the same for all the passengers.

a. Case 1 will be larger. b. Case 2 will be larger. c. The speeds will be the same. (17.1 Q4)

Refer to Q3, how will the speeds of the centers of gravity com- pare for the two cases when θ 5 08?

a. Case 1 b. Case 2 c. The kinetic energy will be the same.

Slender bar A is rigidly connected to a massless rod BC in Case 1 and two massless cords in Case 2 as shown. The vertical thickness of bar A is negligible compared to L. In both cases A is released from rest at an angle θ 5 θ0. When θ 5 08, which system will have the larger kinetic energy?

a. Case 1 b. Case 2 c. The kinetic energy will be the same. (17.1 Q3)

Slender bar A is rigidly connected to a massless rod BC in Case 1 and two massless cords in Case 2 as shown. The vertical thickness of bar A is negligible compared to L. In both cases A is released from rest at an angle θ 5 θ0. When θ 5 08, which system will have the larger kinetic energy?

a. Case 1 b. Case 2 c. The kinetic energy will be the same. (17.1)

Slender bar A is rigidly connected to a massless rod BC in Case 1 and two massless cords in Case 2 as shown. The vertical thickness of bar A is not negligible compared to L. In both cases A is released from rest at an angle θ 5 θ0. When θ 5 08, which system will have the largest kinetic energy?

(b) The tangential acceleration is zero since the speed is constant, so there will only be normal acceleration pointed upwards. (11.5)

The Ferris wheel is rotating with a constant angular velocity ω. What is the direction of the acceleration of Point A? (a) (b) (c) (d) (e) The acceleration is zero.

(b) (15.2)

The ball rolls without slipping on the fixed surface as shown. What is the direction of the velocity of Point A? (a)--> (b) /^(c) |^(d)v (e)\v

(a) (15.3)

The disk rolls without sliding on the fixed horizontal surface. At the instant shown, the instantaneous center of zero velocity for rod AB would be located in which region? (a) region 1 (b) region 2 (c) region 3 (d) region4 (e) region 5 (f) region6

(c) In both cases the car will come to a complete stop, so the applied impulse will be the same (13.3)

The expected damages associated with two types of perfectly plastic collisions are to be compared. In the first case, two identical cars traveling at the same speed impact each other head on. In the second case, the car impacts a massive concrete wall. In which case would you expect the car to be more damaged? (a) Case 1 (b) Case 2 (c) The same damage in each case

(a) Since B has an acceleration component downward the normal force between A and the ground will be less than the sum of the weights. (12.1)

The system shown is released from rest in the position shown. Neglecting friction, the normal force between block A and the ground is (a) less than the weight of A plus the weight of B (b) equal to the weight of A plus the weight of B (c) greater than the weight of A plus the weight of B

The speed is the slope of the curve, so answer c) is true. The acceleration is the second derivative of the position. Since A's position increases linearly the second derivative will always be zero. The second derivative of curve B is zero at the pont of inflection which occurs between t1 and t2. (11.1)

Two cars A and B race each other down a straight road. The position of each car as a function of time is shown. Which of the following statements are true (more than one answer can be correct)? (a) At time t2 both cars have traveled the same distance (b) At time t1 both cars have the same speed (c) Bothcarshavethesamespeedatsometimet<t1 (d) Both cars have the same acceleration at some time t < t1 (e) Both cars have the same acceleration at some timet1 <t<t2

(a) (16.1)

Two pendulums, A and B, with the masses and lengths shown are released from rest. Which system has a larger angular acceleration immediately after release? (a) A (b) B (c) They are the same.

(b) (16.1

Two pendulums, A and B, with the masses and lengths shown are released from rest. Which system has a larger mass moment of inertia about its pivot point? (a) A (b) B (c) They are the same.

(c) (13.1)

Two small balls A and B with masses 2m and m respectively are released from rest at a height h above the ground. Neglecting air resistance, which of the following statements are true when the two balls hit the ground? (a) The kinetic energy of A is the same as the kinetic energy of B. (b) The kinetic energy of A is half the kinetic energy of B. (c) The kinetic energy of A is twice the kinetic energy of B. (d) The kinetic energy of A is four times the kinetic energy of B.

(c) Fr = Iα α= FR = F(2r) = Fr 1 mR2 1 m(2r)2 1 mr2 222 12 F =2F 12 F=2F mrmr (15.1)

Two solid cylinders, A and B, have the same mass m and the radii 2r and r respectively. Each is accelerated from rest with a force applied as shown. In order to impart identical angular accelerations to both cylinders, what is the relationship between F1 and F2? (a) F1 = 0.5F2 (b) F1=F2 (c) F1=2F2 (d) F1=4F2 (e) F1 = 8F2