Physics Homework for Exam #2

Assignment #9 Textbook Sections 4-1 to 4-4 Date Due: Tue. Jan. 28
Assignment #10 Textbook Section 4-6 Date Due: Wed. Jan. 29
Assignment #11 Textbook Section 4-7 Date Due: Fri. Jan. 31
Assignment #12 Textbook Sections 4-6 & 4-7 Date Due: Mon. Feb. 3
Assignment #13 Textbook Section 5-1 Date Due: Tue. Feb. 4
Assignment #14 Textbook Section 5-2 Date Due: Wed. Feb. 5
Assignment #15 Textbook Section 6-1 Date Due: Fri. Feb. 7
Assignment #16 Textbook Sections 6-1 & 6-2 Date Due: Mon. Feb. 10
Assignment #17 Textbook Sections 6-1 & 6-2 Date Due: Tue. Feb. 11
Assignment #18 Textbook Section 6-3 Date Due: Wed. Feb. 12


START for EXAM #2 CHAPTER 4
Assignment #9 Textbook Sections 4-1 to 4-4 Date Due: Tue. Jan. 28
9. Determine the magnitude of net force (i.e. the sum total of all the forces) on the following objects using Newton's second law:
(A) A freely falling 3.26 kg rock (neglect air resistance) that falls for 3.20 seconds.

(B) A 724 gram block that is accelerating at 5.10 m/s2 at an angle of 14.0o relative to horizontal.

(C) A 1.20 kg book that is sitting on a table which is 1.50 m high.

(D) A 211 kg ball that increases its speed by 4.85 cm/s every 3.22 seconds.

(E) A 0.540 kg rock moving at a constant speed of 16.3 m/s vertically upwards.

BONUS:
(G) A 2500 kg car, starting from rest, that reaches a speed of 34.5 m/s in 174 meters, uniformly.

Assignment #10 Textbook Section 4-6 Date Due: Wed. Jan. 29

10-1. A 1.60 kg {390 g} hanging bob is supported by two cords labeled A & B. Cord B makes an angle of 23.0o with the vertical to which it is attached (as shown) when a 5.70 N {1.40 N} force is applied to the bob from the right at an angle of 14.0o relative to the horizontal.
(A) Determine the tension in the two cords ?
Ans: {TA = .283 N, TB = 3.48 N}
Neton's First Law and Mechanical Equilibrium

10-2. A 1.60 kg {390 g} hanging bob is supported by one cord labeled A. The bob is pushed to the left by a horizontal force of 5.70 N that makes an angle of 32.0o with the horizontal.

(A) What is the maximum angle that cord A will reach relative to its initial vertical position when the bob is in equilibrium ? Ans:{21.1o}

(B) What is the tension in cord A at the maximum angle? Ans:{ TA = 3.30 N}


BONUS
10-3. A 1.60 kg {390 g} hanging bob is supported by two cords labeled A & B that have different lengths. The angle between the two cords is 80.0o while the angle between cord A and the ceiling is 68.0o as shown.

(A) Determine the tension in the two cords.
Ans: {TA = 3.29 N, TB = 1.45 N}

Assignment #11 Textbook Section 4-7 Date Due: Fri. Jan. 31
11-1. A 5.60 kg {8.80 kg} block rests on the frictionless, horizontal surface of a table top. The block is connected to a 2.10 kg {3.30 kg} pumpkin by a cord that runs over a frictionless, massless pulley. The block is pulled to the right by a horizontal rope with a tension Tr.
(A) In symbolic form, write down the equations that Newton’s 2nd Law produces for the block and for the pumpkin. Be sure to express the net force on each in terms of the forces acting on each. Also write down Newton’s 2nd Law for the system consisting of both the block and the pumpkin.

(B) If the block is pulled in such a way that it moves at a constant speed of 24.5 m/s to the right, what is the net force on the block and the net force on the hanging pumpkin ? Ans:{?}

(C) If the block is pulled in such a way that it moves at a constant speed of 24.5 m/s to the right, what is the tension in the cord Tc and the rope Tr ? Ans:{?}

(D) If the block is pulled in such a way that it accelerates at 2.80 m/s2 to the right, what is the net force on the block and the net force on the pumpkin ? Ans:{?}

(E) What are the tension in the cord Tc and the rope Tr when block accelerates at 2.80 m/s2 ?
Ans: { Tc = 41.6 N, Tr = 66.2 N}
BONUS:
11-2. If a force is applied to the rope in such a way that the tension in the rope is 81.0 N, what is the acceleration of the blocks and the tension in the cord Tc ? Ans:{?}

Assignment #12 Textbook Section 4-6 & 4-7 Date Due: Mon. Feb. 3
12. Two blocks rest on the slope of a frictionless incline plane that makes an angle of 22.0o {33.0o} with the horizon. A force Fapp is applied to block A, parallel to the incline plane. Block A has a mass of 650 g and block B has a mass of 860 g.
(A) With what force does gravity push block A down the incline plane ? Would the magnitude of this force change if the block were moving up or down the incline plane at a constant speed ? How about a constant acceleration ?
Ans: {3.47 N, ?, ?}
(B) Sketch the free-body diagram for each block and write down the equations generated by Newton’s 2nd Law in symbolic form for each block in terms of the forces acting on each block. Also write down Newton’s 2nd Law for the system consisting of both blocks.
(C) If the force Fapp is 15.2 N, what is the acceleration of block A?
Ans: {4.73 m/s2}
(D) If the force Fapp is 15.2 N, what is the force that block A exerts on block B ? (Hint: This force should appear in your Newton’s 2nd law equations for block A and B. If it doesn’t then you had better look at your equation in part B again.)
Ans: {?}
BONUS:
(E) If the force Fapp is 15.2 N, at what angle must the incline plane be tilted in order for the blocks to accelerate up the incline plane at 3.70 m/s2 {1.40 m/s2} ?
Ans: {62.2o}

HOMEWORK for CHAPTER 5

Assignment #13 Textbook Section 5-1 Date Due: Tue. Feb. 4
13. Two blocks ( mA = 24.0 kg, mB = 18.0 kg) are connected by a light cord that runs through a frictionless pulley. The connected blocks are pulled to the right by a horizontal force applied to a rope connected to block B. Block A rests on an surface inclined at an angle of 38.0o, while block B rests on a horizontal surface. The coefficient of kinetic friction between the blocks and the surface is .480 {.330}. As a result of the action of the applied force, the tension in the cord joining the two blocks is 270 N {390 N}.

(A) What is the force of friction acting on each block ?
Ans: { fA = 61.2 N, fB = 58.2 N}

(B) What is the acceleration of either block ?
Ans: { a = 7.67 m/s2}

(C) Is the size of the net force on block A the same as the net force on block B ? Calculate the net force on each.
Ans: { Fnet,A = 184 N, Fnet,B = 138 N}

(D) What is the magnitude of the applied force Fapp acting on block B that is accelerating the system ?
Ans: { Fapp = 586 N}

BONUS:
(E) If the applied force were removed, the motion of the two blocks would be to the left rather than the right since block A weighs more than block B. At what angle of the incline plane could the two blocks slide at a constant speed to the left ? Note that tension will no longer be the same, and you will not be able solve this problem using algebra alone, you will need to use your calculator.
Ans: {q = 31.6o}

The search for structure in the universe is more important than finding it.
JOSEPH SILK

Assignment #14 Textbook Section 5-2 Date Due: Wed. Feb. 5
14-1. A car starts from rest and travels along a circular track with a radius of 55.0 meters. The car starts out at a position due East of the center of the track, heading due North initially around the track, which is counterclockwise. The car increases its speed by 1.75 m/s {2.50 m/s} each second around the track. (Constant acceleration and centripetal acceleration)
(A) How long does it take for the car to travel 1/4 of the distance around the track?
Ans:{8.31 sec}

(B) How fast is the car traveling when it is 1/4 of the distance around the track ?
Ans:{20.8 m/s}

(C) What is the car’s acceleration towards the center of the track when it 1/4 of the way around the track ?
Ans:{7.85 m/s2}

(D) What is the magnitude and direction of the car’s acceleration when it is 1/4 of the way around the track ? Sketch your answer.
Ans:{8.24 m/s2 at -1080 relative to East}
BONUS:
(E) If the coefficient of static friction between the tires of the car and the roadway is .660, how long will it take (after the car starts) for the car to began slipping off the roadway ?


HOMEWORK for CHAPTER 6
Assignment #15 Textbook Section 6-1 Date Due: Fri. Feb. 7
15-1. A 13,600 N {15,400 N} barge is towed a distance of 4.33 km by a tow line tied to a team of horses on the bank. If the tension in the tow line is 8310 N {5600 N} and the toe line makes an angle of 18.0o with the bank, how much work is done on the barge by the horses ?
Ans: {W = 23.1 MJ}

15-2. What is the net work done on a 835 g {1.33 kg} toy car if its motor propels the car 12.5 m {2.44 m} across a level floor in 3.25 s starting from rest at a constant acceleration ?
Ans: {W = 1.50 J}

15-3. Neglecting friction, what is the maximum height a 33.3 kg trunk could be lifted using 4,560 J {2.03 kJ} of work ?
Ans: {h = 6.22 m}

15-4. How much work does it take to compress a spring by 220 mm if it takes a force of 300 N to compress the spring 480 mm { 11.0 cm} ?
Ans: {66.0 J}

Bonus:
15-5. You push a 1.60 kg physics book a distance of 1.50 m across a rough, horizontal surface that has a coefficient of kinetic friction of .440 {.550}. If you push with 28.0 N of horizontal force and the book costs $78.00, what is the total work done on the book?
Ans: {?}

A great many people think they are thinking when they are only rearranging their prejudices
WILLIAM JAMES


Assignment #16 Textbook Sections 6-1 & 6-2 Date Due: Mon. Feb. 10
16. Calculate the kinetic energy of each of the following:
(A) A 150 g rock moving at 25.3 km/hr {45.5 m/s} for 3.5 seconds.
Ans: {KE = 155 J}

(B) A car that weighs 33,320 N is accelerated from rest at 3.33 m/s2 {14.3 m/s2} for 1.58 seconds.
Ans: {KE = 868 kJ}

(C) A 23.0 kg object accelerated by a spring that is compressed horizontally by 4.30 cm {7.40 cm} and then released. The spring requires 1.60 kJ of energy to compress it 2.40 cm.
Ans: {KE = 15.2 kJ}

(D) A applied force does 1.57 MJ {3.33 MJ} of work on a 3400 kg car initially moving at 25.2 m/s.
Ans: {KE = 4.41 MJ}
BONUS:
(E) A 38.8 kg block is pushed 185 cm up a frictionless incline plane by a 560 N horizontal force. The incline plane is tilted at 34.0o {44.0o} relative to the horizon.
Ans:{KE = 257 J}


Assignment #17 Textbook Sections 6-1 & 6-2 Date Due: Tue. Feb. 11
17-1. A 2.40 kg {1.80 kg} block is pulled 620 cm up a plane inclined at 23.0o, by a rope with a constant tension of 23.0 N {18.0 N}. The coefficient of kinetic friction between the block and the plane is .460.
(A) How much work does the force of the rope, the force of friction, and the force of gravity do on the block ?
Ans: { WT = 112 J, Wf = -46.3 J, Wg = -42.7 J}

(B) What is the final speed of the block if it starts from rest ? Use the work energy theorem to find the final speed and not the equation Fnet = ma.
Ans: {5.01 m/s}
17-2. The work it takes to compress the end of a horizontal, non-linear spring from its uncompressed equilibrium position xo = 7.90 cm is equal to W = a (x - xo)4 {W = a(x2 - xo2)2} where a = 7.30x106 J/m4. The other end of the spring is fixed at the origin.
(A) Starting from the spring’s equilibrium position, determine the amount of work it will take to compress the spring 14.0 mm {1.50 cm}.
Ans: { W = 33.6 J}

(B) Determine an expression for the spring-force as a function of its displacement.
Ans: { F = -4 ax(x2 - xo2)}

BONUS:
(C) How far is the end of the spring from its equilibrium position when 120 J of work are done to stretch the spring ?
Ans: {2.25 cm}

Assignment #18 Textbook Section 6-3 Date Due: Wed. Feb. 12
18. A 26.0 kg {13.0 kg} crate is pulled up a rough incline tilted at 31.0o by a rope attached to a motor. When the power out put of the motor is 250 W {180 W} the crate moves up at a constant speed of 39.0 cm/s {47.0 cm/s}.
(A) What is the net work done on the crate when it has traveled for 7.50 seconds ?
(B) What is work done by the motor during 9.45 seconds of travel ?
Ans: { Wmotor = 1.70 kJ}
(C) With what force does the motor drag the crate up the incline ?
Ans: { Fmotor = 383 N}
(D) How much energy will be lost to friction when the crate has traveled for 5.30 seconds ?
Ans: {Loss = 791 J}
BONUS:
(E) If the crate moves onto a surface with a coefficient of kinetic friction equal to .666, what must be the power output of the motor now in order for the crate to maintain a constant speed of 5.10 m/s up the incline.
Ans: { Pmotor = 706 W}

After grading Assignment #18, I will place it (along with any old assignments you have not picked up) outside my office by Wednesday afternoon.


Exam #2 Friday February 14
Chapters 4, 5, & 6

Newton's Laws of Motion
2nd Law & Net Force
Contact Forces, Tension, & Weight
Incline Planes & Spring Force
Static Equilibrium
Work done by a Force
Kinetic Energy
Circular Motion