shay (des2767) - UT HW 08 - warren - (77402) This print-out should have 23 questions. Multiple-choice questions may continue on the next column or

shay (des2767) – UT HW 08 – warren – (77402) 1 This print-out should have 23 questions.

Multiple-choice questions may continue on the next column or page – nd all choices before answering. 001 10.0 points A ball falls straight down through the air under the in uence of gravity. There is a retarding force ~ F on the ball with magnitude given by F= b v , where vis the speed of the ball and bis a positive constant.

What is the magnitude of the acceleration of the ball at any time?

1. k~a k = g− b v m 2. k~a k = b v m 3. k~a k = g− b 4. k~a k = g b 5. k~a k = g+ b v m 002 10.0 points An ideal spring obeys Hooke’s law, ~ F =−k~x .

A mass of 0.50 kilogram hung vertically from this spring stretches the spring 0.075 meter.

The acceleration of gravity is 10 m /s2 .

The value of the force constant kfor the spring is most nearly 1. k= 33 N/m.

2. k= 6 .6 N/m.

3. k= 0 .33 N/m.

4. k= 0 .66 N/m.

5. k= 66 N/m.

003 10.0 points A block of mass 22 mcan move without fric- tion on a horizontal table. This block is at- tached to another block of mass 34 mby a cord that passes over a frictionless pulley, as shown. 22 m 34m If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?

1. k~a k = 11 30 g 2. k~a k = 2 9g 3. k~a k = 3 5g 4. k~a k = 4 7g 5. k~a k = 15 28 g 6. k~a k = 2 5g 7. k~a k = 14 23 g 8. k~a k = 11 18 g 9. k~a k = 17 28 g 10. k~a k = 13 14 g 004 (part 1 of 5) 10.0 points Two ob jects are connected by a string of neg- ligible mass. The 8 kg block is placed on a smooth table top 1 .76 m above the oor, and the 3 kg block hangs over the edge of the ta- ble. The 3 kg block is then released from rest at a distance of 0 .88 m above the oor at time t = 0. shay (des2767) – UT HW 08 – warren – (77402) 2 8 kg 3 kg 1.76 m 0 .88 m Determine the acceleration of the 3 kg block as it descends. The acceleration of gravity is 9 .8 m /s2 .

Answer in units of m /s2 005 (part 2 of 5) 10.0 points How long dies it take the 3 kg block to strike the oor?

Answer in units of s 006 (part 3 of 5) 10.0 points Describe the motion of the 8 kg block from the time t= 0 to the time when the 3 kg block strikes the oor.

1. It moves with a constant acceleration.

2. It moves with an increasing acceleration.

3. It stays still.

4. It moves with a constant speed.

5. It moves with a decreasing acceleration.

007 (part 4 of 5) 10.0 points Describe the motion of the 8 kg block from the time the 3 kg block strikes the oor to the time the 8 kg block leaves the table.

1. It moves with a constant acceleration.

2. It stays still.

3. It moves with an increasing acceleration.

4. It moves with a decreasing acceleration. 5.

It moves with a constant speed. 008 (part 5 of 5) 10.0 points Determine the distance between the landing points of the two blocks.

Answer in units of m 009 (part 1 of 2) 10.0 points Three ob jects can only move along a straight, level path. The graphs below show the po- sition dof each of the ob jects plotted as a function of time t. d t I d t II d t III The magnitude of the velocity k~v k of the ob ject increases in which of the cases?

1. I and II only 2. II only 3. III only 4. I only 5. II and III only 6. I and III only 7. I, II, and III 010 (part 2 of 2) 10.0 points The sum of the forces Fi on the ob ject is zero in which of the cases?

1. I, II, and III 2. II and III only 3. I only 4. I and III only 5. II only shay (des2767) – UT HW 08 – warren – (77402) 3 6. III only 7. I and II only 011 10.0 points Assume you are on a planet similar to Earth where the acceleration of gravity is approxi- mately 10 m /s2 . A block of mass 10 kg lies on an inclined plane, as shown. The horizon- tal and vertical supports for the plane have lengths of 8 m and 6 m, respectively, and the coe cient of kinetic friction between the plane and the block is 0 .5. 10 kg µ = 0 .5 F 8 m 6 m The magnitude of the force ~ F necessary to pull the block up the plane with constant speed is most nearly 1. k~ F k ≈ 122 2. k~ F k ≈ 152 3. k~ F k ≈ 210 4. k~ F k ≈ 332 5. k~ F k ≈ 138 6. k~ F k ≈ 100 N 7. k~ F k ≈ 190 8. k~ F k ≈ 86 9. k~ F k ≈ 118 10. k~ F k ≈ 184 012 10.0 points A ball initially moves horizontally with ve- locity ~v i, as shown. It is then struck by a stick. After leaving the stick, the ball moves vertically with a velocity ~v f, which has the same magnitude as ~v i. v i v f Which vector best represents the direction of the average force that the stick exerts on the ball?

1. 2. None of these graphs is correct.

9. 013 10.0 points If F 1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F 2 is the magnitude of the force exerted by the satellite on the Earth, then which of the following is true?

1. F 2 > F 1.

2. F 1 > F 2. shay (des2767) – UT HW 08 – warren – (77402) 4 3. F 1 = F 2.

4. F 2 ≫ F 1.

5. F 1 ≫ F 2. 014 10.0 points Pretend you are on a planet similar to Earth where the acceleration of gravity is approxi- mately 10 m /s2 .

The pulley is massless and frictionless. A massless inextensible string is attached to the masses. The ob jects are initially held at rest. 9 m 0 .2 m ω 66 kg 33 kg 66 kg If a third ob ject with a mass of 33 kg is hung on one of the 66 kg ob jects as shown and the ob jects are released, the magnitude of the acceleration ~aof the 33 kg ob ject is most nearly 1. k~a k ≈ 6 m/s 2 2. k~a k ≈ 3 m/s 2 3. k~a k ≈ 1 m/s 2 4. k~a k ≈ 10 m/s 2 5. k~a k ≈ 2 m/s 2 6. k~a k ≈ 8 m/s 2 7. k~a k ≈ 4 m/s 2 8.

k~a k ≈ 30 m/s 2 015 10.0 points A descending elevator of mass 780 kg is uni- formly decelerated to rest over a distance of 9 m by a cable in which the tension is 9916 N. The acceleration due to gravity is 9 .8 m /s2 . Cable 780 kg 9 m v = v i v = 0 Elevator Calculate the speed v i of the elevator at the beginning of the 9 m descent.

Answer in units of m /s 016 (part 1 of 2) 10.0 points A block of mass mis accelerated across a rough surface by a force of magnitude Fthat is exerted at an angle φwith the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. f F φ m What is the magnitude of the acceleration ~a of the block?

1. |~a |= F sin φ− m g m 2. |~a |= F −f m 3. |~a |= F cos φ− f m 4. |~a |= F cos φ m 5. |~a |= F m 017 (part 2 of 2) 10.0 points shay (des2767) – UT HW 08 – warren – (77402) 5 Which of the following expressions for the coe cient of friction is correct?

1. µ= m g f 2. µ= f m g 3. µ= f m g −Fsin φ 4. µ= f m g −Fcos φ 5. µ= m g −Fcos φ f 018 (part 1 of 6) 10.0 points Consider a massless, frictionless pulley at- tached to the ceiling. A massless, inextensible string is attached to the masses M aand M b, where M a> M b.

The tensions T x, T z, T y, and the gravitational constant gare magnitudes. ℓ R ω M a M b Tx T y Tz What is true about the tensions T x and T y?

1. T x > M ag and T y > M bg 2. T x > M ag and T y < M bg 3. T x > M ag and T y = M bg 4. T x < M ag and T y > M bg 5. T x = M ag and T y > M bg 6. T x = M ag and T y = M bg 7.

T x < M ag and T y < M bg 8. T x < M ag and T y = M bg 9. T x = M ag and T y < M bg 019 (part 2 of 6) 10.0 points What is the relationship between T x and T y?

1. T x = T y 2. T x > T y 3. T x < T y 020 (part 3 of 6) 10.0 points Which relationship about T z is true?

1. T z > M ag + M bg 2. T z < M ag + M bg 3. T z = M ag + M bg 021 (part 4 of 6) 10.0 points What is the relationship between the three tensions?

1. T x + T y < T z 2. T x + T y > T z 3. T x + T y = T z 022 (part 5 of 6) 10.0 points How are k~a yk and k~a xk related?

1. k~a yk < k~a xk 2. k~a yk > k~a xk 3. k~a yk = k~a xk 023 (part 6 of 6) 10.0 points What is true about the center of mass of the system?

1. The center of mass is stationary. shay (des2767) – UT HW 08 – warren – (77402) 6 2. The center of mass accelerates.

3. The center of mass has a constant veloc- ity.