### Fall 2009 Physics 211 Hour Exam 1(25 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 109. The exam period was 90 minutes; the mean score was 85.6; the median score was 89. Click here to see the formula sheet that came with the exam.

Unless otherwise stated, ignore air resistance and assume the acceleration of gravity is g = 9.81 m/s2 vertically downward.

### QUESTION 1*

At right is a graph of the acceleration of a point particle as a function of time.

Which choice below is a possible graph of the position of the particle as a function of time ?

(a)
(b)
(c)

### QUESTION 2*

This and the next question are about the following situation.

A block of mass m = 1.5 kg is hung by a massless rope from the ceiling of an elevator. The elevator has an upward acceleration a = 2.6 m/s2.

The tension T of the rope is:

(a)   T = 3.7 N
(b)   T = 8.4 N
(c)   T = 10.8 N
(d)   T = 14.7 N
(e)   T = 18.6 N

### QUESTION 3*

The rope is cut while the elevator continues to accelerate upwards. After the mass is free from the rope, it falls downward with an acceleration afall relative to the earth. The following is true for |afall | .

(a)   |afall | > g
(b)   |afall | = g
(c)   |afall | < g

### QUESTION 4***

A fountain has several water jets with the geometry shown in the figure. The initial speed of the water coming out of the jet is v0 = 8 m/s.

How far from the edge of the upper pool does the water fall? This is the distance labeled x in the diagram.

(a)   The water does not make it all the way to the upper pool.
(b)   1.3 m
(c)   2.2 m
(d)   3.1 m
(e)   4.6 m

### QUESTION 5*

At the end of a wild roller-coaster ride, the train of cars must come to a graceful stop at the loading station. Before the brakes are applied, the speed of the train is 8 m/s, and the distance it travels on horizontal rails with the brakes applied is 32 meters. What is the magnitude of the acceleration of the train, assuming that it is constant?

(a)   0.5 m/s2
(b)   0.8 m/s2
(c)   1.0 m/s2
(d)   2.3 m/s2
(e)   9.8 m/s2

### QUESTION 6*

This question and the next two are about the following situation.

A metal bucket with mass MB = 1 kg containing water of mass MW = 10 kg is swung in a vertical circle using a massless rope as shown in the figure. The tangential speed of the water bucket varies around the circle, but is such that at the top of the circle the tangential speed is just high enough to keep the water in the bucket.

The weight of the {bucket + water} and the tension in the rope when the bucket is at the top of the circle, Ttop, form a Newton's 3rd Law action/reaction pair.

(T)   True
(F)   False

### QUESTION 7*

What is the minimum tangential speed, vt of the bucket at the top of the circle?

(a)   vt = 3.73 m/s
(b)   vt = 5.42 m/s
(c)   vt = 10.56 m/s
(d)   vt = 14.73 m/s
(e)   vt = 18.86 m/s

### QUESTION 8*

Which one of the following is the correct relationship between the tension in the rope when the bucket is at the top, Ttop, and the tension in the rope when the bucket is at the bottom, Tbottom?

(a)   Ttop > Tbottom
(b)   Ttop = Tbottom
(c)   Ttop < Tbottom

### QUESTION 9*

This and the next question are about the following situation.

A space telescope of mass mt = 10,000 kg is in a stable circular orbit above the Earth at an altitude h = 3630 km.

The radius and mass of the Earth are RE = 6370 km and ME = 6 × 1024 kg, respectively. Newton's gravitational constant is GN = 6.672 ×10-11 N m2/kg2.

What is the acceleration of the space telescope as orbits the earth?

(a)   0 m/s2
(b)   4.0 m/s2
(c)   5.7 m/s2
(d)   9.8 m/s2
(e)   30 m/s2

### QUESTION 10**

A new module is added to the space telescope increasing its mass to 15,000 kg. In order to maintain a stable orbit at the same height above the earth, the speed at which the telescope orbits the earth must

(a)   increase.
(b)   remain the same.
(c)   decrease.

### QUESTION 11**

This question and the next three are about the following situation.

Three blocks are placed in contact on a horizontal frictionless surface. A constant force of magnitude F is applied to the box of mass M. There is friction between the surfaces of blocks 2M and 3M (μs = 0.26, μk = 0.15) so the three blocks accelerated together to the right.

Which block has the smallest net force acting on it?

(a)   M
(b)   2M
(c)   3M

### QUESTION 12*

What is the direction of the frictional force on block 3M?

(a)   right
(b)   left

### QUESTION 13*

What is the acceleration of the blocks? (You may assume block 3M does not slide or fall off block 2M.)

(a)   a = 4 m/s2
(b)   a = 2 m/s2
(c)   a = 0.67 m/s2

### QUESTION 14***

What is the maximum force F that can be applied, before the 3M block slides off?

(a)   107 N
(b)   62 N
(c)   54 N
(d)   31 N
(e)   29 N

### QUESTION 15*

This question and the next three are about the following situation.

Two boxes are pulled across a surface by a falling weight as shown below. The coefficients of friction between the boxes and the surface are ms and mk. Neglect the masses of the ropes and the pulley.

For the frictionless case (μs = μk = 0) what is the relationship between T1 and T2?

(a)   T1 < T2
(b)   T1 = T2
(c)   T1 > T2

### QUESTION 16*

What is the acceleration, a, of the falling weight in the frictionless case?

(a)   a = 0
(b)   a = g/5
(c)   a = g/4
(d)   a = g/3
(e)   a = 4g

### QUESTION 17*

If the blocks are sliding, but mk = 0.2, what is the new acceleration af relative to the acceleration a in the frictionless case?

(a)   af > a
(b)   af = a
(c)   af < a

### QUESTION 18*

Suppose the blocks are not moving. What is the minimum coefficient of static friction, μs needed to keep them from moving?

(a)   μs = 0.01
(b)   μs = 0.20
(c)   μs = 0.25
(d)   μs = 0.33
(e)   μs = 0.50

### QUESTION 19*

This and the next question are about the following situation.

A physics 211 student is trying to pull a box of books of mass m = 40 kg across the floor as shown in the figure. The coefficient of static friction is μs.

If the angle θ = 0, the normal force, N is:

(a)   N < mg
(b)   N = mg
(c)   N > mg

### QUESTION 20*

If the angle θ = 36.9° and the coefficient of friction μs = 0.3, what is the minimum tension, T, required to get the box moving?

(a)   T = 85 N
(b)   T = 120 N
(c)   T = 211 N
(d)   T = 322 N
(e)   T = 389 N

### QUESTION 21*

A mass m = 3 kg is attached to a spring with spring constant k = 75 N/m. The other end of which is attached to the ceiling. With the mass attached, the spring is observed to have a length of 0.67 m. What is the equilibrium length of the spring without the mass?

(a)   0 m
(b)   0.28 m
(c)   0.39 m
(d)   0.46 m
(e)   0.57 m

### QUESTION 22*

A truck accelerates with a heavy box on its trailer. The box does not slip; which direction does the friction force on the box point during the acceleration?

(a)   in the same direction as the acceleration
(b)   in the direction opposite the acceleration
(c)   There is no friction force because the box does not slip.

### QUESTION 23*

This question and the next two are about the following situation.

Two groups of tourists are paddling their canoes towards each other on a river as shown in the figure below. The water in the river flows at 3 mph from left to right in the figure. The group in the canoe #1 paddling with the flow of the river travels at vc1 = 7 mph with respect to the ground, and the group in the canoe #2 paddling against the flow of the river travels at vc2 = 1 mph with respect to the ground. The directions of the velocities are as shown in the figure.

What is the speed of canoe #1 with respect to the water?

(a)   3 mph
(b)   4 mph
(c)   7 mph

### QUESTION 24*

What is the speed of canoe #2 with respect to canoe #1?

(a)   1 mph
(b)   3 mph
(c)   4 mph
(d)   7 mph
(e)   8 mph

### QUESTION 25*

If the speed of canoe #2 with respect to canoe #1 is changed to 10 mph and they begin 5 miles apart, how long does it take before they meet each other?

(a)   0.1 hr
(b)   0.2 hr
(c)   0.5 hr
(d)   1.0 hr
(e)   2.0 hr

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.