### Fall 2004 Physics 101 Hour Exam 3(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 111. The exam period was 90 minutes; the average score was 90.4; the median score was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the following two questions relate to the same situation:

Oil (ρo = 920 kg/m3) flows through a horizontal cylindrical pipe of radius R1 = 12 cm with a speed of v1 = 2 m/s. Along the flow direction the pipe widens to a radius R2 = 24 cm (as shown in the figure), the speed of the oil is then equal to v2.

What is the speed of the water in the wide part of the pipe?

(a)   v2 = 0.5 m/s
(b)   v2 = 1.0 m/s
(c)   v2 = 2.0 m/s
(d)   v2 = 4.0 m/s
(e)   v2 = 8.0 m/s

### QUESTION 2*

What is the pressure difference ΔP = P2 – P1 between the wide and narrow parts of the pipe?

(a)   ΔP = 660 Pa
(b)   ΔP = 1185 Pa
(c)   ΔP = 1520 Pa
(d)   ΔP = 1725 Pa
(e)   ΔP = 1950 Pa

### QUESTION 3*

Let ΔP be the answer to the previous question. If the pipe was tilted such that the narrow end was higher than the wide end, and the speed of the water in the narrow end was the same as above (that is, v1 = 2 m/s), the pressure difference between the wide and narrow parts of the pipe would be

(a)   less than ΔP.
(b)   equal to ΔP.
(c)   larger than ΔP.

### QUESTION 4*

This and the following three questions relate to the same situation:

A block of mass 20 kg is resting on a horizontal frictionless surface and is attached to a spring with a force constant k = 270 N/m. A force of F is applied to the block in the x-direction, thereby compressing the spring from its equilibrium length by 0.2 m.

What is the magnitude of the force F?

(a)   33 N
(b)   49 N
(c)   54 N

### QUESTION 5*

The force is removed and the block starts to oscillate. What is the period of this oscillation?

(a)   0.33 sec
(b)   1.71 sec
(c)   2.51 sec
(d)   3.69 sec
(e)   4.76 sec

### QUESTION 6*

What is the speed of the block when it reaches the equilibrium position for the first time?

(a)   0.24 m/s
(b)   0.73 m/s
(c)   1.31 m/s
(d)   1.64 m/s
(e)   2.28 m/s

### QUESTION 7***

If there was friction between the block and the horizontal surface and the block was released from rest a distance of 0.2 meters away from the equilibrium position of the spring, what would be the coefficient of kinetic friction between the block and the surface if the block stopped the very first time it reached the equilibrium position of the spring?

(a)   0.14
(b)   0.22
(c)   0.31
(d)   0.45
(e)   0.52

### QUESTION 8*

This and the following two questions relate to the same situation:

A 50-kg child rides on a merry-go-round that has a radius of 3 meters. When the child is 1 meter from the center, the merry-go-round spins with an angular frequency of 12 rad/s. The moment of inertia of the merry-go-round alone is I = 250 kg m2.

If the child slides to the outer edge of the merry-go-round, what will the new angular velocity be?

(a)   ω = 1.3 rad/s
(b)   ω = 5.1 rad/s
(c)   ω = 12 rad/s
(d)   ω = 28 rad/s
(e)   ω = 110 rad/s

### QUESTION 9**

As the child moves to the outer edge of the merry-go-round, the kinetic energy of the child

(a)   increases.
(b)   remains the same.
(c)   decreases.

### QUESTION 10**

As the child moves to the outer edge of the merry-go-round, the total kinetic energy of the merry-go-round and child

(a)   increases.
(b)   remains the same.
(c)   decreases.

### QUESTION 11*

This and the following question relate to the same situation:

A person steps onto a spring scale in the bathroom, and the spring compresses by 0.57 cm. The spring constant is 1100 N/cm.

What is the mass of the person?

(a)   30 kg
(b)   57 kg
(c)   64 kg
(d)   77 kg
(e)   81 kg

### QUESTION 12*

If the same spring scale were placed in an elevator that accelerated upward, and the same person stepped onto the spring, the compression of the spring would be

(a)   smaller than 0.57 cm.
(b)   equal to 0.57 cm.
(c)   larger than 0.57 cm.

### QUESTION 13*

This and the following question relate to the same situation:

A scuba diver swims 50 meters below the surface of the ocean (ρ = 1020 kg/m3). Her facemask has a surface area of 0.06 m2, her volume (including equipment) is 0.070 m3 and her mass (including equipment) is 80 kg.

What is the increase in force of the water on her face mask when she is 50 meters below the surface compared with when she is at the surface of the water?

(a)   6,000 N
(b)   18,000 N
(c)   30,000 N

### QUESTION 14*

What is the buoyant force on the diver when she is 50 meters below the surface?

(a)   700 N
(b)   780 N
(c)   810 N

### QUESTION 15**

An astronaut lands on a distant planet and wants to measure the planet’s gravitational acceleration. She takes a 0.02-kg ball out of her pocket and attaches it to a 0.7-m string. She finds that this simple pendulum has a period two times smaller than when she tested it on Earth. What is the acceleration due to gravity on this planet in terms of g, the acceleration due to gravity at the surface of the Earth?

(a)   g/4
(b)   g/2
(c)   g
(d)   2g
(e)   4g

### QUESTION 16*

This and the following question relate to the same situation:

An object of mass 5 kg is hung on a vertical spring and set into vertical simple harmonic motion with an amplitude of 2 m and an angular frequency, ω = 25 radians/s.

What is the spring constant?

(a)   752 N/m
(b)   1333 N/m
(c)   2024 N/m
(d)   2890 N/m
(e)   3125 N/m

### QUESTION 17*

Another mass is added at the end of the spring together with the 5-kg mass. The system is set into vertical simple harmonic motion. The angular frequency is

(a)   smaller than 25 radians/s.
(b)   equal to 25 radians/s.
(c)   larger than 25 radians/s.

### QUESTION 18*

This and the following question relate to the same situation:

A hydraulic lift with a rectangular platform of length 1.5 m and width 0.8 m is used to raise cars above the ground. The cross-sectional area of the narrow, fluid-filled tube connected to the lift-platform is 0.06 m2 (as shown in the figure).

If a 500-kg car is placed on the lift-platform what force, F, must be applied to the small piston to balance the weight of the car?

(a)   6240 N
(b)   4960 N
(c)   1150 N
(d)   245 N
(e)   85 N

### QUESTION 19*

Through what distance must the piston in the small tube be forced downwards to raise the car up 0.5 m ?

(a)   25 m
(b)   10 m
(c)   0.5 m

### QUESTION 20*

This and the following three questions relate to the same situation:

A 3 kg solid plastic cylinder (I = (1/2) M R2) with radius 0.15 meters starts from rest at the top of a 1.44-meter ramp. It rolls without slipping down to the bottom of the ramp and has a final speed of 3.2 m/s.

Calculate the angular acceleration of the disk as it rolls down the ramp.

(a)   α = 18.1 rad/s2
(b)   α = 22.1 rad/s2
(c)   α = 23.7 rad/s2

### QUESTION 21*

Calculate the torque on the disk as it rolls down the ramp.

(a)   τ = 0.8 N-m
(b)   τ = 1.2 N-m
(c)   τ = 1.6 N-m

### QUESTION 22**

Calculate the frictional force on the cylinder from the ramp.

(a)   f = 5.3 N
(b)   f = 6.1 N
(c)   f = 8.3 N

### QUESTION 23**

Which of the objects below would beat the above cylinder in a race to the bottom of the ramp? (Assume that all of the objects have uniform density.)

(a)   a cylinder made out of the same material, but with twice the radius
(b)   a metal cylinder with the same dimensions but with twice the mass of the original
(c)   a hoop made out of the same material with radius 0.15 meters
(d)   a sphere made out of the same material with radius 0.15 meters
(e)   They all reach the bottom at the same time.

### QUESTION 24*

This and the following question relate to the same situation:

A wooden raft of length 2 m, width 1.5 m, and height 0.25 m, is floating in water. (The density of water is 1000 kg/m3). When there is nothing on the raft it is found to float in the water such that it is submerged to a depth of 0.15 m, as shown in the figure.

What is the density of the wood?

(a)   400 kg/m3
(b)   600 kg/m3
(c)   1,600 kg/m3

### QUESTION 25**

To what depth is the raft submerged when three 20-kg children are standing on the raft?

(a)   0.12 m
(b)   0.15 m
(c)   0.17 m
(d)   0.21 m
(e)   0.23 m

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.