PHYSICS 254

EXAM 3

Fall 2021

Dr. Jennifer Cash

Name _____________________________

SHOW ALL WORK, USING THE BACK OF A PAGE IF NECESSARY. DRAW A

BOX AROUND THE FINAL ANSWER.

For questions 1-6, either indicate the correct answer in the blank or select the answer which

most correctly answers the question. These questions do not require calculations and you do

not have to show your work. Please clearly indicate your answers!!

1) For each of the following variables, list the symbol used in equations to represent it and

the units you would expect for it: (1 pts each)

symbol unit

(a) angular velocity ______ ______

(b) angular acceleration ______ ______

(c) period ______ ______

(d) momentum ______ ______

(e) force ______ ______

2) In the equation, Σ τ= I α , the symbol τ is called? (1pt)

a) Tension b) Tangential c) Torque d) Time

3) In the equation, Σ τ= I α , the symbol I is called? (1pt)

a) Inertia b) Impulse c) Initial d) Instantaneous

4) In an elastic collision, which of the following MUST be true? (2 pt)

a) momentum is conserved, but kinetic energy is not

b) kinetic energy is conserved, but momentum is not

c) neither momentum nor kinetic energy are conserved

d) both momentum and kinetic energy are conserved

5) For the diagram shown to the right a particle is moving

clockwise around the circle. Draw an arrow in the direction of the

centripetal acceleration at point H and E (2 pts)

6) A child is playing with a birthday present “barrel of monkeys” by hanging his monkeys

along a ruler. He places one small monkey with a mass of m1 at a distance of r1 from the

center pivot point and one bigger monkey with a mass of m2 at distance of r2 from the pivot

point as shown in the diagram below. The pivot point is located at the geometric center of the

ruler.(6pt)

Construct the FULL torque equation for this situation

(Note you are not solving the equation or plugging in values)

For problems 7-12 , you need to SHOW YOUR WORK, and may get partial credit if your

work demonstrates your understanding of the concepts.

Clearly indicate your final answer!!!

7) Ira spins the propeller on his drone helicopter around through an angle of 24,500 degrees,

what is this angle in revolutions? (3 pts)

8) Ira spins his fidget spinner around through an angle of 75.2 revolutions, what is this angle

in radians? (3 pts)

9) An average of force of 1250 N is applied to a block over a short time interval resulting in

an impulse of 53.8 Ns. What was the time span during which the force acted? (6 pts)

10) A large 25.0 kg solid sphere with a radius of 1.24 m is rolled along the floor. Calculate

the moment of inertia for the sphere. (clearly show the equation you are using) (6 pts)

11) A force of 12.0 N is applied to the end of a 3.12 m

beam at a 35o angle as shown in the figure to the right.

Calculate the torque applied to this beam? (6 pts)

12) Calculate the momentum of a garbage truck that is 13500 kg and moving to the right at

12.5 m/s? (6 pts)

Questions 13-19, all related to the following word problem,

You must answer ALL questions on this page (6 pts each)

Ira flies a 0.750 kg toy airplane connected to string at a constant tangential speed of 5.36 m/s

such that the plane goes once around a circular path every 0.75 seconds.

13) Calculate the radius of the circular path

14) Calculate the centripetal acceleration on the toy airplane.

15) Calculate the force of the string keeping it in circular motion

16) Calculate the angular velocity of the toy airplane

(The following problem will be worth 24 points)

(SHOW ALL WORK!!! including your knowns, what you are solving for, equations,

units, diagrams, and the solution; partial credit is given for the problem setup as well as

the solution)

A flywheel accelerates from an angular speed of 5.80 rad/s to an angular speed of 22.2 rad/s

with a constant angular acceleration of 6.12 rad/s2. Calculate a) the time for this motion and

b) the angular displacement of the flywheel during this motion.

Knowns: (symbols, numbers, and units) Solving for: (symbols/words)

a)

b)

Equations: (in symbols)

Math:

Final Answers: (including units)

a) b)

PHYSICS 254

FINAL EXAM – Fall 2021 – v2

Name _____________________________

SHOW ALL WORK, USING THE BACK OF A PAGE IF NECESSARY. DRAW A

CIRCLE AROUND THE FINAL ANSWER.

For questions 1-11 choose the answer which best answers the question or fill in the blank with

the needed information.

1) For each of the following quantities list the standard variable symbol and the standard unit.

(1 pt each)

variable symbol unit

mass

time

wavelength

normal force

acceleration

coefficient of friction

momentum

wave speed

angular frequency

frequency

2) Indicate the variable names for each symbol. (1 pt each)

Δ θ is called

ax is called

v⃗ is called

Δ y is called

T is called

3) In the equation, Σ τ=I α , list the name and units for each variable.

τ is called and has units of

I is called and has units of

α is called and has units of

4) The standard unit for power, the Watt, is equivalent to which of the following

a) Jm b) Js c) J /m d) J /s

5) The standard unit for power, the Watt, is equivalent to which of the following

a)

kg m

s b)

kg m

s2 c)

kg m2

s

3 d)

kg m2

s2

6) For the position verses time graph shown to the right, describe the motion at each point, using

the options of positive, negative, or zero?

(1 pt each)

a) At point B, the velocity is ________

b) At point C, the velocity is ________

c) At point D, the velocity is ________

d) The average acceleration from A to C is ________

7) A collision in which the two objects stick together after the collision is also called: (2 pt)

a) general b) recoil c) elastic d) inelastic

8) A situation in which the two objects are stuck together and then separate is also called: (2 pt)

a) general b) recoil c) elastic d) inelastic

9) For the force diagram shown to the right, construct the

full force equations

(x and y directions). (4 pts total)

ΣFx=

ΣF y=

10) On the graphical wave shown to the right,

use the grid lines to determine the following

values:

(2 pts each)

a) The amplitude of the wave _______

b) The wavelength of the wave ______

11) On the standing wave shown below, (2 pt each)

a) clearly label one location which is a node with ‘N’

b) clearly label one location which is an anti-node with ‘A’

c) What harmonic is shown ______

0 1 2 3 4 5 6 7 8 9 10 11 12

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

x(m)

y

(m

)

INDIVIDUAL CALCULATION PROBLEMS

For problems 12-14, you need to show your work and may get partial credit if your work

demonstrates your understanding of the concepts (6 pts each)

You may skip one of these questions

12) The position of a particle moving along the x-axis is given by x=(5 +3t−4 t

2

)

(note units have been intentionally left off this equation and can be left off your answers here)

Use the derivative to construct the equation for the velocity of this particle?

13) A position vector has a magnitude of 34m at an angle of 54 ˚ above the horizontal.

Calculate the components of the vector and fill out the vector position equation below.

r⃗= î+ ĵ

14) A child starts from rest and runs straight towards his ball which is 12.0 meters away. If he

accelerates at a constant rate and reaches a final velocity of 3.1 m/s , calculate his acceleration.

INDIVIDUAL CALCULATION PROBLEMS

For problems 15-18, you need to show your work and may get partial credit if your work

demonstrates your understanding of the concepts (6 pts each)

You may skip one of these questions

15) A truck with a mass of 2566 kg is moving with a momentum of 41580kgm/s ; calculate

the velocity of the truck.

16) What is the Force of gravity on an object with a mass of 88.1 kg?

17) What is the tangential velocity of a 2.0 kg toy plane rotating in a circle of radius 0.95 m at a

angular speed of 8.0 rad/s?

18) The mass of the block is 0.400 kg and the spring constant is 527 N/m. Calculate the angular

frequency of the oscillation.

INDIVIDUAL CALCULATION PROBLEMS

For problems 19-21, you need to show your work and may get partial credit if your work

demonstrates your understanding of the concepts (6 pts each)

You may skip one of these questions

19) Calculate the mass of an object that experiences an acceleration of 3.03m/s2 when a net

force of 779 N is applied.

20) If an object moves at 9.48 m/s and has a kinetic energy of 587 J, what is the object’s mass?

21) A large motor pulls a crate horizontally 4.42 m with a force of 30.6 N; how much work was

done by the motor in this situation?

STEP BY STEP

For problems 22-25, you need to show your work and may get partial credit if your work

demonstrates your understanding of the concepts

Complete all problems on this page

An oscillating wave is described by the equation:

y(x,t)=2.20msin (7.77

rad

m

x+16.7

rad

s

t+ π

2

rad)

Either circle the correct answer from the choices listed

or fill in the blanks with the correct answer.

22) Based on this wave equation, what are the values for: (2 pts each)

Phase shift ________

Angular wave number ________

Amplitude ________

Angular frequency ________

23) Calculate the wave speed. (7 pts)

24) Calculate the wavelength of the wave. (7 pts)

25) How far will the wave travel in 47.0 s (7 pts)

For the following problem, SHOW ALL WORK including your knowns, what you are

solving for, equations, mathematical steps, the solution and units. Credit is divided between

the problem setup as well as the solution. (The following problem will be worth 24 points)

A pendulum which is 0.4 m long and has a mass of 3.0 kg moves in simple harmonic motion on

Earth. Find a) the angular frequency of the oscillation and b) the period of the pendulum.

Knowns: (symbols, numbers, and units) Solving for: (words and symbols)

part a)

part b)

Equations: (in symbols)

Math:

Final Answers: (including units)

part a) part b)

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