physics math

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)