Physics Question & Answer Key

Question:

Two identical ice skaters are holding onto opposite ends of a very long spring with 

a spring constant of 650 N/m. While spinning in a circle, the skaters frequency of 

revolution is measured to be 0.85 Hz. Calculate the mass of the skaters. 


Answer:

f = (1/2 π)(√ k/m)

0.85 = (1/2 π)(√ 650/m)  

m = 22.8 kg 

22.8 x 2 = 45.6 kg  (the mass need to double since circular motion is the resultant 

of two perpendicular SHM with the same frequency and amplitude and phase 

difference of π/2.)

Physics Question & Answer Key

Question:

A car traveling at constant speed negotiates a frictionless banked curved. Calculate the speed of the car when the road is banked at 20 degrees and the radius of its path is 50 meters.

Answer:

When the road is banked at angle 20 degrees,
The normal force is inclined at angle 20 degrees to the vertical
Its horizontal component
mg sin 20 = centripetal force = mv^2/r
Its vertical Component balances the weight 
mg cos 20 = mg 
Dividing the first by the second equation
tan 20 = v^2/(rg)
v^2 / 50 = (9.8)(tan 20)
v = 13.35 m/s

Physics Question & Answer Key

Question 1:

A 75 kg person escapes from a burning building by walking out a window 25m above a catching net. Assuming that air resistance is a constant 95N on the person during the fall, calculate the person's velocity just before hitting the net.

F = ma

(75)(9.8) - 95  = 75a

a = 8.53 

s = (1/2)(a)(t^2)

25 = (1/2)(8.53)(t^2)

t = 2.42

 v = u + (a)(t)
    = 0 + (8.5)(2.42)
    = 20.66 

 

Question 2:

The maximum force a grocery sack can withstand and not rip is 250 N. Calculate the greatest acceleration 20kg of groceries can be lifted from the floor to the table such that the sack does not break?

Fg = mg

     = (20)(9.8) = 196

F = ma

250 - 196 = (20)(a)

 a = 2.7 

   

WHAT DO COLLEGES CONSIDER FOR ADMISSION?

ACADEMIC QUALIFICATIONS ARE INDICATED BY:

1.    High School courses--substance, diversity, and level of difficulty

2.    High school grades, including senior year

3.    Trends in grades (steady improvement, strong 11th grade record desirable)

4.    Relationship of grades to standardized test scores (high scores and poor grades undesirable)

5.    Rank in class

6.    Standardized test scores

7.    Academic honors and awards

8.    Recommendations from guidance counselor and teachers

PERSONAL QUALIFICATIONS ARE INDICATED BY:

1.    Extracurricular activities, interests, and hobbies (most important for the very selective colleges)

2.    Long-term commitment and talent in a few activities (e.g. sports, arts, community service, religious activities)

3.    Recommendations from your guidance counselor, one or two teachers

4.    Application essays

5.    Personal interviews

College Essays: show colleges why they want you!

The college admissions essay is an opportunity for students to share something about themselves that cannot be found in the resume,  SAT score,  GPA, academic awards, or any other document  include  in the application package.  Admissions officers try to gain insight into the applicant after reading 150 to 500 words.

The college essay is not something that will get students admitted or denied. However, it can help students get in, but it can also work against students. Admissions officers are  looking at how well students communicate their ideas and describe the information they are sharing. They want to get to know the students, and they are more concerned about what students want them to know about.

A strong essay shows what students are interested in, what they're committed to, what they will do with the lessons learned, and what actions they took because of the experience.

Tips for college essays:

1. Stay focused and personal. Don’t just give the admissions officers a laundry list of what you’ve done. Write to show them who  you are.

3. Do not just repeat information that is already in the application.

2. Use strong, focused words in the essay. Don't use weak vocabulary, a word you don't know, or text messaging lingo in the essays.

4. Remember this is your essay, not your parents’ or teachers'. The essay must be your own words and thoughts.

5. Proofread closely. For example, spell check won’t catch that you wrote "form" instead of "from."

6. Make sure the essay clearly describes you. If you lose your essay, a friend should be able to return it to you even without your name on it.

7. Don't turn in essays overflowing with errors or which fail to answer what the college wants to know. It will suggest that you are not serious about the college.

Need help with your college essays?

Kris can take you into the heart of the writing process and come up with an exceptional, genuine final draft. She is accustomed to reviewing drafts by email and helping students over phone or by email; she can work with students from anywhere and at a mutually convenient time.

Consult with Kris on as many essays as you like from either only need proofreading or need to be coaxed from a blank page. If interested, send me an email, and we will work out price depending on what you need.

Ivy League Colleges or Public Colleges?

Due to a horrendous job market for new grads and student loan debt piling up by the billions, the decision-making process has changed. The Wall Street Journal reports on the trend for students to not only question the value of an Ivy League education, but to attend cheaper (or free) public colleges even though they were admitted to much “better” universities.

Princeton professor and economist Alan Krueger and his fellow researcher Stacy Berg Dale found that when a student performed high enough to enter an Ivy League school, but instead went to a second-tier school, they earned just as much money as their Ivy League counterparts.

It used to be a degree did all the speaking for you but many employers have found that those who hold these big degrees are likely to lack communication and interpersonal skills. No longer can you ride on your degree alone. Employers are more interested now in what a student has made of his or her college experience."

Employers today are looking for the entire package and therefore you will find that holding an Ivy League degree as you walk through the door for an interview is not going to be enough. The current marketplace is flooded with eligible candidates and therefore you are going to have to do more than just show up with a prestigious degree. You are also going to have to be progressed with incredible communication skills, be a leader and extremely innovative, in addition to being a go getter and hard worker.

Math Question of the week (5)

The originator of a chain letter writes 5 letters instructing each recipient to write 5 similar letters to additional people.  Then these people each send 5 similar letters to other people.  Determine the number of people who should receive letters if the chain continues unbroken for 12 steps.                      

Physics Question of The Week (5)

1. Electrons are ejected from a surface with speeds ranging up to 4.6 x 10⁵ m/s when light with a wavelength  λ = 625 nm is used.  

        a)    What is the work function of this surface?  

        b)    What is the threshold frequency for this surface?  

Answer Key for Physics Question of The Week (4)

F = qvB = mv² / r

F = (1.6 x 10^-19)(2 x 10⁷)(0.1)

   = 0.32 x 10^-12

r = [(1.67 x 10^-27)(2 x 10⁷)²] / 0.32 x 10^-12

   = 2.09 m

Physics Question of The Week (4)

A proton moves at a speed of 2 X 10⁷ m/s at right angles to a magnetic field with a magnitude of 0.10 T.  Find the radius of its circular orbit.  

Answer Key for Physics Question of The Week (3)

μ₀  =  ₄π x 10^-7  

I  =  5

r  =  30 cm =  .3 m

B  = 2 x 10^-5

B  =  (μ₀I) / (2πr)

(₄π x 10^-7)(5)  / (2π)(0.3)  =  (20 x 10^-7)  /  (0.6)  =  (10 x 10^-7)  /  (0.3)

(2 x 10^-5)(tan θ)  =  (10 x 10^-7)  /  (0.3) 

θ = 9.46⁰

Summer Tutoring

*****  Summer Tutoring  ***** 

It's time to sign up Summer Tutoring Schedule now!

The subjects are as follows:

Honor and regular courses: Algebra 1, Geometry, Algebra 2, Pre-cal, Physics

AP & IB courses: AP Calculus, IB Calculus, AP physics, IB physics

The dates: June 4 - August 4

Physics question of the week (3)

A boat is sailing due north, as indicated by its compass needle, in a location where Earth's magnetic field is 2.0 X 10^-5 T. The boat’s captain inadvertently places his radio on the shelf directly above the compass.  If the 5.0 A current carrying wire of the radio is aligned in a north-south direction and is 30 cm directly above the compass, how much from due north with the compass needle be deflected?  

Answer Key for Math question of the week (4)

a.    d = 3

       u_n = a + n − d

       u₁₀₁ = 2 +100—3

       u₁₀₁ = 302 

b.   152 = 2 + (n −1)(3)

      150 = (n −1)(3),

      50 = n −1,

      152 = −1+ 3n

       n = 51

Math Question of the week (4)

Consider the arithmetic sequence 2, 5, 8, 11, .......

a. Find U<sub>101

b. Find the value of n so that</sub> U_{n = 152.}

Answer Key for Math question of the week (3)

a.  6C4 (0.4)^4 (0.6)^2 = 0.13824


b. (0.6)(0.6)(0.4) = 0.144

Answer Key for Physics question of the week (2)

a. v = (3050)(-4) - (1750)(15) / (1300)
      = -30 m/s (or 30 m/s west)


b. p = (1750)(-4 - 15)
       = -33000 Ns


c. Inelastic  

Physics question of the week (2)

A 1750 kg truck is heading east at 15 m/s when it collides with a 1300 kg car traveling
west. After the collision the car and truck are stuck together and slide west at 4.0 m/s.

a)What was the initial velocity of the car?
b) What was the impulse felt by the truck?
c) Was this collision elastic or inelastic?

Math question of the week (3)

When John throws a stone at a target, the probability that he hits the target is 0.4 He throws a stone 6 times. 

(a) Find the probability that he hits the target exactly 4 times. 

(b) Find the probability that he hits the target for the first time on his third throw.

Answer key for Math question (2)

a) 7C4 [ (0.9)^4 * (1 - 0.9)^(7 - 4) ] 
     = 7!/(4!*3!) [(0.9)^4 * (0.1)^3] 
     = 35(0.0006561) 
        =0.023

b) 7C4 [p^4 * (1 - p)^3] 
     = 35p^4(1 - 3p + 3p^2 - p^3) 
     = 35p^4 - 105p^5 + 105p^6 - 35p^7

c) 0.15 = 35p^4 - 105p^5 + 105p^6 - 35p^7
    p = 0.356 or

    p = 0.770

Answer key for physics question (1)

(a) R = v /I = 120 / 0.25 = 480 Ω


(b) P = IV = (0.25)(120) = 30 w


(c) I = q / t ; q = (0.25)(15) = 3.75 C


     (3.75)(1 / 1.6 x 10^-19) = 2.34 x 10^-19  e^-

Math question of the week (2)

Evan likes to play two games of chance, A and B.

For game A, the probability that Evan wins is 0.9. He plays game A seven times.

(a) Find the probability that he wins exactly four games. 

     For game B, the probability that Evan wins is p . He plays game B seven times.

(b) Write down an expression, in terms of p , for the probability that he wins exactly

     four games. 

(c) Hence, find the values of p such that the probability that he wins exactly four

     games is 0.15.