Review Exercise Number 2

Section 1: Fill in the Blanks and Definitions

 

¢  The field of physics is usually divided into the following two branches

 

     Ø  _____________________ physics and      classical

 

     Ø  ______________________ physics.          modern

 

    The former deals with topics such as fluids, heat, and sound. The latter deals with topics such as relativity and cosmology.                            

 

¢  When scientists are trying to understand a set of phenomena, they often make a  _________________. This is a kind of analogy of the

    phenomena expressed in terms of something already known. It usually relatively simple.  model

 

¢  A ________________ is broader and more detailed than the above. It can give testable predictions.    theory

 

¢  A _______________ is a concise and general statement about how nature behaves (that energy is conserved, for example).   Law

 

¢  Chapter 3 deals with the connection between force and motion, which is the subject of ___________________ dynamics.

 

¢  Intuitively, we experience ___________________ as any kind of push or pull on an object. force

 

¢  Reference frames in which Newton’s first law holds are called _____________________ reference frames.  inertial

 

¢  The ______________ of an object is a measure of the inertia of the object.  mass

 

¢  Define a newton without using symbols or an equation.

 

It is the amount of force required to give a mass of 1 kg an acceleration of 1 m/s².

 

¢  What are the units of the newton?    kg m/s²

 

¢  The magnitude of the force of gravity on an object is commonly called the object's _______________  weight.

 

¢  The number of reliably known digits in a number is called the number of ________________ figures.  significant

 

¢  In the SI system, the meter, second, kilogram, ampere, kelvin, mole, and candela quantities are called ___________________ units.  base

                      

Section 2: True-False

 

Indicate whether the following statements are true or false by placing a check mark (P) in the appropriate column.

 

Statement	True	False
The speed of a falling object is not proportional to its mass or weight	P
Velocity is a scalar quantity		P
Acceleration and velocity are always in the same direction		P
Newton’s first law deals with inertia	P
Newton’s third law equates force to mass times acceleration		P
Mass refers to an object’s “quantity of matter”	P
Weight is a force	P
For a given force, the acceleration of an object is inversely proportional to its mass	P
A reference frame attached to an accelerating train is an inertial reference frame		P
If the acceleration of an object is 0, there are no forces acting on it		P
If only one non zero force acts on an object, it cannot have zero acceleration	P
Acceleration is the rate of change of velocity	P
Acceleration can be negative	P
The normal force is always in the vertical direction		P

 

Section 3: Problems and Analysis

 

¢  An object of mass m₁ rests on a table with friction. It is connected to a pulley and on the other end of the pulley is an object with mass m₂.

    Draw the 2 free body diagrams for this situation.

 

¢  A graph was provided in the text that illustrated the relationship between the magnitude of the force of friction as a function of the external

    force applied to an object initially at rest.  This graph is shown below. Identify the indicated parts by placing the correct letter in the

    appropriate box. For example, the horizontal axis is correctly labeled.

 

A. Horizontal axis   B. No motion   C. Sliding   D. Static Friction Region   E. Kinetic Friction Region   F. Ffr =  msFN   G. msFN

 

 

 

¢  Assume that a hockey puck slides across frictionless ice on a horizontal plane. Indicate which of the following free body diagrams is correct

    by placing a check (P ) mark by the appropriate one: A, B, or C

 

    A___________                           B_____P_____                    C._____________   

 

                                                        

 

¢  A box is on a plane at an angle of 23 degrees to the horizontal. The coefficient of kinetic friction of the plane is 0.13. The mass of the box is

    2 kg. The front of the box is 9.1 meters from the bottom of the incline. The box starts from rest.

 

a. Draw a free-body diagram to include angles, forces, coordinate system, etc.

 

 

 

 

b. Write the equation, using Newton’s law(s) for the summation of forces in the x direction. Insert values but do not evaluate the expression.

 

mg sin q -  F_fr= ma         (2)(9.80)sin(23) - F_fr= (2)a

 

c. Write the equation for the summation of forces in the y direction. Insert values but do not evaluate the expression.

 

F_N - mg cos q = 0           F_N    = (2)(9.80) cos (23)

 

d. Assume that you have solved the appropriate equations and found the acceleration of the box,

 

Write an expression that, if solved, would give the velocity of the box when it reaches the bottom of the incline. Use standard names for the

variables. Do not solve for a numerical value of the velocity.

 

v_x0 = 0, x₀ = 0, x = 9.1

 

v² = v²_x0 + 2a(x – x₀)          v = Ö(2a(x - x₀)= Ö(2a(9.1)

 

 

¢  The free body diagram for a system (object on a flat table being pulled by the indicated force) is shown below, along with the coordinate

     system to use.                                          

 

 

 

 

a. Using the appropriate laws of Newton, write an expression for the summation of the forces in the x direction.

 

 

SF_x = F_Pcos(35) - F_fr = ma

 

 

b. Using the appropriate laws of Newton, write an expression for the summation of the forces in the y direction.

                        

SF_y =  F_N - mg +  F_Psin (35) = 0

 

 

¢  A 4.0 kg bucket (bucket 1, on the bottom) is hanging by a massless cord from 3.0 kg bucket (bucket 2, on the top). The 3.0 kg bucket is

     hanging by another massless cord from the ceiling. The buckets are at rest.

 

 

 

a. Draw the 2 free body diagrams. Refer to the tension in the top cord as F_T2 and the tension in the

    bottom cord as F_T1

 

 

 

b. Write an expression for the tension in each cord.

 

Since the buckets are at rest, their acceleration is 0.  Write Newton’s 2^nd law for each bucket, with up as the positive direction.

 

åF₁ = F_T1 – mg = 0

F_T1 = m₁g = (4.0 kg)(9.8 m/s²) N

 

åF₂ = F_T2 – F_T1 – m₂g = 0

F_T2 = F_T1 + m₂g = m₁g + m₂g = g(m₁ + m₂) = (9.8)(4.0 + 3.0) N

 

 

¢  A student drives east from her home for a distance of 3 km. She then drives north for a distance of 4 km.

 

a. What is the magnitude of her final displacement, d, from her home?

 

d = (3² + 4²)^1/2 = 5 km

 

b. Write an expression for the angle, q,  measured from the horizontal to her displacement vector.

 

q = tan^-1(4/3)

 

1.  A monkey leaps horizontally from a 6.5-m-high rock with a speed of 3.5 m/s. How far from the base of the rock will the monkey land?

    Choose downward to be the positive y direction.  The origin will be at the point where the monkey leaps from the rock.  Do not evaluate to a

    number – present the answer in terms of an appropriate expression with correct numbers and units inserted.  

 

Choose downward to be the positive y direction.  The origin will be at the point where the tiger leaps from the rock.  In the horizontal direction,

V_x0 = 3.5 m/s and a_x = 0. In the vertical direction V_y0 = 0, a_y = 9.80 m/s², y₀ = 0

and the final location y = 6.5 m.

The time for the tiger to reach the ground is found from applying Eq. 2-11b to the vertical motion.

y = y₀ + v_y0t + (1/2)a_yt²  Substituting in the values and solving for t gives 1.15 s

The horizontal displacement is calculated from the constant horizontal velocity.

 

delta x = v_xt = (3.5 m/s)(1.15 sec)

  =  4.0 m (number not required)

 

 

2.  A diver running 1.8 m/s dives out horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff.

    Choose downward to be the positive y direction.  The origin will be at the point where the diver dives from the cliff.  Do not evaluate to a

    number – present the answer in terms of an appropriate expression with correct numbers and units inserted.

 

In the horizontal direction v_x0 = 1.8 m/s and a_x = 0. 

In the vertical direction  v_y0 = 0, a_y = 9.8 m/s² , y₀ = 0

and the time of flight is t = 3.0 s. The height of the cliff is found by applying equation 2-11b to the vertical motion.

 

y = y₀ + v_y0t + (1/2)a_yt² 

 

gives y = 44 m   (answer not required)

 

 

Section 4: Extra Credit

 

 

¢  This intellectual giant lived during the period 384-322 B.C. He   believed that a force was required to keep an object moving along      a horizontal plane. To him, the natural state of an object was at rest, and a force was believed necessary to keep an object in      motion.  His name: _____________________________ Aristotle
¢  This individual lived 2000 later. Now regarded by many as the Father of Science, he disagreed with the above belief. He      maintained that it is just as natural for an object to be in motion with a constant velocity as it is for it to be at rest.       His name:_____________________________ Galileo
¢  Using the foundation laid by the Father of Science, this giant built his great theory of motion and his 3 laws. He was given the title     of Sir by his country.  His name:_____________________________ Newton

 

¢  "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." This is a

     quote from _______________________  Richard Feynman

 

¢  ___________________was once asked by a Caltech faculty member to explain why spin one-half particles obey Fermi Dirac statistics.

    Rising to the challenge, he said, "I'll prepare a freshman lecture on it." But a few days later he told the faculty member, "You know, I couldn't do

    it. I couldn't reduce it to the freshman level. That means we really don't understand it."  Richard Feynman

 

¢  There is a picture of _______________________________ on the first page of this Review Exercise.  Albert Einstein

 

¢  There is a clock in the back of the room that runs backwards. This clock was placed there by me in honor of the person that wrote the first

     compiler.  Her name is   __________________ Grace Murray Hopper

 

¢  Given the following expression

 

at² + bt = - c

 

Express t as a function of a, b, and c. In other words, solve for t

 

First, place the equation in standard form

 

at² + bt + c = 0

 

t =  ± (b² – 4ac)^1/2/2a