DYNAMIC OF PARTICLE

Newton's Laws of Motion



1. Which of the following statements are true of inertia? List all that apply.

a.        Inertia is a force.

b.        Inertia is a force which keeps stationary objects at rest and moving objects in motion      at constant velocity.

c.         Inertia is a force which brings all objects to a rest position.

d.        All objects have inertia.

e.        A more massive object has more inertia than a less massive object.

f.         Fast-moving objects have more inertia than slow-moving objects.

g.        An object would not have any inertia in a gravity-free environment (if there is such a place).

h.        Inertia is the tendency of all objects to resist motion and ultimately stop.

i.          In a gravity-free environment (should there be one), a person with a lot of inertia would have the same ability to make a turn as a person with a small amount of inertia.

Answer: DE a. False - Inertia is not a force. b. False - Inertia is NOT a force. c. False - Inertia is NOT a force. Inertia is simply the tendency of an objects to resist a change in whatever state of motion that it currently has. Put another way, inertia is the tendency of an object to "keep on doing what it is doing." Mass is a measure of an object's inertia. The more mass which an object has, the more that it sluggish towards change. d. True - Bet money on this one. Any object with mass has inertia. (Any object without mass is not an object, but something else like a wave.) e. True - Mass is a measure of an object's inertia. Objects with greater mass have a greater inertia; objects with less mass have less inertia. f. False - The speed of an object has no impact upon the amount of inertia that it has. Inertia has to do with mass alone. g. False - Inertia (or mass) has nothing to do with gravity or lack of gravity. In a location where g is close to 0 m/s/s, an object loses its weight. Yet it still maintains the same amount of inertia as usual. It still has the same tendency to resist changes in its state of motion. h. False - Inertia is NOT the tendency to resist motion, but rather to resist changes in the state of motion. For instance, its the tendency of a moving object to keep moving at a constant velocity (or a stationary object to resist changes from its state of rest). i. False - Once more (refer to g), inertia is unaffected by alterations in the gravitational environment. An alteration in the g value effects the weight of an object but not the mass or inertia of the object

2. Which of the following statements are true of the quantity weight? List all that apply.

a.        The weight of an object is dependent upon the value of the acceleration of gravity.

b.        Weight refers to a force experienced by an object.

c.         The weight of an object would be less on the Moon than on the Earth.

d.        A person could reduce their weight significantly by taking an airplane ride to the top of Mount Everest.

e.        Two objects of the same mass can weigh differently.

f.         To gain weight, one must put on more mass.

g.        The weight of an object can be measured in kilograms.

h.        The weight of an object is equal to the force of gravity acting upon the object.

i.          When a chemistry student places a beaker on a balance and determines it to be 84.3 grams, they have weighed the beaker.

Answer: ABCH and possibly EF a. True - The weight of an object is equal to the force of gravity acting upon the object. It is computed by multiplying the object's mass by the acceleration of gravity (g) at the given location of the object. If the location of the object is changed, say from the Earth to the moon, then the acceleration of gravity is changed and so is the weight. It is in this sense that the weight of an object is dependent upon the acceleration of gravity. b. True - This statement is true in the sense that the weight of an object refers to a force - it is the force of gravity. c. True - The weight of an object depends upon the mass of the object and the acceleration of gravity value for the location where it is at. The acceleration of gravity on the moon is 1/6-th the value of g on Earth. As such, the weight of an object on the moon would be 6 times less than that on Earth. d. False - A trip from sea level to the top of Mount Everest would result in only small alterations in the value of g and as such only small alterations in a person's weight. Such a trip might cause a person to lose a pound or two. e. Mostly True - Two objects of the same mass can weigh differently if they are located in different locations. For instance, person A and person B can both have a mass of 60 kg. But if person A is on the Earth, he will weigh ~600 N, whereas person B would weight ~100 N on the moon. f. Kinda True (Mostly False) - Weight is the product of mass and the acceleration of gravity (g). To gain weight, one must either increase their mass or increase the acceleration of gravity for the environment where they are located. So the statement is true if one disregards the word MUST which is found in the statement. g. False - By definition, a free-falling object is an object upon which the only force is gravity. Such an object is accelerating at a rate of 9.8 m/s/s (on Earth) and as such cannot be experiencing a balance of forces. h. True - This statement is the precise definition of weight. Weight is the force of gravity. i. False - This student has determined the mass of the beaker, not the weight. As such, he/she has massed the beaker, not weighed it.

3. Which one(s) of the following force diagrams depict an object moving to the right with a constant speed? List all that apply.

Answer: AC If an object is moving at a constant speed in a constant rightward direction, then the acceleration is zero and the net force must be zero. Choice B and D show a rightward net force and therefore a rightward acceleration, inconsistent with the described motion.

EXERCISE

Question 1

Sophia, whose mass is 52 kg, experience a net force of 1800 N at the bottom of a roller coaster loop during her school’s physics field trip to the local amusement park. Determine Sophia’s acceleration at this location.

 F =1800 N                                                  F = ma

m = 52 kg                                        1800 = 52a

a = ?                                                         a = 1800/52

                                                                  a = 34.6 m/s/s

Question 2

Kelli and Jarvis are members of the stage crew for the Variety Show. Between acts, they must quickly move a Baby Grand Piano on to the stage. After the curtain closes, they exert a sudden forward force of 524 N to budge the piano from rest and get it up to speed. The 158 kg piano experienced 418 N of friction.

a)      What is the piano’s acceleration during the phase of motion?

b)      If Kelli and Jarvis maintain this forward force for 1.44 seconds, then what speed will the piano have?

a.       F = 524 – 418

                                                                    

    = 106 N

m = 158 kg

a  = ?

                                                                         F = ma

                                                             106 = 158 a

                                                                         a = 106/158

                                                                         a = 0.671 m/s

b.      Speed = (0.671)(1.44)

                                           = 0.966 m/s/s

Question 3

A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s/s. Determine the mass of the encyclopedia.

F = 15 N

a = 5 m/s/s

m = ??                                                     F = ma

                                                                  15 = m (5)

                                                                  m = 15/5

                                                                  m = 3 kg

Momentum and Collisions

1. Which of the following are true about the relationship between momentum end energy?

a.        Momentum is a form of energy.

b.        If an object has momentum, then it must also have mechanical energy.

c.         If an object does not have momentum, then it definitely does not have mechanical energy either.

d.        Object A has more momentum than object B. Therefore, object A will also have more kinetic energy.

e.        Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy.

Answer: BE a. FALSE - No. Momentum is momentum and energy is energy. Momentum is NOT a form of energy; it is simply a quantity which proves to be useful in the analysis of situations involving forces and impulses. b. TRUE - If an object has momentum, then it is moving. If it is moving, then it has kinetic energy. And if an object has kinetic energy, then it definitely has mechanical energy. c. FALSE - If an object does NOT have momentum, then it definitely does NOT have kinetic energy. However, it could have some potential energy and thus have mechanical energy. d. FALSE - Consider Object A with a mass of 10 kg and a velocity of 3 m/s. And consider Object B with a mass of 2 kg and a velocity of 10 m/s. Object A clearly has more momentum. However, Object B has the greatest kinetic energy. The kinetic energy of A is 45 J and the kinetic energy of B is 100 J. e. TRUE - When comparing the momentum of two objects to each other, one must consider both mass and velocity; both are of equal importance when determining the momentum value of an object. When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity. This greater velocity will tip the scales in favor of the least massive object when a kinetic energy comparison is made.

2. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____.
a. 4 N down b. 5 N down c. 5 N up d. 10 N up e. zero

Answer: E If an object is at rest, then all the forces acting upon the object must be zero. The net force on any one of the boxes is 0 Newtons. Subsequently, in each case, the support force (which we have called the "normal force throughout this course) acting upwards on any of the boxes must be equal to the force of gravity on that box (i.e., the weight) plus the amount of load exerted from above (which would be equivalent to the weight of the other boxes located above the box). So for box Y, the support force acting upward would be equal to 9 N while the net force is still 0 Newtons. And for box Z, the support force is 19 N, sufficient to balance the 10-N gravitational force plus the 9-N of force resulting from the other two boxes bearing down on it.

3. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces.

a. 0.5 m/s

b. 0.33 m/s

c. 0.67 m/s

d. 1.0 m/s

e. none of these

Answer: A Use 1 kg as the mass of the carts (or any number you wish) and then set the expression for initial total momentum equal to the expression for the final total momentum: (1 kg)*(2) + (1 kg) *(-1) = (1 kg) *v + (1 kg) *v Now solve for v using the proper algebraic steps. (2 kg•m/s) - (1 kg•m/s) = (2 kg) v 1 kg•m/s = (2 kg)v (1 kg•m/s) / (2 kg) = v 0.5 m/s = v

KINEMATICS NOTES

Kinematics Physics Notes

DEFINITION
"It is the branch of Physics which deals with description of motion without reference to any opposing or external force".


MOTION
"When a body changes its position with respect to its surrounding so the body is said to be in the state of motion".

TYPES OF MOTION
There are three types of motion:
          1) Linear or Translatory motion

          2) Rotatory motion

          3) Vibratory motion


1. Linear or Translatory Motion
If a body moves in a straight path so the body is to be in Linear motion or Translatory motion.

Example : A bus is moving on the road, A person is running on the ground.


2. Rotatory Motion
If a body spins or rotates from the fixed point ,so the body is to be in Rotatory motion.

Example : The blades of a moving fan, The wheel of a moving car.


3. Vibratory Motion
To and fro motion about the mean point so the body is to be in Vibratory motion.

Example: Motion of a spring.





REST
"When a body does not change its position with respect to its surrounding so the body is said to be in the state of rest".

Example: A book is laying on the table,A person is standing on floor,A tree in the garden.





SPEED
"The distance covered by a body in a unit time is called speed."

                               OR

"The rate of change of distance is called speed."


FORMULA
Speed = Distance/Time
       V = S/t


UNIT
The S.I unit of speed = Meter/second.
                                = m/s

Kinds Of Speed
1. Uniform Speed :
          If a body covers an equal distance in equal interval of time so the body is said to be in uniform speed.

2. Variable speed :
          If a body does not cover an equal distance in equal inteval of time so the body is said to be in variable speed.




VELOCITY
"The distance covered by a body in a unit time in a particular direction is called velocity."

                                       OR

"The rate of change of displacement is called speed."

                                       OR

"Speed in a definite direction is called velocity."


FORMULA
Velocity = Displacment/Time
          V = S/t


UNIT
The S.I unit of Velocity = Meter/second.
                                  =m/s


Kinds Of Velocity
1. Uniform Velocity : 
             If a body covers an equal distance in equal interval of time in a Constant direction so the body is said to be in uniform Velocity.

2. Variable Velocity :
             If a body does not cover an equal distance in equal interval of time in a particular direction so the body is said to be in variable velocity.


ACCELERATION
"The rate of change of velocity is called acceleration."

                                 OR

"Acceleration depends upon the velocity if the velocity continously increases or decreases the accelerattion will be produced."


1) Positive Acceleration :
          If the velocity continously increases then the acceleration will be positive.

2) Negative acceleration :
          If the velocity continously decreases then the acceleration will be negative.


FORMULA
Acceleration = change of velocity/Time
                a = (Vf-Vi)/t


UNIT
The S.I unit of Velocity = Meter/second+square
                                  =m/S2


EQUATION OF MOTION
The relationship of initial velocity, final velocity, acceleration, time,and linear distance.


FIRST EQUATION OF MOTION
suppose an object moves with initial velocity "Vi" in a time "t" and covers a distance "S" in an acceleration "a" and the final velocity of an object becomes "Vf"

According to the defination of the acceleration "The rate of change of velocity is called acceleration"

i.e. Acceleration = Change of velocity/time

=> a = Vf - Vi/t


DERIVATION

a = Vf - Vi/t

at = Vf - Vi

or Vf = Vi + at


SECOND EQUATION OF MOTION

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

i.e. Acceleration = Change of velocity/time

=> a = Vf - Vi/t

at = Vf - Vi

or Vf = Vi + at -------------(1)

Substituting the average velocity:

Vav = (Vi + Vf)/2 -----------(2)

The distance covered by the body in a unit:

S = Vav/t

Putting the value of Vav from equation 2:

S = [(Vi + Vf)/2] * t

Putting the value of Vf from equation 1:

S = [(Vi + Vi + at)/2] * t

S = [(2Vi + at)/2] * t

S = (Vi + at/2} * t

S = (Vit + 1/2at2) {Here 2 is the square of the time "t". Dont write this sentence in the examination}


THIRD EQUATION OF MOTION

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

Acceleration = Change of velocity/time

=> a = (Vf - Vi)/t

=> at = Vf - Vi

or t = (Vf - Vi)/a -------------(1)

Subsituting the average velocity:

Vav = (Vi + Vf)/2 -----------(2)

We know that:

Vav = S/t

=> S = Vav * t

Putting the value of Vav from equation 2 and value of t from eq 1:

S = [(Vi + Vf)/2] * [(Vf-Vi)/a]

S = Vi2 - Vf2/2a since {(a+b) (a-b) = a2 - b2}

or 2as = Vf2 - Vi2

KINEMATICS

One-Dimensional Kinematics

1. Which of the following statements about velocity and/or speed are TRUE? List all that apply.

a.        Velocity is a vector quantity and speed is a scalar quantity.

b.        Both speed and velocity refer to how fast an object is moving.

c.         Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X.

d.        The velocity of an object refers to the rate at which the object's position changes.

e.        For any given motion, it is possible that an object could move very fast yet have an abnormally small velocity.

f.         The phrase "30 mi/hr, west" likely refers to a scalar quantity.

g.        The average velocity of an object on a round-trip journey would be 0.

h.        The direction of the velocity vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.

Answer: ADEG a. TRUE - Yes! Speed is a scalar and velocity is the vector. Know this one! b. FALSE - Speed refers to how fast an object is moving; but velocity refers to the rate at which one's motion puts an object away from its original position. A person can move very fast (and thus have a large speed); but if every other step leads in opposite directions, then that person would not have a large velocity. c. FALSE - Person Y has one-half the speed of Person X. If person Y requires twice the time to do the same distance, then person Y is moving half as fast. d. TRUE - Yes! That is exactly the definition of velocity - the rate at which velocity changes. e. TRUE - An Indy Race car driver is a good example of this. Such a driver is obviously moving very fast but by the end of the race the average velocity is essentially 0 m/s. f. FALSE - The presence of the direction "west" in this expression rules it out as a speed expression. Speed is a scalar quantity and direction is not a part of it. g. TRUE - For a round trip journey, there is no ultimate change in position. As such, the average velocity is 0 m/t seconds. Regardless of the time, the average velocity will be 0 m/s. h. FALSE - The direction of the velocity vector depends only upon the direction that the object is moving. A westward moving object has a westward velocity.

2. A fullback is running down the football field in a straight line. He starts at the 0-yard line at 0 seconds. At 1 second, he is on the 10-yard line; at 2 seconds, he is on the 20-yard line; at 3 seconds, he is on the 30-yard line; and at 4 seconds, he is on the 40-yard line. This is evidence that

a.        he is accelerating

b.        he is covering a greater distance in each consecutive second.

c.         he is moving with a constant speed (on average).

Answer: C The fullback is moving 10 yards every second. He has a constant speed and thus covers the same distance (10 yd) in each consecutive second. He is not accelerating.

3. Which one of the following statements is NOT true of a free-falling object? An object in a state of free fall ____.

a.        falls with a constant speed of -10 m/s.

b.        falls with a acceleration of -10 m/s/s.

c.         falls under the sole influence of gravity.

d.        falls with downward acceleration which has a constant magnitude.

Answer: A A free-falling object is an object upon which the only force is gravity. As it falls, it accelerates at a rate of approx. 10 m/s/s. This acceleration value is constant during the entire trajectory of the motion. Since this is the case, the speed can not be constant.

EXERCISE

Question 1

An airplane accelerate down a runaway at 3.20 m/s/s for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.

a = 3.2 m/s/s                                    t = 32.8 s                              Vi = 0m/s                          d =??

                                                     d = Vi(t) + 0.5 at^2

                                                     d = (0)(32.8) + (3.2)(32.8)^2

                                                     d = 1720 m.

Question 2

A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car?

d = 110 m                                    t = 5.21 s                                            Vi = 0 m/s                                  a = ??

                                                      

                                                d = Vi(t) + 0.5 at^2

                                                110 = (0)(5.21) + 0.5 (a)(5.21)^2

                                                110 = (13.57)a

                                                    a = (110)/(13.57)s/s

                                                    a = 8.10 m/s/s

Question 3

Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far wil he fall?

a = -9.8

t = 2.6 s

Vi = 0 m/s

d = ??

Vf = ??

                                                                d = Vi(t) + 0.5at^2

                                                                d = (0)(2.6) + 0.5 (-9.8)(2.6)^2

                                                                d = -33 m

                                                                Vf = Vi + at

                                                                Vf = 0 + (-9.8)(2.6)

                                                                Vf = -25.5 m/s

EXAMPLE 1 :

ž  A car traveling on a straight road increases its speed from 20 km/h to 100 km/h in 45 s. What is the distance covered by the car?

Solution

ž  In this question we have u = 20 km/h, v = 100 km/h and t = 45 s. If we know the magnitude of a, then all the parameters will fit the equation v² = u² + 2as.

ž  First we have,  a = (v – u)/t = (100 – 20) km/h /(45/3600)h

                                                         = 6400 km/h^-2

 

ž  Thus the distance covered by the car is 0.75 km.

  

EXAMPLE 2 :

A drag racer starting from rest accelerates in a straight line at a constant rate of 5.5 m/s² for 6.0 s.

(a)     What is the racer’s velocity at the end of this time?

(b)     If a parachute deployed at this time causes the racer to slow down uniformly     at 2.4 m/s², how long will the racer take to come to a stop?

Solution,

ž  Within the two intervals (before and after parachuted), the final velocity, v₁ in the first interval becomes the initial velocity, v_o for the second interval.

ž  To find the final velocity v₁, we use equation

                 v₁ = v_o + a₁t₁ = 0 + (5.5 m/S²)(6.0 s) = 33 m/s

ž  For the second interval we use equation

                v₂ = v_o + a₂t₂  (where v_o = v₁ = 33 m/s)

 

EXAMPLE 3:

A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed.

SOLUTION :

Given: vi = 0 m/s vf = 88.3 m/s d = 1365 m

Find: a = ?? t = ??

v_f² = v_i² + 2*a*d

(88.3 m/s)² = (0 m/s)² + 2*(a)*(1365 m)

7797 m²/s² = (0 m²/s²) + (2730 m)*a

7797 m²/s² = (2730 m)*a

(7797 m²/s²)/(2730 m) = a

a = 2.86 m/s²

v_f = v_i + a*t

88.3 m/s = 0 m/s + (2.86 m/s²)*t

(88.3 m/s)/(2.86 m/s²) = t

t = 30. 8 s