General physics 1, Lec 3, By/ T.A. Eleyan Lecture 3 Discussion

General physics 1, Lec 3, By/ T.A. Eleyan

Lecture 3

Discussion


]tka[]s[ nm

m2nmnm2m TLTTLL

1m 2n0m2n

Solution

and

[1 ]The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = kam tn where , k is a dimensionless constant. Show by dimensional analysis that this expression

is satisfied if if m = 1 and n = 2


Mm

FrG

r

MmGF

2

2

2

2

2

322

kg

m.N

s.kg

m

kgkg

ms/m.kgG

Solution:

[2 ]Newton’s law of universal gravitation is represented by

Here F is the magnitude of the gravitational force exerted by one small object on another , M and m are the masses of the objects, and r is a distance. Force has the SI units kg ·m/ s2. What are the SI units of the proportionality

constant G ?

2r

MmGF


336

3

m/kg104.111010.2

1094.23

V

m

Solution

One centimeter (cm) equals 0.01 m.

One kilometer (km) equals 1000 m.

One inch equals 2.54 cmOne foot equals 30 cm…

cmin

incm

in

cmininin 065.12)54.275.4(

1

54.2)75.4(1)75.4()75.4(

Example:

]3[ A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kg/ m3).


,r

xcoscosrx

3

34

3

4r

r

ysinsinry

3

32y

Solution:

then

then

212

212 )yy()xx(d

m74)43()23(d 22

a(Solution:

[4 ]If the rectangular coordinates of a point are given by (2, y) and its polar coordinates are ( r , 30°), determine y and r .

[4 ]Two points in the xy plane have Cartesian coordinates (2.00, -4.00) m and ( -3.00, 3.00) m. Determine (a) the distance between these points and

(b) their polar coordinates .


b For (2,-4) the polar coordinate is (2,2√5) since

m52164yxr 22

5.2692tanx

ytan 1


[5 ]Vector A has a magnitude of 8.00 units and makes an angle of 45.0 ° with the positive x axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x axis. Using graphical methods, find (a) the

vector sum A + B and (b) the vector difference A - B .

Solution:


j4i5BAC

Solution:

j8i)B(AD

7.385

4tan 1

2.978tan 1

[6 ]Given the vectors A = 2.00 i +6.00 j and B = 3.00 i - 2.00 j, (a) draw the vector sum , C = A + B and the vector difference D = A - B. (b) Calculate C and D, first in terms of unit vectors and then in terms of polar coordinates,

with angles measured with respect to the , +x axis .


Solution:

j6i2j)42(i)13(BA j2i4j)42(i)13()B(ABA

10240364BA

5220416BA

2883tan 1

6.262

1tan 1

Direction of A+B

Direction of A-B

[7 ]Consider the two vectors A = 3 i - 2 j and B = i - 4 j. Calculate (a) A + B, (b) A - B, (c) │A + B│, (d) │A - B│, and (e) the directions of A + B and A - B .


k4j12i8A

k16j48i32A4B

k12j36i24A3C

Solution:

a(

b(

c(

[8 ]The vector A has x, y, and , z components of 8.00, 12.0, and -4.00 units, respectively. (a) Write a vector expression for A in unit vector notation. (b) Obtain a unit vector expression for a vector B four time the length of A pointing in the same direction as A. (c) Obtain a unit vector expression for a vector C

three times the length of A pointing in the direction opposite the direction of A .


unit5.4945cos3045cos40dx

unit2745sin3045sin4020dy

unit4.56)d()d(R 2y

2x

55.0d

dtan

x

y 8.28

Solution:

[9 ]Three displacement vectors of a croquet ball are shown in Figure, where A = 20.0 units, B = 40.0 units, and C = 30.0 units. Find the magnitude and

direction of the resultant displacement


[ 10 ]Find the magnitude and the direction of resultant force

N30240cos853cos1525Fx N15240sin853sin1510Fy

N5.33)F()F(R 2y

2x

5.0F

Ftan

x

y

5.26

Solution:

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General physics 1, Lec 3, By/ T.A. Eleyan Lecture 3 Discussion