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

General physics 1, Lec 3, By/ T.A. Eleyan 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 = ka m t n where, k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if if m = 1 and n = 2

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

General physics 1, Lec 3, By/ T.A. Eleyan Solution One centimeter (cm) equals 0.01 m. One kilometer (km) equals 1000 m. One inch equals 2.54 cm One foot equals 30 cm… Example: [3] A solid piece of lead has a mass of g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kg/ m3).

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

General physics 1, Lec 3, By/ T.A. Eleyan b For (2,-4) the polar coordinate is (2,2√5) since

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

General physics 1, Lec 3, By/ T.A. Eleyan Solution: [6] Given the vectors A = 2.00 i j and B = 3.00 i 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.

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

General physics 1, Lec 3, By/ T.A. Eleyan Solution: a) b) c) [8] The vector A has x, y, and, z components of 8.00, 12.0, and 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.

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

General physics 1, Lec 3, By/ T.A. Eleyan [10] Find the magnitude and the direction of resultant force Solution: