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Additional Questions

General Physics 1, additional questions, By/ T.A. Eleyan

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[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

[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, additional questions, By/ T.A. Eleyan

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[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).

[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.

[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.

General Physics 1, additional questions, By/ T.A. Eleyan

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[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.

[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.

[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.

General Physics 1, additional questions, By/ T.A. Eleyan

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[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] A rectangular building lot is 100 ft by 150 ft. Determine the area of this lot in m2

[11] 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).

General Physics 1, additional questions, By/ T.A. Eleyan

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[12] If an equation is dimensionally correct, does this mean that the equation must be true? If an equation is not dimensionally correct, does this mean that the equation cannot be true?

[13] Which of the following equations are dimensionally correct?

[14] (a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The Newton is the SI unit of force. According to the results for (a), how can you express a force having units of Newton's using the fundamental

units of mass, length, and time?

[15] The volume of a wallet is 8.50 in.3 Convert this value to m3, using the definition ( 1 in= 2.54 cm.)

General Physics 1, additional questions, By/ T.A. Eleyan

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[16] The polar coordinates of a point are r = 5.50 m and = 240°. What are the Cartesian coordinates of this point?

[5] If the polar coordinates of the point (x, y) are (r,θ), determine the polar coordinates for the points:

(a) (-x, y ), (b) (-2x, -2y), and (c) (3x, -3y).

[17] A force F1 of magnitude 6.00 units acts at the origin in a direction 30.0° above the positive x axis. A second force F2 of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F1 + F2.

[18] A vector has an x component of -25.0 units and a y component of 40.0 units. Find the magnitude and directionof this vector.

[19] Consider the three displacement vectors A =(3ˆi - 3ˆj) m, B = (ˆi -4ˆj) m, and C = (-2ˆi + 5ˆj) m. Use the component method to determine (a) the magnitude and direction of the vector D = A + B + C, (b) the magnitude and direction of E = -A - B + C.

General Physics 1, additional questions, By/ T.A. Eleyan

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[20] If A = (6.00ˆi - 8.00ˆj ) units, B = (-8.00ˆi + 3.00ˆj ) units, and C = (26.0ˆi +19.0ˆj ) units, determine a and b such that a A + b B + C =0.

[21] A vector is given by R =2ˆi + ˆj + 3ˆk. Find (a) the magnitudes of the x, y, and z components, (b) the magnitude of R, and (c) the angles between R and the x, y, and z axes.

[22]If  v =  2i + 3j + k and w  =  4i + j + 2k

Find dot and cross product

Find the angle between V and W

General Physics 1, additional questions, By/ T.A. Eleyan