WebAssign Chapter 1 - Conceptual Questions

How many significant figures are there in each of the following? (a) 7.0 × 109 (b) 3.24 × 10−6 (c) 2.6 × 10−6 (d) 0.020

(a) 2 (b) 3 (c) 2 (d) 2

(a) If an equation is dimensionally correct, does this mean that the equation must be true? (b) If an equation is not dimensionally correct, does this mean that the equation can't be true?

(a) no (b) yes

Estimate the number of atoms in 1 cm3 of a solid. (Note that the diameter of an atom is about 10-10 m.)

10²⁴

Find the order of magnitude of your age in seconds.

10⁹

A house is advertised as having 1420 square feet under roof. What is the area of this house in square meters?

132 m²

Use the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003.

58

A displacement is related to time as x = A sin(2πft), where A and f are constants. Find the dimensions of A. [Hint: A trigonometric function appearing in an equation must be dimensionless.]

L

Suppose that the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B?

L / T2

Newton's second law of motion (Chapter 4) says that the mass of an object times its acceleration is equal to the net force on the object. Which of the following gives the correct units for force?

kg·m/s²

Newton's law of universal gravitation is represented by the following formula, where F is the gravitational force, M and m are masses, and r is a length. F=G (M m)/(r^2) Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G? (Use the following as necessary: m, kg, and s.)

m³/kgs²

Which of the following relationships is dimensionally consistent with an expression yielding a value for acceleration? Acceleration has the units of distance divided by time squared. In these equations, x is a distance, t is time, and v is velocity with units of distance divided by time.

v²/x