Chapter 1 Questions & Conceptual Problems

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

(a) L/T^2 (b) L

Consider the following. (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

In a certain right triangle, the two sides that are perpendicular to each other are 5.80 m and 6.00 m long. What is the tangent of the angle for which 5.80 m is the opposite side?

5.80/6.00

How many significant figures are there in each of the following? (a) 85.8 ± 0.6 (b) 3 ✕ 10^9 (c) 2.7600 ✕ 10^−6 (d) 0.0041

(a) 3 (b) 1 (c) 5 (d) 2

The diameter of a sphere is measured to be 3.40 in. (a) Find the radius of the sphere in centimeters. (b) Find the surface area of the sphere in square centimeters. (c) Find the volume of the sphere in cubic centimeters.

(a) 4.33 cm (b) 235.61 cm2 (c) 340.06 cm3

Answer each question yes or no. (a) Must two quantities have the same dimensions if you are adding them? (b) Must two quantities have the same dimensions if you are multiplying them? (c) Must two quantities have the same dimensions if you are subtracting them? (d) Must two quantities have the same dimensions if you are dividing them? (e) Must two quantities have the same dimensions if you are equating them?

(a) Yes (b) No (c) Yes (d) No (e) Yes

A certain car has a fuel efficiency of 23.7 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).

10.03 km/L

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 high fountain of water is located at the center of a circular pool as shown in the figure below. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 35.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0°. How high is the fountain?

7.96 m

The magnitude of vector A is 21.5 units and points in the direction 305° counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.

Ax = 12.33 units Ay = -17.61 units

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

distance 246 km angle 21.3° west of north

Newton's second law of motion 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 kg · m2/s2 kg/m · s2 none of these

kg · m/s2

A vector has an x-component of −25.5 units and a y-component of 46.5 units. Find the magnitude and direction of the vector.

magnitude 53.03 units direction 118.74° (counterclockwise from the +x-axis)

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.) m2/kg · s2 m3/kg · s3 m3/kg · s2 m2/kg · s3

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 v/t2 v/x2 v2/t none of these

v^2/x