Newton's Law of Gravitational Attraction, F = G(m1*m2)/r^2, gives the force F in newtons. If the base units of the SI system are used for mass (kg), distance (m), and time (s), what must be the units of the universal constant of gravitation, G?

Correct answer: m^3/(kg·s^2)

Explanation

This question, based on problem 1-19, checks the understanding of dimensional analysis by requiring the determination of units for the constant G within Newton's Law of Gravitational Attraction to ensure the equation is dimensionally homogeneous.

Other questions

Question 1

Which of the following best describes the branch of mechanics known as Statics?

Question 2

What are the four basic quantities used throughout the study of mechanics as outlined in the text?

Question 3

According to the idealizations discussed in mechanics, what is a 'rigid body'?

Question 4

Newton's First Law of Motion states that a particle at rest or moving in a straight line with constant velocity will remain in that state provided it is not subjected to what?

Question 5

What is the weight in newtons of an object that has a mass of 4.50 Megagrams? Express the result to three significant figures using an appropriate prefix.

Question 6

In the U.S. Customary system of units (FPS), length is measured in feet, time in seconds, and force in pounds. What is the corresponding unit of mass, and is it a base or derived unit?

Question 7

Convert the quantity 52 slug/ft^3 to appropriate SI units, rounding to three significant figures.

Question 8

Which of the following expressions is written in the correct SI form according to the 'Rules for Use'?

Question 9

What does the concept of 'Dimensional Homogeneity' imply for any equation describing a physical process?

Question 10

What is the weight in SI units of a body that has a mass of 1 slug, rounded to three significant figures? Use g = 9.81 m/s^2.

Question 12

When rounding a number to three significant figures, if the fourth digit is a 5 followed by no other digits, and the third digit is an even number, what is the general rule?

Question 13

Evaluate the expression (50 mN)(6 GN) and express the answer with SI units having an appropriate prefix.

Question 14

A car is traveling at 55 mi/h. What is its speed in meters per second, rounded to three significant figures?

Question 15

What is the primary reason that statics, although a special case of dynamics where acceleration is zero, deserves separate treatment in engineering education?

Question 16

How is a 'concentrated force' best described as an idealization in mechanics?

Question 17

According to Newton's Second Law, if an unbalanced force F is applied to a particle of mass m, the particle experiences an acceleration 'a'. What is the relationship between the direction of the force and the direction of the acceleration?

Question 18

An object's weight is a force that depends on its location. For most engineering calculations, the acceleration due to gravity, g, is determined at a 'standard location'. What is this location?

Question 19

What is the weight of a 2-kg body in newtons at the standard location?

Question 20

A body weighing 64.4 lb has a mass of how many slugs?

Question 21

When using SI prefixes, what does the prefix 'giga' (G) represent as a multiple?

Question 22

What is the correct way to express the unit (micrometer)^2 using SI symbols?

Question 23

When performing numerical calculations, the text suggests keeping intermediate values between a certain range to decide on a suitable prefix for the final answer. What is this recommended range?

Question 24

Round the number 4.65735 m to three significant figures.

Question 25

A rocket has a mass of 250 x 10^3 slugs on Earth. What is its mass in SI units, expressed with an appropriate prefix and rounded to three significant figures?

Question 26

Which historical figure is noted for his formulation of the three fundamental laws of motion and the law of universal gravitational attraction?

Question 27

Mass is a property of matter that provides a measure of resistance to a change in velocity. What other property does it manifest as?

Question 28

Evaluate the expression (0.631 Mm) / (8.60 kg)^2 and express the answer in SI units using an appropriate prefix and three significant figures.

Question 29

Evaluate the expression 45 MN^3 / 900 Gg and express the result using an appropriate prefix and base SI units.

Question 30

According to the 'General Procedure for Analysis,' what is the recommended maximum number of significant figures to report in the final answer of a problem?

Question 31

The quantity force has three key characteristics that completely define it. What are they?

Question 32

If a body has a mass of 0.5 g, what is its weight in newtons, expressed to three significant figures and using an appropriate prefix?

Question 33

Convert 2 km/h to ft/s, rounding the final answer to three significant figures.

Question 34

What is the key difference between the quantities 'mass' and 'weight'?

Question 35

In the SI system, the newton is a derived unit. What combination of base units is equal to 1 newton?

Question 36

What is the equivalent of 1 kip (kilo-pound) in pounds?

Question 37

Which of the following is NOT listed as a step in the 'General Procedure for Analysis'?

Question 38

The density of water is 1.94 slug/ft^3. What is this density expressed in SI units (kg/m^3), rounded to three significant figures?

Question 39

When is it appropriate to model a body, such as the Earth, as a particle?

Question 40

What is the result of evaluating (400 mm)(0.6 MN)^2, expressed with an appropriate SI prefix?

Question 41

The 'Important Points' section summarizes that a rigid body does not deform under load. This is an example of what concept in mechanics?

Question 42

According to the principles for applying the SI system, how many of the four basic quantities (length, time, mass, force) have their units defined as 'base units'?

Question 43

If you are converting the specific weight of brass, which is 520 lb/ft^3, to density (mass/volume) in SI units, what is the first step you must take?

Question 44

A pressure of 1 Pascal (Pa) is defined as 1 N/m^2. How many pascals are equivalent to the atmospheric pressure at sea level, which is 14.7 lb/in^2? Use three significant figures.

Question 45

Why did the subject of statics develop very early in history, while dynamics developed much later?

Question 46

Evaluate the expression (354 mg)(45 km) / (0.0356 kN) and express the answer to three significant figures in SI base units.

Question 47

Which prefix should be avoided in science and engineering calculations, except for some volume and area measurements?

Question 48

Newton's laws of motion are stated to apply to the motion of a particle as measured from what type of reference frame?

Question 49

Convert a force of 1 pound (lb) to newtons (N), using the conversion factor from the textbook.

Question 50

What is the primary purpose of drawing a free-body diagram (FBD) in the analysis of mechanics problems?