Introduction

Dynamics is that branch of physics which deals with the causes of motion or, more correctly, with the causes of changes in motion.  We will begin the study of dynamics with an examination of Newton's first two laws of motion.  In addition, we will examine two special forces which often occur in dynamics problems.

Newton's First Law - the Law of Equilibrium

Newton's first law of motion can be stated as follows:

The condition  described by the first law is called "equilibrium."  Note that an object which is moving in a straight line at a constant speed is in equilibrium as well as an object which is at rest.  For an object to be in equilibrium, any forces acting on it must be balanced.  This does not mean that there are no forces acting on the object, only that any forces acting on the object must balance each other.  It will be necessary to delay a complete study on combining forces until we have studied vectors.  For now, all problems will have forces which act opposite to each other.  Here, it is a simple matter to determine if the forces are balanced.

Examples of Newton's first law are very familiar to everyone.  When you are riding in a car which suddenly stops you will keep going until some force (seatbelt, dash, window, etc.) stops you.  When a car turns a corner at high speed you would keep going in a straight line, ultimately ending outside the car unless there is a force on you (seatbelt, friction with the seat, door etc.).  Anyone who has ever kicked something massive, a stone for example, knows about the tendency of an object to remain at rest.

Newton's Second Law - the Law of Acceleration

Newton's second law says that:

This can be simply stated with the following equation:

Where F is the magnitude of the unbalanced force, M is the mass of the object and a is the acceleration of the object.  We must use a consistent set of units.  If the force is measured in newtons, mass will be in kilograms and acceleration in .  This set of units is called the MKS system for meter, kilogram, and second.  The newton is equal to a .  The other common set of units based on the metric system is the CGS system for centimeter, gram and seconds.  In the CGS system mass is measured in grams, acceleration in and force in dynes where 1 dyne = 1 .  There are systems of units based on the foot and pound but they will not be studied here.  Of the two systems presented, the MKS system is generally preferred and will be used almost exclusively here.

It should be obvious that application of Newton's second law is very simple.  Indeed, the hardest part will generally be to decide the magnitude of the unbalanced force, and, in this chapter where all forces will be acting along the same line, even this should present little problem.  Study the sample problems below.

Weight

Weight is the force of gravity on an object.  Since it is a force, it is measured in newtons.  It will always be directed down toward the center of the earth.  Near the surface of the earth the weight of an object depends on its mass as follows:

Where F_g is the weight, M is the mass and a_g is the acceleration of gravity.  The acceleration of gravity on the earth is very close to 9.81 .  The symbol, F_g, is used for weight rather than a W for two reasons.  First, it is to remind us that weight is a force, and secondly the symbol W will be reserved for use with the term "work" when that term is defined in a later chapter.  Be sure to use consistent units: newtons, kilograms, and ; or dynes, grams and .

Be sure to make a clear distinction between mass and weight.  Mass measures the inertia or resistance of an object to changes in its motion.  Weight is the force of gravity on an object.  The mass of an object is a constant and does not depend on where the object is located.  An object has the same inertia in outer space or on the moon as it has on the earth.  Weight depends on the gravitational field.  An object will weigh more on the earth than on the moon and will be weightless in outer space.

Sample Problem #1

Calculate the net force required to give a 1000kg car an accelera­tion of 3m/sec2.

Sample Solution #1

Apply Newton's second law,

Sample Problem #2

Calculate the acceleration of a 2000lb car if a net force of 500 lbs is applied to it.

Sample Solution #2

Note that you have been given the weight (force of gravity) of the car, not its mass.  Since F_g = ma_g we can find the mass by solving this equation for m =.  The value of a_g in English units is 32 , thus m= 62.5. The units, in terms of lb, ft and sec, are .

Now the solution is straight forward.  Apply Newton's second law to obtain:

1.

A car with a mass of 1 000kg has an acceleration of 2.50 . What resultant force is required to produce this acceleration?

2.

What net thrust is needed to accelerate a 40kg rocket sled at 5.0 ?

3.

X‑rays are produced when electrons (mass about 10^-30 kg) are accelerated and allowed to hit a target. Calculate the acceleration if the electrons are subjected to a force of 10^-13N.

4.

In the previous problem, how long will it take for an electron to move across the X‑ray tube if the gap is 10 cm wide?

5.

A 10 kg block has a rope attached to it which has a maximum tensile strength of 250 N. What is the least time in which the block can be raised vertically through a distance of 30 m by pulling on the rope?

6.

A 4.0 kg hammer moving at a speed of 6.0 strikes a nail and drives it 1.0 cm into a block of wood. Assume that the hammer is decelerated at a constant rate. How much time is required for the hammer to stop after it comes into contact with the nail?

7.

In the previous problem, what is the force exerted on the nail?

8.

What is the resultant force on a body weighing 48 lb when its acceleration is 6.0

9.

An object of 0.10 kg is at rest. A net force of 2.0 N is applied for 10 sec.What is its final velocity?

10.

In the previous problem, how far will the object have moved in the 10 second interval?

11.

A baseball pitcher throws a ball weighing lb with an acceleration of 480 . How much force does he apply to the ball?

12.

A 500kg ore bucket is raised and lowered in a vertical mine shaft using a cable. Determine: the upward force exerted by the cable when: the upward acceleration is 4.0 and the speed is 10 ; the bucket is moving upward with a constant speed of 5.0 .

13.

A bellhop holds a 10 kg suitcase while he is in an elevator which accelerates upward at 2 . What force does the bag exert on his hand? Supposing the bag to be 0.60 m from the floor, how long would it take to strike the floor of the elevator if it were dropped while the elevator were accelerating?

14.

The normal motorist has a "reaction time" of 0.7sec. Assume that, by means of the brakes, a retarding force equal to 2/3 of the weight of the car can be applied to the car. A 2800‑lb car is traveling at 45mi/hr. Find the acceleration if the brakes are applied with maximum force. How far will the car travel before being brought to rest? How does the stopping distance compare with the stopping distance required by a car which is twice as heavy. What will be the stopping distance if the car were going two times as fast?