Mechanics

The study of motion, forces and energy.

Reference Point

A point against which position is measured.

(Remember: All motion is relative; it depends on the reference point that is used.)

Speed

How quickly motion occurs.

Equation for Speed

speed =  Distance traveled

            Time Traveled

(Ex.: miles/hour  or meters/second)

Using the Speed Equation, answer the following question:

A car travels 78 miles down the highway.  It takes the car 1.2 hours to travel that far.  At what speed is the car traveling?

The car is traveling 65 miles/hour.

                 speed = 78 miles  =  65 miles/hour

                              1.2 hrs.      

If a car has traveled 78 miles in 1.2 hours, how fast is it going in meters per second?

There are 1609 meters/mile.

There are 3600 seconds/hour.

1. Convert 78 miles to meters.There are 1609 meters/mile.

78 miles x 1609 meters =  125,502 meters

      1            1 mile

2. Convert hours to seconds.

1.2 hours x 3,600 seconds =  4,320 seconds (in 1.2 hrs.)

    1                 1 hour

3. Use speed equation:

speed = 125,502 meters = 29.1 meters/second

              4,320 second

Velocity

Speed and Direction

Vector Quantity

A physical measurement that contains directional information.

(e.g. Velocity)

Scalar Quantity

A physical measurement that does not contain directional information.

(e.g. Speed)

How do you find the relative speed of two objects that are traveling the same direction?

When objects travel in the same direction, their relative speed is the difference between their individual speeds.

How do you find the relative speed of two objects that are traveling in opposite directions?

When objects travel in opposite directions, their relative speed is the sum of their individual speeds.

From relative speed to relative velocity:

Two cars are traveling down a road. The first car is traveling north at 55 miles/hour. The second car is a few hundred yards behind, traveling north at 45 miles/hour. What is their relative velocity?

1. Relative speed = 55 miles/hr - 45 miles/hr.

                         = 10 mile/hr

2. Add direction to determine velocity. Thus, despite the fact that they are moving the same direction, one is moving faster than the other, so they are moving away from each other. 

The relative velocity = 10 miles/hr. away from each other.

From relative speed to relative velocity II:

Two cars are traveling down a road. The first car is traveling north at 55 miles/hr and the second is a few hundred yards south, traveling south at 45 miles/hr.  What is their relative velocity?

1. Relative speed = 55 miles/hr. + 45 miles/hr. (Add because they are traveling different directions.)

Relative speed = 100 miles/hour

2.  Add direction: The car moving south is already south of the first car, so they are moving away from each other.

Answer: Relative velocity = 100 miles/hour away from each other.

Relative Velocity Practice

A plane is flying due east at 520 miles/hour.  Another plane is 20 miles east of that plane, flying with a velocity of 650 miles/hours due west.  What is their relative velocity?

Answer: 1170 miles/hr. toward each other

1. Relative speed:

             520 miles/hr + 650 miles/hr = 1170 miles/hr

2. Relative velocity: Because they are flying towards each other and one has not yet passed the other, the direction is going to be toward each other. Thus, the relative velocity is:

     1170 miles/hr. toward each other.

Acceleration

The time rate of change of an object's velocity

What is the

equation for acceleration?

         acceleration = final velocity - initial velocity

                                            time

Using the equation for acceleration:

Suppose a ball is falling. A person with a radar gun measure the velocity to be 2.0 feet/second straight down.  Just 0.30 seconds later, he measure the velocity again and find that it is 11.6 feet/second straight down.  What is the ball's acceleration?

Answer: The ball's acceleration is 32 ft./sec.² downward.

1. acceleration = final velocity - initial velocity

                                         time

2. 11.6 ft/sec. - 2.0 ft./sec. = 9.6 ft./sec. = 32 ft./sec.

                  0.30 sec.              0.30 sec.         sec.

3.  32  feet    ÷ second = 32 feet     x  __1__  =

         second                      second     second

       32 ft./sec² downward.

Acceleration NOT deceleration!

Remember: in physics all changes in an object's velocity are designated "acceleration" even if that change is to slow the velocity down.  "Deceleration" is not used in physics.

Free Fall

The motion of an object when it is falling solely under the influence of gravity.

Which will fall faster, a book or a piece of paper?

Trick Question! 

Remember, acceleration due to gravity is independent of the object falling.  Thus, size of an object doesn't affect how fast it falls due to gravity.

The book appears to fall faster because the heavy weight of the book allows it to fall through the air resistance (atoms and molecules that make up the air) more efficiently than the light weight of the paper.

What is the rate of acceleration due to gravity in both meters/second² and feet/second²?

The acceleration due to gravity for any object is:

9.8 meters/second² and

32 feet/second² .

Equation for determining the distance of a free fall.

distance = ½ x (acceleration) x (time)²

Using the free fall equation:

A young woman is standing on a bridge overlooking a river. If she drops a rock from the bridge, and it takes 1.2 seconds for it to hit the river, how many meters did the rock fall?

Answer:  7.056 meters

1. distance = ½ x (acceleration) x (time)²

2. distance = ½ x 9.8 meters x (1.2 sec.)²

                           second²

                 ⁼ ½ x 9.8 meters x 1.44 sec.²

                           second²

                 = 7.056 meters