PHYSICAL SCIENCE IIMotion

Motion• Why is being able to describe motion important?

Motion• Being able to accurately describe motion has been a vital

part of our global culture.

• As a race, humans have made significant advantages in being able to describe location and motion.

• Examples• Using Landmarks• Magnetic Compass• Detailed Maps• Global Positioning System (GPS)• Odometers and Speedometers

Motion• Describing motion can be tricky.• Take for example the following statement:

• “Everything is moving.”

• Do you agree with that statement? Why or why not?

Frame of Reference• In order to accurately describe motions in the universe,

there needs to be a Frame of Reference.

• A Frame of Reference is simply a group of objects that are not moving with respect to one another.• Examples: The classroom, the floor, the ground, Hershey, Pa.

Frame of Reference• Let us go back to the previous quote:

• “Everything is moving.”

• This statement can be right or wrong depending on your chosen frame of reference.

• If your frame of reference is this room, then certainly not all objects are moving.

• However, if your frame of reference is the sun, then this room along with everything inside is moving as the Earth rotates and revolves around the sun.

Frame of Reference• Let us try another example:

• A man and a woman are seated inside a train that is driving from Harrisburg toward Philadelphia at 65mph.

• The woman believes they are not moving, while the man believes they are moving.

• Who is correct in this situation?

Distance vs. Displacement• Assume for a minute that you are lost somewhere in

Pennsylvania.

• A helpful resident tells you that you are 50 kilometers from Hershey.

• With this information can you get back home?

• What other information would you need?

Distance vs. Displacement• Imagine again you are lost somewhere in Pennsylvania.

• The same helpful resident instead tells you that you are 50 kilometers northwest of Hershey.

• Can you find your way home?

Distance vs. Displacement• What we have just discovered is there are two types of

length measurements.

• The first scenario describes a measurement of distance.

• Distance is simply a measurement of length, it has no direction.

• Examples: • You are 50 kilometers from Hershey.• I am 3 meters from the door.• The athlete ran 5 kilometers.

Distance vs. Displacement• The second scenario described a measurement of

displacement.

• Displacement is a length measurement that also has a specific direction.

• Examples:• You are 50 kilometers northwest of Hershey.• I am 3 meters to the south of the door.• The athlete ran 5 kilometers to the east.

Distance vs. Displacement• We’ve identified the difference between distance and

displacement, but what is the importance of having two different types of length measurements?

Speed vs. Velocity• In the previous section we looked at the difference

between distance and displacement and determined there are two distinct ways of measuring the length you’ve traveled.

• In addition to measuring how much length something has travelled, it is often important to know how fast an object is or was moving.

Speed vs. Velocity• Imagine you are going to travel to the beach on vacation.• In your preparations before travel, you may want to know

things like:• Directions – What roads do I take?• Travel Time – How long will I be driving?

• Travel time is of course dependent on many factors:• How much traffic.• How far must you travel.• How many stops you make.• How fast can you drive.

Speed vs. Velocity• The final bullet point “How fast can you drive.” is a

measurement of speed.

• Instantaneous Speed – a measurement of how fast you are moving at one particular moment.• Example: At 8:30 am we were traveling at 15 m/s (meters per

second)

• This measurement is only a snapshot in time, since at 8:31 you may have been traveling at 40 m/s.

Speed vs. Velocity• Average Speed – a measurement of how much distance

you’ve traveled in a certain amount of time.• While driving to the beach our average speed was 20 m/s.

• To calculate average speed use the following equation:

Speed vs. Velocity• Example Problems:

• A runner traveled 1000m in a time of 250s. What was the runner’s average speed?

• How long did it take a bullet to travel 300m if it had an average speed of 350m/s?

Speed vs. Velocity• Sometimes knowing only how fast something travels is

not enough information to completely analyze a situation.• It may also be important to know which way an object is or

was moving.• Instantaneous Velocity – measures how fast an in what

direction and object is moving at one particular moment.• At 8:30 we were traveling 15m/s to the east.

• Again this measurement is only a snapshot in time.

Speed vs. Velocity• Average Velocity – a measurement of how much

displacement occurred in a certain amount of time.• While driving to the beach our average velocity was 10m/s to the

southeast.

Speed vs. Velocity• Example Problems

• A truck traveled 2000m north in 65s. What was the average velocity for this vehicle?

• A cheetah ran at an average velocity of 25m/s west for 15s. What was the displacement of the cheetah?

Velocity Vectors• Sometimes the motion of an object involves more than

one velocity.

• When this happens it becomes necessary to find the resultant velocity.

• The resultant velocity is the sum of all the individual velocities of an object’s motion.

• When finding this sum it is important to consider the direction of the velocity as well as the numerical value.

Velocity Vectors• This involves using vectors.

• A vector is simply an arrow that is used to represent velocity.

• The length of the tail indicates the size of the velocity and the arrow head points out the direction.

Tail

Head

Velocity Vectors• When vectors are in the same direction, they are added

together.

• If velocity vectors are in opposite directions they are subtracted from each other.

• When velocities are at right angles to each other you must add them using the Pythagorean Theorem.

Velocity Vectors• Examples:

• A river is flowing downstream at a speed of 2-m/s. If a person is floating in a raft on this river, how fast are they moving past the shoreline?

• A boat is traveling downstream at a speed of 10-m/s in a river that is flowing at a speed of 2-m/s. What is the resultant velocity of the boat with respect to the shoreline?

• A boat is traveling upstream at a speed of 10-m/s in a river that is flowing at a speed of 2-m/s. What is the resultant velocity of the boat with respect to the shoreline?

• While in a canoe, two people row with a velocity of 4-m/s north across a river that is flowing with a velocity of 3-m/s east. What is the resultant velocity of these two people?

Displacement Vectors• Displacement can also be represented by a vector.

• Examples:• A girl rides her bike 200-m east, pauses for a moment and then

continues to ride another 50-m east. What was the resultant displacement of the girl?

• A person drives their car 20-mi to the north, then turns and drives 5-mi to the south. What is the resultant displacement of the person?

• A man drives his car 3-mi to the east, then turns left and drives 4-mi to the north. What is the resultant displacement of the man?

Acceleration• In the previous section we discussed how most objects do

not travel at a constant velocity.

• When the velocity of an object is changing, the object is undergoing an acceleration.

Acceleration• Acceleration – the rate at which velocity is changing.

• Three ways an object can experience an acceleration:• The object’s speed can increase.• The object’s speed can decrease.• The object can change direction.

• Changing any one of these three will cause the velocity of an object to change, but in many cases of acceleration both speed and direction will be altered.

Acceleration• Mathematically, acceleration is defined as:

Acceleration is measured in meters per seconds squared:

Acceleration• Example:

• A car experiences a change in velocity from 7-m/s to 12-m/s, which is caused by an acceleration of 2.5-m/s2. How long was the car accelerating?

• In a time period of 4 seconds a truck accelerates from rest to a velocity of 10-m/s. What was the acceleration experienced by this truck?

• While driving a car at a velocity of 20-m/s, a person spots a deer standing in the roadway. To avoid striking the animal the person applies the brakes and brings the car to rest. If the brakes caused the car to stop in 2 seconds, what was the vehicle’s acceleration?

Gravitational Acceleration• The acceleration due to gravity on Earth is approximately

9.8-m/s2.• This acceleration affects all objects that are near the

surface of the planet Earth regardless of their size, shape or mass.

• Example: • Which object accelerates faster: a penny or a feather?

• In the absence of air resistance, both objects fall at the same rate!

• This shows that Earth’s gravitational acceleration affects all objects equally.