FORCES, MASS, AND MOTION

VELOCITY AND ACCELERATION

• Velocity: How fast on object (speed) travels and the direction it travels in

• Ex) Speed: 50 miles/hour

• Ex) Velocity: 50 miles/hour East

• v = d/t

• d = distance; t = time

• Acceleration: The rate that velocity changes. (Change in speed or direction)

• a = (vf – v0) / t or

• vf = v0 + at

• Unit: m/s²

• vf = final velocity

• v0 = initial velocity

GRAPHING VELOCITY AND ACCELERATION

http://www.physicsclassroom.com/Class/1DKin/U1L4a.cfmConstant Velocity

Changing Velocity: Acceleration

No Acceleration: Constant Velocity

Acceleration: Changing Velocity

FORCES• Force: the cause of acceleration, or

change in an object’s velocity. (a push or a pull)

• An object’s motion or direction can only change by a net (total) force.

• F = ma

• Balanced Forces: no change in velocity

• Unbalanced Forces: acceleration of the object

Newton’s First Law: The Law of Inertia

• An object at rest remains at rest and an object in motion remains in motion unless acted on by an outside force.

• This law is also called the Law of Inertia.

• Inertia is the tendency of an object to remain at rest or in motion with a constant velocity.

Newton’s First Law: The ladder continues to move even when the truck stops (an object in motion

stays in motion).

http://www.physicsclassroom.com/mmedia/newtlaws/il.cfm

Newton’s First Law: The book will remain on the table until an outside

force causes it to move.

http://www.tuckahoe.k12.ny.us/Science%20pdfs/Force%20and%20Motion/ds%20Force%20Motion%20Presentation.pdf

GRAVITY• Gravity is a force of attraction that exists

between all objects. Depends on the mass of the objects and the distance between them.

• All objects have gravity. • The force of gravity is greater for larger masses

and smaller if the distance is large.• F = mg• F is the force pulling objects toward the Earth; • m is the mass of the object • g is the acceleration due to gravity; this number

is a constant for all masses of matter

FREE-FALL AND GRAVITY• All objects have the same

free-fall (not including air resistance) acceleration (9.8 m/s²) on Earth. Objects fall at the same rate if there is no air resistance.

• The Force of Gravity pulls objects to the Earth at a constant rate. This means that (not counting air resistance) all objects gain 9.8 m/s of velocity every second they fall to the Earth.

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FREE-FALL – NO AIR RESISTANCE

OBJECTS FALL AT THE SAME RATE

FALLING WITH AIR RESISTANCE

DENSER OBJECTS FALL FASTER

http://www.physicsclassroom.com/mmedia/newtlaws/efar.cfm

WEIGHT AND MASS• MASS: the amount of

matter in an object• Measured in kilograms

(kg)• Regardless of where you

were in the universe your mass would not change.

• Ex) mass on Earth = 56.76 kg

• Mass on the moon = 56.76 kg

• WEIGHT: is the gravitational force an object experiences due to its mass

• Measured in Newtons (N)• Weight = mass x acc.

gravity• Weight changes due to

the gravitational force.• Ex) weight on Earth =

556.25 N (125 lb)• Weight on the moon =

92.1 N (20.7 lb)

WORK• A force that causes a displacement of an

object does work on the object.

• Work = Force x distance

• W = Fd

• The SI unit for work is the Joule (J).

• Work is not done on an object unless the object is moved because of the action of the force. The force and distance must be in the same direction for work to occur.

Physicsclassroom.com

EXAMPLE WORK PROBLEM

• A student with a force of 1.5 N lifts a sandwich 0.30 m from the table. How much work does she do?

• Work = Force • Distance • 1.5 N •0.30 m = 0.45 N•m

MACHINES• Machines make work easier.

• This can be done in 3 ways:

• 1) Decrease the required input force.

• 2) Increase the distance the resistance force moves

• 3) Change the direction of the input force.

• The efficiency of a machine can never greater than 100% because work output is always less than work input (due to friction).

http://sln.fi.edu/qa97/spotlight3/spotlight3.html

MECHANICAL ADVANTAGE

• The advantage in using a machine is the Mechanical Advantage (MA). The larger the MA the less effort is needed to do the work.

• MA can be calculated in 2 ways.

• MA = resistance force/effort force

• MA = effort distance/resistance distance

MA OF SIMPLE MACHINES• Inclined plane: the longer the incline the

greater the MA (MA = ramp length/height of incline)

• Wedge: the longer and thinner the wedge the greater the MA

• Screw: (an inclined plane wrapped around a cylinder) the closer the threads the greater the MA

• Pulley: The greater the number of ropes supporting the resistance, the greater the MA.

MA OF SIMPLE MACHINES• Wheel and axle: The larger the wheel

compared to the axle, the greater the MA.• Lever: a bar that pivots around a fixed point

(fulcrum) – MA = effort distance/resistance distance

(measured from fulcrum)– 3 classes of levers

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Example Problem: What is the mechanical advantage of this lever?

de = 6 mE F

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dr = 3 m

Answer:

MA = de/dr

6 m/3m = 2

GHSGT PRACTICE QUESTIONS• 1) Gravity is a force present on Earth between two

objects. Which of the following examples experiences the greatest amount of gravitational force? (The distance between the two objects in each example is the same.)a) Earth and a car b) Earth and a moonc) Earth and a human d) all of the above

• 2) A train increases its speed uniformly from 30 m/s to 50 m/s in 5.0 seconds. The train’s average acceleration during this time isa) 5 m/s² b) 0.25 m/s² c) 20 m/s² d) 4.0 m/s²

ANSWERS• 1) B: Earth and the moon (Gravity

depends on mass and distance; if the distance is the same the greater the mass of the objects the greater the gravity)

• 2) D: 4.0 m/s² (a = (vf – v0) / t so (50m/s – 30m/s)/ 5s = 4.0 m/s²

GHSGT PRACTICE QUESTIONS• 3) The work output of a machine is less than the

work input. What factor causes this?a) distance b) friction c) time d) weight

• 4) Many public buildings now have entrance ramps in addition to entrance stairs. Which principle explains the idea behind entrance ramps?a) By increasing the distance, the required force decreases.b) By increasing the distance, the required force increases.c) By increasing the force, the required distance decreases.d) By increasing the force, the required distance increases.

ANSWERS

• 3) B: friction

• 4) A: By increasing the distance, the required force decreases (Machines make work easier)

GHSGT PRACTICE PROBLEMS• 5) The speed of sound is 344 m/s when the air is

20C. How far away is the source of the sound if it takes 8 seconds for the sound to reach you?a) 43 m b) 344 m c) 2,580 m d) 2,752 m

• 6) Which of the following situations best illustrates the principle of inertia?a) Steve throws a ball straight up and notices it slowing down.b) Emily asks for a push to get started on a swing.c) Paula decides to sit in an outside seat of a merry-go-round so that she will have a faster ride.d) When Dave drops a bowling ball, it does not bounce as high as a basketball dropped from the same height.

ANSWERS• 5) D: 2,752 m (v = d/t therefore d = vt

d = (344 m/s)(8 s) = 2,752 m)

• 6) B: Emily asks for a push to get started on a swing (Inertia – the tendency for an object not to change it’s velocity; Emily was at rest and can only get out of rest when an outside force acts on her)

GHSGT PRACTICE QUESTIONS• 7) An inclined plane is 5 meters long and 1 meter

high. The mechanical advantage of the incline isa) 0.2 b) 1 c) 5 d) 100

• 8) If a car is moving in a straight line at constant speeda) a net force is acting on it b) no gasoline is being consumed c) it is accelerating

d) no net force is observed• 9) The measure of gravitational force on an object

is calleda) mass b) weight c) momentum d) resistance

ANSWERS• 7) C : 5

MA = effort distance/resistance distance MA = 5 m/1 m = 5

• 8) D: No net force is observed (a force is required to change the speed)

• 9) B: Weight (determined by the mass of the object and gravity)

GHSGT PRACTICE PROBLEMS• 10) Which of these graphs illustrates the fastest

acceleration?

a) b) c) d)

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v

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v

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v

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• 11) In which of the following situations is work not being done:

a) A chair is lifted vertically with respect to the floor.

b) A bookcase is slid across carpeting.

c) A table is dropped onto the ground.

d) A stack of books is carried at waist level across a room.

ANSWERS• 10) B (the slope of a velocity-time

graph indicates the acceleration)

• 11) D: A stack of books is carried at waist level across a room (the applied force and distance must be in the same direction for work to be done)