Forces and Motion

Chapters 11-12

Frame of reference

• A system of objects that are not moving with respect to one another– To describe motion accurately and completely, a

frame of reference is necessary.

Relative Motion

• Movement in relation to a frame of reference.

Distance v. Displacement

Distance• The length of the path between two points

– Scalar quantity– SI unit = meter (m)– Ex. 100 meters

Displacement• The direction from the starting point and the length of a

straight line from the starting point to the ending point.– Vector Quantity– SI unit = meter (m)– Ex. 100 meters East

Combining Displacements

• Vector – A quantity that has magnitude and direction

• Magnitude can be size, length, or amount

– Vectors are represented by arrows• Length of the arrow shows magnitude• The way the arrow is pointing shows direction

• Displacements are combined using vector addition– Vector addition is the combining of vector magnitudes

and directions

Combining Displacements (cont.)

• Vectors that have the same direction are added together.

• Vectors that are in different directions are subtracted

Combining Displacements (cont.)

•When two or more displacement vectors have different directions, they are combined by graphing.

Combining Displacements (cont.)

• The vector in red is called the resultant vector– A resultant vector is the SUM of two or more

vectors– The resultant vector WILL ALWAYS point from the

starting point to the ending point

Instantaneous v. Average Speed

• Average speed is for the entire time of the trip

• Instantaneous speed is the speed at a particular instant

NOTE: both are scalar quantities!!!

Speed

• Average Speed– The total distance traveled, d, divided by the time, t, it takes to travel that distance

– SI unit is meter per second (m/s)

Problems

While traveling on vacation, you measure the times and distances traveled. You travel 35 kilometers in 0.4 hour, followed by 53 kilometers in 0.6 hour. What is your average speed?

Problems

A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometer in 16 minutes. What is the jogger’s average speed in kilometers per minute?

Problems

A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed?

Speed (cont.)

• Instantaneous speed– V, is the rate at which an object is moving at a

given moment in time– Si unit is meter per second (m/s)

Graphing Motion

• To graph speed, you place time (independent variable) on the x-axis, and distance (dependent variable) on the y-axis– These graphs are called distance v. time graphs– The slope on the graph equals the speed• A positive slope shows positive direction• A negative slope shows opposite direction• A horizontal slope shows standing still

– The steeper the slope is, the higher the speed

Velocity

• Velocity is both speed and direction– Therefore velocity is a?????

Vector Quantity!

• A long vector shows a faster speed• A short vector shows a slower speed

• Velocities are added using vector addition• SI unit is meter per second (m/s)• Average velocity = displacement/time ( Δx / t )

– Displacement = vector quantity from starting point to ending point

Are distance and displacement the same???

Problems

A kayak is moving across a stream that is flowing downstream at a velocity of 4 km/h. The kayak’s velocity is 3 km/h. What is the magnitude of the kayak’s velocity relative to the river bank?

Acceleration

• Acceleration, a, is the rate at which velocity changes– Acceleration = ANY CHANGE IN velocity

• Magnitude • Direction

– Increase in velocity = positive acceleration– Decrease in velocity = negative acceleration– SI derived unit is meters per second squared (m/s2)– Acceleration is a vector quantity!Note: “change in” = delta (Δ)

Constant Acceleration

• Constant acceleration is a steady change in velocity– Ex. Taking off in an airplane or stopping at a red

light. Both are constant acceleration.• Which one is positive and which is negative?

Calculating Acceleration

• If change in velocity is positive than acceleration is positive

• If change in velocity is negative, than acceleration is negative

Problems

An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s2. What is its change in velocity during this time?

Problems

A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration?

Problems

A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball?

Graphing Acceleration

• Acceleration is graphed by putting time (independent variable) on the x axis, and velocity or speed (dependent variable) on the y axis.

• The slope of the graph is equal to the acceleration– Positive slope = positive acceleration– Negative slope = negative acceleration

Graphing Acceleration (cont.)

• Constant acceleration is represented by a straight line on a speed v. time graph.– Constant acceleration is

ALWAYS linear on a speed v. time graph

• Constant acceleration is represented by a curved line on a distance v. time graph

Instantaneous Acceleration

• Instantaneous acceleration is how fast a velocity is changing at a specific instant–Acceleration is rarely constant, and motion is rarely in a straight line. –Acceleration involves a change in velocity or direction or both, so the vector of acceleration can point in any direction. –The vector’s length depends on how fast velocity is changing.–For an object that is standing still, the acceleration vector is zero.

Force

• Force is a push or pull that acts on an object• Forces cause:– A resting object to move– A moving object to accelerate

Measuring Force

• A Unit of Force– Newton (N)• 1 kilogram to accelerate at a rate of 1 meter per second

each second• 1 N = 1 kg·m/s2

Combining Forces

• The net force is the overall force acting on an object after all of the forces are combined.– Same direction – add – Opposite direction – subtract

• When the net force = zero– Forces are balanced

• When the net force ≠ zero– Forces are unbalanced– Forces add up to resultant force

Friction

• Friction is a force that opposes the motion of objects that touch

• Static friction– Acts on objects that are at rest– Acts in opposite direction of applied force

• Dynamic (sliding) Friction– Acts on moving objects as they slide over a surface– Dynamic friction < static friction

• Coefficient of Friction– The ratio of the frictional force compared to the normal force (force

due to gravity)– μ = Ff/FN

Gravity

• Gravity is a force that acts between any two masses– Attractive force– Causes objects to accelerate as they are pulled

toward center of mass• Terminal velocity – force of air resistance = force of

gravity

– Can act over large distances

Free Fall

• Free fall is the movement of an object toward Earth due to the pull of gravity– For every second of fall

time, the object’s velocity increases by 9.8 m/s

– Therefore, acceleration due to gravity, g, is 9.8m/s2

t = 0 sv = 0 m/s

t = 1 sv = 9.8 m/s

t = 1 sv = 9.8 m/s

t = 1 sv = 9.8 m/s

Problems

A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water?

Problems

A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy’s hand?

Projectile Motion

• Projectile motion is the motion of a falling object (projectile) after it is given an initial forward velocity– Only two forces act on a projectile• Air resistance• Gravity

Famous Men In Physics

• Aristotle– Incorrectly proposed that a force is required to keep an

object moving at a constant speed • Galileo– Studied how gravity produces constant accleleration

• Rolled balls down ramps yo!• Concluded that moving objects not subject to friction or any

other force would continue to move forever

• Newton– First defined mass and force– Introduced three laws of motion

Newton’s Laws of Motion

• First Law of Motion– An object in motion stays in motion and an object at rest

stays at rest unless acted upon it by another object• Inertia – the tendency of an object to resist a change in motion

– Second Law of Motion• The acceleration of an object is directly proportional to the net

force acting on it and the mass of the object• Mass is a measure of the inertia of an object• ΣF=ma; ΣF – net force, m – mass, a – acceleration

• Third Law of motion– For every action there is an opposite but equal reaction

Problems

An automobile with a mass of 1000 kilograms accelerates when the traffic light turns green. If the net force on the car is 4000 newtons, what is the car’s acceleration?

Problems

A boy pushes forward a cart of groceries with a total mass of 40.0 kg. What is the acceleration of the cart if the net force on the cart is 60.0 N?

Problems

What is the upward acceleration of a helicopter with a mass of 5000 kg if a force of 10,000 N acts on it in an upward direction?

Problems

An automobile with a mass of 1200 kg accelerates at a rate of 3.0 m/s2 in the forward direction. What is the net force acting on the automobile? (Hint: Solve the acceleration formula for force.)

Problems

A 25-N force accelerates a boy in a wheelchair at 0.5 m/s2. What is the mass of the boy and the wheelchair? (Hint: Solve Newton’s second law for mass.)

Weight and Mass

• Mass– Measure of inertia– Amount of material an object contains

• Weight – The force of gravity on the mass of an object– Weight = mass times acceleration due to gravity

Problems

If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to gravity is 9.8 m/s2?

Momentum

• Momentum is the product of an object’s mass and its velocity– Objects with large momentums are harder to stop

than those with smaller momentums– All objects at rest have zero momentum– Mass is in kg; velocity is in m/s– SI unit for momentum is kg m/s∙

Problems

Which has more momentum, a 0.046-kilogram golf ball with a speed of 60.0 meters per second, or a 7.0-kilogram bowling ball with a speed of 6.0 meters per second?

Conservation of Momentum

In a closed system, the loss of momentum of one object equals the gain in momentum of another object— momentum is conserved.

• A closed system means other objects and forces cannot enter or leave a system– Objects within a closed system can exert forces on one

another– According to the law of conservation of momentum, if

no net force acts on a system, then the total momentum of the system does not change

Universal Forces

There are four fundamental forces in the universe

• Electromagnetic• Strong Nuclear• Weak Nuclear• Gravitational

Electromagnetic Force

• Electric and magnetic force are two different aspects of the electromagnetic force– Electric force and magnetic force are the only

forces that can both attract and repel• Opposite charges attract• Like charges repel

• Electromagnetic force is associated with charged particles

Nuclear Forces

• Strong Nuclear Force– Holds a nucleus of an atom together– Strong force that acts on the protons and neutrons

• Weak Nuclear Force– An attractive force found in certain types of

radioactive processes– Is found inside protons and neutrons

Gravity

• Gravitational force acts between any two masses– Force is dependant on mass and distance– Force decreases and distance between objects

increases– The weakest of the universal forces