Preparing for Six Flags Physics Concepts

Preparing for Six Flags Physics Concepts

uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given by Displacement = velocity x time d = vt

Examples How far will you go while traveling at 23 m/s for 12 seconds? d = vt = 23 m/s x 12 s = 276 m

How long will it take to travel a distance of 240 km traveling at 12 m/s? Convert 240 km to meters first! 240 km x = 240000 m Rearrange the equation d = vt to solve for t t = d v = 240000 m 12 m/s = 20000 s 1000m 1km

How far, in meters, will you go while traveling at 70 km/h for 18 seconds? Convert to the 70 km/h to m/s first, then calculate the distance. 70 km h 1000m 1km = 19.4 m/s 1h 3600s d = vt = 19.4 m/s x 18 s = 349 m

Acceleration Acceleration: the rate at which velocity changes Acceleration = final Δ velocity time velocity - original time velocity Unit: Δ velocity m/s time s m 2 s

Constant velocity means that neither the speed nor the direction of motion can change. A race car driving around a circular path at a constant 80 mi/h has a constant speed but not a constant velocity since its direction is changing.

So An object accelerates when its speed OR its direction changes!

Free Fall: the movement of an object in response to a gravitational attraction Earth s gravity, ignoring air resistance, produces an acceleration of we often just call g, the acceleration due to gravity. The size of g is 9.8 m/s 2, but since the acceleration is always downward, the value of the acceleration is a = - g = - 9.8 m/s 2 (approximately -10 m/s 2 )

What does this mean? Each second of free-fall, the speed of an object increases by about 10 m/s T = 1s Speed = 10 m/s T = 2s Speed = 20 m/s T = 3s Speed = 30 m/s

What s the speed? 10 m/s 0 m/s 10 m/s 20 m/s 20 m/s 30 m/s 30 m/s

Newton s First Law of Motion: The Law of Inertia An object at rest remains at rest unless a net external force acts on it. An object in motion continues that motion unless a net external force acts on it. Newton s law of inertia confirmed what Galileo concluded: Once an object is moving, it requires no additional force to keep it moving. It will continue to move in a straight line unless a NET force acts upon it. I knew it first!!

Second Law If there is a net external force acting on an object, it will accelerate... Newton s Second Law is expressed as an equation: F net ma or F ma (I call this the granddaddy of all physics equations!)

Third Law For every force, there is an equal but opposite force. Action / Reaction forces

The gun pushes on the bullet. The bullet pushes back on the gun!

Weight Weight, Wt. is the gravitational force on an object Weight = mass x gravity Wt. = mg Since weight is a force, it is measured in Newtons, N Remember, g on Earth is 9.8 m/s 2

A child pulls up on a string that is holding 2 fish of total mass 5 kg. If he is providing a tension of 60 N, what is the net force on the fish? F net = Tension Weight F net = 60 N 50 N F net = 10 N What is the acceleration of the fish? a = F net / m a = 10 N / 5 kg a = 2 m/s 2

A 50 kg woman steps on a scale in an elevator that accelerates upward at 1.5 m/s 2. What is her weight (use g = 10 m/s 2 )? Weight = mg = 500 N How heavy does she feel? What is her APPARENT weight? F = ma N mg = ma Her APPARENT weight is what she feels like she weighs, which is determined by how hard the floor is pushing up against herthe Normal force. N = mg + ma N = 500 N + 50 kg x 1.5 m/s 2 Apparent weight = 575 N N mg

Experiencing g s When you have positive accelerating, you feel heavier than you actually are. Sometimes that acceleration is measured in g s, in other words- a multiple of 9.8 m/s 2. On amusement park rides, you may experience an acceleration of 40 m/s 2 or even larger. 40 m/s 2 9.8 m/s 2 = about 4 g s. People who experience more than 7 g s will often black out!

Friction, f A force that always opposes motion Depends on two things: the roughness of the surfaces and how hard they are pressed together. f = mn m, mu- the coefficient of friction tells how rough the surfaces are. N, the Normal force tells how hard the surfaces are pressed together

There are two kinds of friction: static friction (not moving) must be overcome to initiate motion. kinetic friction must be overcome while an object is moving Static friction > Kinetic friction

Linear speed, v How far you go in a certain amount of time Miles per hour, meters per second Rotational (angular) speed, w How many times you go around in a certain amount of time Revolutions per minute, rotations per hour, radians per second

Which horse has a larger linear speed on a merry go round, one on the outside or one on the inside? Outside. Which horse has a greater rotational speed? Neither, all the horses complete the circle in the same amount of time. So... There is a relationship between linear speed, v, and rotational speed, w. v = wr The larger your radius, the faster your linear speed!

How do you find the velocity if it is not directly provided? Velocity = distance / time In circular motion, the distance traveled is all around the circle the circumference. The circumference = 2pr So v = 2pr / T

Uniform Circular Motion, UCM: moving in a circle with a constant speed. Question: Is there a constant velocity when an object moves in a circle with a constant speed? No, the direction changes, therefore the velocity changes. If the velocity changed, the object is actually ACCELERATING even while moving at the same speed. Now on to some new things..

Suppose an object was moving in a straight line with some velocity, v. According to Newton s 1 st Law of Motion, An object in motion continues that motion unless a net external force acts on it. If you want the object to move in a circle, some force must push or pull it towards the center of the circle. Any force that pushes or pulls an object towards the center of a circle is called a centripetal force Centripetal means center seeking

According to Newton s 2 nd Law, F = ma, If there is are centripetal forces, there must be a centripetal acceleration. a c = v2 r Where r is the radius of the circle and v is the velocity of the object.

Centripetal force Since F centripetal = ma, the net centripetal force is given by F centripetal = m v2 r

Lots of forces can help in pushing or pulling an object towards (or away from) the center of a circle. Sometimes it takes more than one force to get an object to move in uniform circular motion. Centripetal force is NOT a new kind of force. If an object moves in a circle (or an arc), there must be at least one force that is acting toward the center of the circle.

When can these forces be centripetal Gravity? Moon revolving around the Earth Tension? Twirling a pail at the end of a string Friction? Cars rounding a curve. Air Resistance ( Lift )? Airplane or birds flying in a circle. Normal? Riders in a carnival ride forces?

Free body diagrams Never, ever, EVER label a force centripetal force. Label the specific forces acting: tension, friction, Normal, weight, etc.!

What happens if the string breaks? Which way will the ball move? The ball will continue to move in a straight line path that is tangent to the circle.

Tension in a string as a centripetal force A student twirls a rock around and around in a horizontal circle at the end of the string. The only force that contributes to a NET centripetal force is the tension in the string.

Example A boy twirls a ½ kg rock in a horizontal circle on the end of a 1.6 meter long string. If the velocity of the rock was 4 m/s, what is the Tension in the string? m = ½ kg r = 1.6 m v = 4 m/s The only centripetal force is Tension. T = m v 2 / r T = ½ 4 2 / 1.6 T = 5 N F m v r 2

What you FEEL If YOU were twirled at the end of a string, you would FEEL as if you were being pushed outward, when in reality, you are experiencing a net force inward, toward the center of the circle! The net force exerted on you is CENTRIPETAL- center seeking. The effect you feel is called CENTRIFUGAL. F m v r 2

What about an object on a vertical track? At the top of the track, both the Normal force (the track pushing against the ball) and the weight point down toward the center of the circle, therefore, they are both positive: mg N N F centripetal = N + mg = m v2 r At the bottom of the track, the Normal force points toward the center and the weight points away from the center: mg F centripetal = N mg = m v2 r

Loop the Loop What is the minimum speed that a rider must be moving at in order to complete a loop the loop of radius 12 m? At the top of the loop, both the Normal force and weight point towards the center of the circle, so F centripetal = N + mg = m v2 r However, at the minimum required speed, called the critical velocity, contact is lost for a moment at the top of the loop, so that The Normal force goes all the way to ZERO. Therefore, weight is the only centripetal force when the rider is moving at the minimum required speed. F m v r 2 mg = m v2 r v 2 = rg v 2 = 12 x 10 v = 10.95 m/s

Doing WORK is one way to transfer energy from one object to another. Work = Force x displacement W = F d Unit for work is Newton x meter. One Newton-meter is also called a Joule, J.

Work- the transfer of energy

Work = Force x displacement Work is not done unless there is a displacement. If you hold an object a long time, you may get tired, but NO work was done. If you push against a solid wall for hours, there is still NO work done.

For work to be done, the displacement of the object must be along the same direction as the applied force. They must be parallel. If the force and the displacement are perpendicular to each other, NO work is done by the force.

For example, in lifting a book, the force exerted by your hands is upward and the displacement is F upward- positive work is done. Similarly, in lowering a book, the force exerted by your hands is still upward, and the displacement is downward. F d d The force and the displacement are STILL parallel, so work is still done. But since they are in opposite directions, now it is NEGATIVE work.

On the other hand, while carrying a book down the hallway, the force from your hands is vertical, and the displacement of the book is horizontal. Therefore, NO work is done by your hands. Since the book is obviously moving, what force IS doing work??? The static friction force between your hands and the book is acting parallel to the displacement and IS doing work! F d

Power is the rate at which work is done- how fast you do work. Power = work / time P = W / t You may be able to do a lot of work, but if it takes you a long time, you are not very powerful. The faster you can do work, the more powerful you are.

The unit for power is Joule / seconds which is also called a Watt, W (just like the rating for light bulbs) In the US, we usually measure power developed in motors in horsepower 1 hp = 746 W

Kinetic Energy the energy of motion K = ½ mv 2

Gravitational potential energy GPE = weight x height GPE = mgh Since you can measure height from more than one reference point, it is important to specify the location from which you are measuring.

Conservation of Mechanical Energy The ball starts with kinetic energy Which changes to potential energy. Which changes back to kinetic energy What about the energy when it is not at the top or bottom? E = ½ mv 2 + mgh PE = mgh Energy bottom = Energy top ½ mv b 2 = mgh t K = ½ mv 2 K = ½ mv 2

Example of Conservation of Mechanical Energy Rapunzel dropped her hairbrush from the top of the castle where she was held captive. If the window was 80 m high, how fast was the brush moving just before it hit the ground? (g = 10 m/s 2 ) mgh 1 + ½ mv 1 2 = mgh 2 + ½ mv 2 2 mgh = ½ mv 2 gh = ½ v 2 2gh = v 2 Don t forget to take the square root!

And another one A woman throws a ball straight up with an initial velocity of 12 m/s. How high above the release point will the ball rise? g = 10 m/s 2 mgh 1 + ½ mv 1 2 = mgh 2 + ½ mv 2 2 ½ mv 2 = mgh h = ½ v 2 / g

Conservation of Mechanical Energy more difficult A stork, at a height of 80 m flying at 18 m/s, releases his package. How fast will the baby be moving just before he hits the ground? Energy original = Energy final mgh + ½ mv o 2 = ½ mv f 2 V f = 43.5 m/s

The car on a roller coaster starts from rest at the top of a hill that is 60 m high. How fast will the car be moving at a height of 10 m? (use g = 9.8 m/s 2 ) mgh 1 + ½ mv 1 2 = mgh 2 + ½ mv 2 2 mgh 1 = mgh 2 + ½ mv 2 2

Conservation of Mechanical Energy 1. Draw a sketch and choose a reference point for height. 2. Look at the first position of your object. If it is moving, it has Kinetic energy. If it has some height above or below your reference point, it has Potential energy. 3. Repeat for the second location. 4. If there is no friction or air resistance, set the mechanical energies at each location equal. E 1 = E 2 mgh 1 + ½mv 1 2 = mgh 2 + ½ mv 2 2 5. If there is friction or air resistance, use E 1 E 2 to find the energy lost.

Efficiency No machine or motor or system in the real world is perfect. That is reflected in the efficiency. In the real world, the efficiency will always be less that 100%. It is found by Efficiency Energy out Energy in work out (resis tance) work in (effort)

Momentum: A measure of how difficult it is to stop a moving object. Momentum = mass x velocity p = mv Unit for momentum: kg m s

Momentum of a system of objects Momentum is a vector and therefore has both magnitude and direction. If two objects are moving in opposite direction, then one direction must be chosen as negative and the other as positive before determining the momentum of the system. What is the momentum of this two-object system, taking right to be the positive direction?

How do you change the momentum of an object? PUSH on it for a period of TIME. Impulse: the product of the force exerted on an object and the time interval during which it acts. Impulse = Force x time Impulse = F t

Whether you drop an egg on the floor or on a pillow, it loses all of its momentum. The same impulse is applied in either case, but the stopping time is so much less for the floor, the force is proportionally greater. Impulse = Force x time

The impulse given to an object is equal to the change in momentum of the object. Impulse = change in momentum Impulse = F t Change in momentum = D mv = mv f mv o Therefore: F t = D mv = mv f mv o Impulse Change in momentum

A boy pushed on a 8 kg crate at rest with a net force of 20 N for 4 seconds. How fast was the crate moving afterwards? F t = Dmv = mv f mv o F t = mv f

A boy pushed on a 8 kg crate initially moving at 2 m/s with a net force of 20 N for 4 seconds. How fast was the crate moving afterwards? Ft = Dmv = mv f mv o Ft + mv o = mv f

Momentum before = momentum after m 1 v 1 = (m 1 + m 2 ) v Momentum after a completely inelastic collision

Three Examples of conservation of momentum in collisions with equations: m 1 v 1o = m 2 v 2f m 1 v 1o - m 2 v 2o = - m 1 v 1f + m 2 v 2f m 1 v 1o + m 2 v 2o = m 1 v 1f + m 2 v 2f

Circuits ELECTRIC CIRCUIT: Charges moving in a closed loop A circuit requires a both a conductor, usually metal wires, and a charge pump. CHARGE PUMP: a device that provides a potential difference so that charges keep moving. Alessandro Volta The Potential Difference, DV, provided by the charge pump is called its VOLTAGE.

Resistance all conductors offer some resistance to the flow of charges, even metal wires. RESISTANCE = R voltage current V The unit for resistance is the OHM, W. This equation is often called OHM S LAW I

Example What is the resistance of an appliance if 2 amps of current run through it when supplied with 120 V? R = V / I R = 120 V / 2 A R = 60 W

WATER ANALOGY Water Electricity Flow of water current flow of charge Water pump keeps flow going charge pump psi. pressure voltage Pipes of different resistance wires of diameter different diameter

Electric Power Power is the rate that work is done or energy is transferred, that is Power = Energy (Joules) Time (seconds) Power is measured in Watts, W

Electric power delivered to a circuit by a power supply is given by Power = Current x Voltage P = IV

Parallel Circuit Series Circuit

Convection- the bulk flow of fluids, (gases or liquids, NOT solids) convection currents Conduction- direct contact Radiationelectromagnetic waves Transfer of Thermal Energy