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Chapter 1-6 Numerical Examples and Conceptual Questions

• Speed is distance divided by time, denoted as s = d/t.
• Distance equals speed multiplied by time: d = st.
• Momentum quantifies mass in motion and equals mass times velocity.
• The equation vf = vi + at relates final velocity to initial velocity, acceleration, and time.
• Impulse, a change in momentum, is force multiplied by time interval: Impulse = Ft = m△v.
• Gravity's acceleration is g = 10 m/s².

The Dawn of Physics

• Aristotle, an early and influential Greek philosopher, proposed that the four elements are earth, water, air, and fire.
• Aristotle believed all motion is either natural or violent, with violent motion requiring a sustained push or pull.
• Copernicus was the first scientist credited with postulating that Earth circled the Sun.
• Galileo introduced the concept of inertia.
• Inertia is defined as a property of matter.
• Galileo used inclined planes to slow down changes in speed.
• Galileo's interpretation of motion emphasized rates of time, differing from Aristotle.

Motion and Forces

• If no external forces act on a moving object, it will continue moving at the same speed.
• Galileo showed that a ball rolling on a level surface would keep rolling if friction were absent.
• A hockey puck set in motion across a frozen pond experiences no force to maintain constant velocity if ice friction and air resistance are neglected.
• Outer space requires no force to sustain the motion of a rock.
• A rock whirled at the end of a string, when released, tends to follow a straight-line path.
• Inertia is illustrated when a tablecloth is quickly yanked from under dishes.
• Inertia causes a coin to remain nearly still when a card beneath it is flicked away.
• Inertia allows a sheet of paper to be jerked from beneath a milk container without toppling it.

Mass and Acceleration

• A roller-coaster ride with 12 passengers takes approximately the same time as one with 6 passengers, assuming friction is negligible.
• A package falling off a truck moving at 30 m/s has a horizontal speed of about 30 m/s just before hitting the ground, air resistance is neglected.
• Inertia is why an automobile continues moving when it runs out of fuel.
• A rocket ship gaining speed in outer space runs out of fuel and no longer gains speed.
• A moving van with a stone glued to its ceiling moves at a constant velocity, when the glue fails, the stone falls directly below the midpoint of the ceiling.
• The tendency to keep moving forward causes a person to lurch to the right when a bus makes a left turn.
• Opposing forces prevent a railroad train in motion from continuing indefinitely when its engine is turned off, due to inertia.
• Tension is a force that tends to stretch something.
• A force of 50 N results in zero net force on a rope that is tied to a tree at rest and has a rope tension of 50 N.
• Two students in a tug-of-war who each pull with 400 N results in zero net force on the rope and a rope tension of 400 N.
• When a cart with a ball in the middle is quickly jerked forward, the back of the cart hits the ball.
• A block pulled to the left with 15 N and to the right with 5 N experiences a net force of 10 N.
• A tree stump pulled northward by a 10-N force and southward by a 25-N force has a resultant force magnitude of 15 N.
• The net force on a box of candy can vary, depending on the direction of paired 10-N forces.

Vector Quantities

• The resultant of two 10-N vectors at right angles to each other is approximately 14 N.
• A 40-N force at right angles to a 30-N force has a resultant of 50 N.
• When Nellie Newton hangs by a rope draped over a pulley, the tension in each supporting vertical strand is half her weight.
• The angle of the ropes affects the tension when Nellie hangs from a pair of ropes at an angle.
• The net force on any object in equilibrium is zero.
• The equilibrium rule, ΣF = 0, applies to objects or systems at rest and in uniform motion in a straight line.
• The applied force needed to maintain a constant velocity on a sliding object experiencing 10 N of friction is 10 N.
• When standing at rest on bathroom scales, the readings add up to equal a person's weight.
• Standing on tiptoes does not change a scale reading of a person's normal weight.

Orbital Mechanics

• Gravity causes Earth to orbit the Sun, inertia keeps it moving.
• A coin tossed in a train moving at a constant velocity lands as if at rest.
• If the train gains speed, the coin lands in back.
• If the train slows down, the coin lands in front.
• There's no adjustments needed for a gymnast performing somersaults in a plane moving at a constant velocity.
• When jumping vertically, you are moving horizontally just as fast as the wall, therefore the wall doesn't slam into you.
• The faulty reasoning that a bird dropping to a worm would miss due to Earth's rotation is countered by Newton's first law of inertia.

Relative Movement

• A mosquito flying at 3 m/s encountering a breeze blowing in the same direction at 3 m/s has a speed of 6 m/s.
• A mosquito flying at 3 m/s encountering a breeze blowing in the opposite direction at 3 m/s has effectively 0 m/s speed.
• Katelyn's speed relative to the ground depends on her running direction, when on a train that moves at 8 m/s, while she runs at 3 m/s.
• To hover in a 2-m/s breeze, a mosquito should fly against the breeze at 2 m/s.

Speed and Acceleration

• Jake's ground speed is 14 m/s, as he jogs at 4 m/s on a flatcar train that moves at 10 m/s in the same direction.
• Jake's speed relative to the ground is 6 m/s, as jogs at 4 m/s on a train flatcar that moves at 10 m/s in the opposite direction.
• A speedometer reads instantaneous speed.
• The measurements for calculating average speed are distance and time.
• Walking at an average speed of 4 m/s, in 5 s covers 20 m.
• A vehicle undergoes acceleration when it gains or loses speed, or changes direction . Acceleration and Inclined Planes
• An average speed of a horse that gallops 10 kilometers in 30 minutes is 20 km/h.
• On a track with a dip, a ball rolls along a horizontal track in less tim compared to a flat track.
• A ball rolls along a horizontal track in a smaller time, with a small upward dent the time increases to roll the length of the track.
• Despite constant speed, a car traveling around a circular track experiences non-zero acceleration.
• The acceleration is 6 m/s², for a car increasing its velocity from zero to 60 m/s in 10 seconds
• An object that covers 8 meters each second has zero acceleration.
• A cart maintaining a constant velocity has zero acceleration.
• A cart changing its speed from 90 m/s to 100 m/s in 10 seconds has an acceleration of 1 m/s².
• An object with constant acceleration changes its velocity by the same amount each second.
• Acceleration of a rock dropped from 2.5 m is the same as if from 5-m height which is 10 m/s². A car that has a speed of 6 m/s after 3 seconds as it is accelerating from rest at 2 m/s².
• A ball gaining a speed of 2 m/s each second it rolls down an inclined plane shows an acceleration down the incline of 2 m/s².
• A ball starting from rest at the top of an inclined plane accelerates at 2 m/s² and reaches in 3 seconds to the bottom is 9 m.

Time and Calculations

• Accelerating from rest at 2 m/s² it takez 15 s for a car to attain a speed of 30 m/s.
• Reaching a speed of 20 m/s after 5 seconds results in 4 m/s², for a car that starts from rest.
• A car has a speed of 4.0 m/s², 10 seconds after starting from rest given the car is moving at 40 m/s.
• For one minute at a rate of 50 m/s² a rocket that initially accelerates at rest will have a speed of 3000 m/s.
• The accelerations possible for a ball on an inclined plane range from zero to g.

Freely Falling Objects and Projectiles

• A freely-falling watermelon falls with constant acceleration.
• Speed increases in an iron block undergoing free fall near Earth's surface.
• The distance a freely falling bowling ball falls increases each second.
• A freely-falling cantaloupe has a speed of more than 100 m/s, 12 seconds after starting from rest.
• About 10 m/s is ground speed if an falling apple travel 5 meters below from a tree .
• A depth of about 180 m happens if an falls to the bottom of a mineshaft in 6 seconds.
• Due to a speedometer, a freely falling object would increase an average of 10 m/s.
• The speed reading jumps 20 m/s on another planet with accleration due to gravity 20m/s^2.
• Amount of distance travels keeps growing when measuring with an odometer during free fall, distance the object travels grow each succeeding second.
• If accleration on planet is twice earth, the freely falling object will have a speed one second later of 20 m/s.
• Its same speed compared with its initial speed when the ball is thrown upwards and then returns to the same location..
• One second later its approximately 40m/s speed at one instant as heavy object is moving upward at 50 m/s.
• A none of the above distance is freely falling from rest in one-half secon.
• Its 5 m/s one half after starting to rest as a freely object is about to fall.
• An object has a speed of 100 m/s after 5 seconds, as an object falls freely from gravity of 20 m/s².
• The the first 5 seconds it falls a distance of 250 m, as planet falls freely twoice earth gravity as much on earth.
• After leaving the hand, the accleration is 10 m/s², as you throw a ball straight downward is (in the absence of air resistance).
• About 1 s has projectile fire up at 10 m/s to reach top of path.
• 2 s, the path reaching for projectile fired at 10 m/s, returns at stating point ,
• Neglecting air resistance, throwing a ball takes 6 seconds, then you must toss 30 m/s to return to level.
• Its 10 m/s² as ball is thrown, has accleration is when it upwards reaches very top.
• Has a distance of (100-5) m after a one second if bullet's velocity is 100 m/s.
• Acceleration is 10 m/s^2 as bullet after neglecting has been fired high cliff.
• Same for each bullet, as acceleration is just before hitting water from river compared to the water is is fired or just dropped.
• Same speed but as if neglecting, hits the ground, the edge is throw upward or down.
• Needs a speed of 50 m/s, negelecting with air resistance remains projected above ground.

Velocity

• Pot that falls from ledge hits ground 45 m below at 30 m/s , .
• Has full of 1 s is 1.2 m hangtime by basketball player achieve.
• Is greater hang time compared with time on Earth, .
• Get farther apart steady of rate .

Air Resistance Physics

• About 5 m/s speed later, the air throwing upwards on cliff the the force of .
• As the rocks speed is 15 m/s after two seconds, the edge is pushing on a a cliff.
• It is 10 m 2 later as throwing to rocks is at the cliff
• The velocity is vector, not speed.
• Has headwind, so has ground speed.

Speed Force Motion Examples

The questions are examples of applied speed, force and motion.