Forces, Momentum, & Gravity (Chapter 3)

Student Learning Objectives Recall and apply each of Newton’s Laws. Relate momentum to impact force. Use conservation of momentum to analyze motion. Describe gravity and its applications.

What is a force & when are forces balanced?  A force is the amount of push or pull on an object.  Forces can cause a change in motion; a net force results in acceleration. F net = ∑ F

 An object in mechanical equilibrium maintains its motion. There is no change.  F net = 0  Forces are balanced

Practice 1) If a car engine provides 700 Newtons of push, and there is 200 Newtons of opposing friction, what is the net force on the car? 2) When the car engine continues to provide 700 Newtons of push, but the friction force is increased to 700 Newtons, what is the net force on the car? Would this cause the car to stop?

More Practice 3) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why must you keep pressure on the accelerator? 4) A 150 lb person is standing still on the floor. What is the net force?

What are Newton’s Laws of Motion?  Newton’s 1 st Law of Motion: Inertia An object will remain at rest or maintain a constant velocity unless an unbalanced force causes the object’s motion to change.  Inertia is the tendency of an object to maintain its motion.

Examples of Inertia Quick stops Cornering Coffee on your dash The tablecloth trick

Mass  Inertia depends on mass.  Mass is a fundamental quantity. more mass  more inertia  harder to change motion

 Mass is the amount of material contained in an object. Empty 747 Jet160,000 kg Average Man73 kg 5¢ coin kg

Practice Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct?

 Newton’s 2 nd Law of Motion: F = ma An unbalanced force acting on a mass gives the mass an acceleration in the same direction as the unbalanced force. F = ma

friction  When an object is in motion, friction is always in the opposite direction of the motion.  The normal force is perpendicular to the surface. Support Force Big Box FfFf Motion Normal Force FNFN

Practice 1) If the force on a 5 kg mass is tripled, what will happen to the rate of acceleration? 2) A 2000 kg car engine provides 9800 N of push southward. The opposing frictional force is 1200 N. What is the average acceleration?

Weight  Weight is a force.  Weight is the gravitational force acting on a mass.  On Earth, 1 kg of mass weighs 9.8 Newtons or 2.2 pounds. W = mg

Practice 1) Does weight depend on volume? 2) Would 1 kg of mass weigh 2.2 pounds on the Moon? 3) If you were instantly transported to Mars, which would change: Mass? Weight? Inertia?

More Practice 4) A person weighs150 lb (667 N) on Earth. a)What is the mass of this person? b)What would a person weigh on Mars? The acceleration due to gravity on Mars is 3.72 m/s 2.

Vectors  Forces are vectors, and vector addition is the addition of both the size and direction of each quantity.  The resultant vector shows the result of two or more vectors acting simultaneously.

Practice An airplane’s speedometer reads 500 mph North. What is the net velocity of the airplane in each case? a)Wind is blowing North at 50 mph. b)Wind is blowing South at 50 mph. c)Wind is blowing East at 50 mph.

 Newton’s 3 rd Law of Motion: Action-Reaction When two objects interact, they create equal and opposite forces on each other. F 1 = −F 2

 To every action force there is an equal (in magnitude) and opposite (in direction) reaction force when two objects are in contact. Pushing on a Wall Bat & Ball Rockets

Space X

Practice If I give the chair a good push, it goes from rest to having a velocity, and then stops. How do each of Newton’s laws apply to this system?

What is momentum?  Linear momentum is the combination of mass (inertia) and velocity.  The greater the momentum, the harder it is to stop an object! p = mv

Practice 1) What is an example of a moving object that could have a large momentum because it has a large mass? 2) What is an example of a small object that could have a large momentum because it has a large velocity?

More Practice 3) Which has the most momentum? a)10,000 lb (4535 kg) 18-wheeler parked at the curb b)300 lb (136 kg) football player running 10 mph (4.46 m/s) c)150 lb (68 kg) sprinter running 22 mph (9.83 m/s) d)1200 kg car moving at 1 m/s

 Angular momentum is momentum in a circular path.  The angular momentum vector is perpendicular to the plane of the circular path. L = mvr L v

How does momentum affect the force of impact?  During an impact, the force of impact depends on how quickly the momentum is changed. Barrels & Divided Highway Carpet vs. Concrete F =  p t

Practice 1)What are some features of car design that decrease force of impact? 2)You (75 kg) are riding in your 2000 kg car at 30 m/s (67 mph) when suddenly a squirrel runs in front of you; you swerve, and hit a tree. If the duration of the impact is 1/2 of a second, what is the impact force?

More Practice 3) Two 2000 kg cars, each with a 75 kg person, are traveling toward each other with a speed of 30 m/s (67 mph); suddenly one swerves into the wrong lane and there is a head-on collision. If the duration of the impact is 1/2 of a second, what is the impact force on each car?

How is conservation of momentum applied?  The total momentum of an isolated system remains constant. Collisions & Ice Skaters p f = p i L f = L i

Practice 1) Two cars of equal mass collide. One is traveling West at 30 m/s, the other is at rest. Then there is an inelastic collision between the two cars. If linear momentum is conserved, what is the final velocity of each car? 2) An ice skater spins 5 m/s with outstretched arms. The radius of the circular path traced by her arms is 1 meter. Then she pulls her arms in, changing the radius of the circular path to 1/3 m. If angular momentum is conserved, what is her new spinning speed?

What is Newton’s description of gravity?  Newton’s Universal Law of Gravitation Every object with mass attracts every other object with mass, with a force that depends directly on the masses of the two objects and decreases with the distance squared. F g = GMm d 2

Gravity  Mutual force of attraction  All masses pull the same on each other!  Causes acceleration due to gravity g = 9.81 m/s 2

Practice 1) Would the acceleration due to gravity (9.81 m/s 2 ) be different for an object dropped from a high mountain top than it is at sea level? 2) If Earth had twice as much mass, would this change our weight? Would it change our mass? 3) How would the gravitational force change if the distance doubled?

More Practice 4) What is the gravitational attraction between Earth and a 75 kg person standing on the surface, at sea level (M E = 6 x kg, r E = 6.4 x 10 6 m)? What do we normally call this? 5) Is the gravitational force zero in space?

What are some effects of gravity?  The feeling of weightlessness occurs when an object and its reference frame accelerate at the same rate. Airplane drops Large “dip” in the road Freefall ride  If there is no support force, then objects will fall together.

Practice If you were standing on a bathroom scale in the elevator, how would the reading change as the elevator a)Accelerates up b)Accelerates down c)Free falls

Gravitational Effects Gravity is a Universal Force  Orbits  Atmospheres  Tides

 Our Earth-Moon system is changing.  Earth’s rotation is slowing ( seconds/century)  Our Moon is drifting away (3.8 cm/year)  The synchronous orbit of the Moon (same face)

Practice The Sun's tidal affects are weak compared to the Moon. Why?

What is Einstein’s description of Gravity?  Every object with mass creates a curvature of space-time.

 According to Einstein, mass does not create a force, but rather a warping of space which other objects follow.  Objects fall independent of their mass because they all follow the same path in curved space-time. More Mass = More Curvature