Newton's Second Law of Motion Chapter 4 Newton's Second Law of Motion

FORCE CAUSES ACCELERATION m a The combination of forces that act on an object is the net force. (Only the net force is shown in the figures on this slide.) F a m F a m This symbol means proportional to The acceleration of an object is directly proportional to the net force.

2. FRICTION Friction opposes the motion between surfaces in contact with one another. When there is a tendency for movement between two surfaces and yet there is no motion, the friction is static friction. Static friction has an upper limit. When there is motion between the two surfaces, the friction is sliding (kinetic) friction.

FA FA FA F F FA F FA F On the verge of slipping Sliding Maximum Static Friction Friction, F Sliding (Kinetic) Friction Applied Force, FA

Static and kinetic friction (In stopping a car, shoot for static friction.)

3. MASS AND WEIGHT slug) A slug weighs 32 lb. Every object possesses inertia (mass). Inertia is the sluggishness of an object to changes in its state of motion. Mass - a measure of the inertia of an object (Units - kg and slug) A slug weighs 32 lb. Inertia deals with how hard it is to start and stop an object.

Weight - force that earth exerts on an object (Units - N and lb) A Newton is approximately the weight of a small apple. Slide - Newton’s apple 1 kg weighs 2.2 lb. Mass and size are often confused. Galileo introduced inertia. Newton grasped its significance.

Chapter 4 Review Question

Which is a better way to get a feeling for the inertia of an object? (a) hold it in your hand (b) shake it back and forth

4. MASS RESISTS ACCELERATION The acceleration of an object not only depends on the force applied to an object but it also depends on the mass of the object.

a Consider the same net force applied to different mass objects. The acceleration is inversely proportional to the mass of the object. F m a

5. NEWTON’S SECOND LAW OF MOTION or The force in each of these equations represents the vector sum of all of the forces acting on the object of mass m. Units of force - N and lb

If the net force is parallel to the velocity, then the speed of the object increases. If the net force is anti-parallel to the velocity, then the speed of the object decreases.

Acceleration is always in the direction of the net force. If the net force is perpendicular to the velocity, the direction of the velocity changes. Acceleration is always in the direction of the net force.

For those asleep!!

Force is usually thought of as a push or pull. Examples - gravitational electrical "Force is anything that can accelerate an object.”

Net Force “Net” means the total force acting on an object. It is the vector summation of all the forces acting on the object. Net Force Video - Scale in Elevator

Force only changes the state of motion. Zero acceleration does not imply zero velocity. Demo - Spool and string Story - Wicked king & beautiful princess

THE WICKED KING AND THE BEAUTIFUL PRINCESS The Physics Teacher -- October 1971 -- Volume 9, Issue 7, pp. 387-388 Samuel Derman New York University and Hunter College, New York, N. Y. ©1971 American Association of Physics Teacher Once upon a time there was a terribly wicked King who had a daughter who was very beautiful. This daughter was in love with a handsome prince who didn’t take Physics 101, and before long the prince and the princess had become inseparable. The King, however, was wicked and did not believe in happiness and so he had his daughter locked up in a prison at the top of a tall tower.

The prince learned of this and was determined to rescue the one he loved, so he started out for the tower where the unhappy princess sat imprisoned. When he arrived at the base of the tower the prince looked up and noticed that there was a wooden beam protruding from the top of the structure. He immediately contrived a method to use this to reach his princess.

He attached a sturdy basket to one end of a very long rope and to the other end he tied a stone. Then with a mighty heave he threw the stone across the top of the beam so that the rope was looped across the beam. The prince had thus constructed a simple pulley. He then stepped into the basket, and since the pulley had a mechanical advantage of two, he proceeded to hoist himself up.

In due time the prince reached the top and was rewarded with a long embrace by the King’s daughter. The prince could not return the embrace, nor could he begin his work to release the princess, since letting go of the rope would cause the basket to fall. So he began searching for a way to fix the rope to the tower wall.

Luck seemed to be smiling on the young man because close by he discovered a metal hook imbedded in the stone wall. The prince tugged on the hook with one hand (the other hand holding the rope tightly), and finding it secure, he proceeded to tie the rope to the hook.

But the instant he did that, the supporting beam broke and the basket, together with the poor prince, came crashing to the ground. What had happened was this. The King, who was very wicked, also happened to have had Physics 101 (no connection between the two), and he had originally designed the beam to support the weight of the prince and the weight of the basket, but no more.

During the time the unsuspecting prince was hoisting himself up, the total load on the beam was simply his weight plus the weight of the basket. But as soon as one end of the rope was hooked onto the tower, the situation changed drastically. Now the weight of the prince plus the weight of the basket all exerted a force on one end of the rope while the tower, via the hook, pulled down on the other end with an equal and opposite force. The total force on the beam was now twice the original weight. The beam broke. Why?

Demo – Block and tackle

6. WHEN ACCELERATION IS g – FREE FALL Only force of gravity is acting on object All objects accelerate the same. a = g or F/m = g . The weight of an object of mass m is the force that the earth exerts on the object. W = mg . One kilogram weighs 9.8 Newtons. One slug weighs 32 pounds.

7. WHEN ACCELERATION IS LESS THAN g – NONFREE FALL Consider the net force acting on the object. The force due to air resistance depends on the size and speed of the object.

Terminal Velocity Net Force Acceleration = g Velocity = 0 but motion is about to begin mg F 0<Acceleration < g v increasing downward mg F 0<Acceleration << g v still increasing downward just not as rapidly as before mg F Acceleration = 0 Terminal velocity mg

Example: Mouse in a mine shaft Light and heavy parachutists

Chapter 4 Review Questions

Which of the following represents a situation when the acceleration of an object is not in the same direction as the net force acting on the object. (a) a bowling ball swinging by a cord attached to the ceiling (b) a car speeding up along a straight line on the highway (c) a book sliding to a stop on the top of a table (d) All of the above (e) None of the above

What is the magnitude of the acceleration of a 2 kg object when the net force on the object is 10 N? (a) 10 m/s2 (b) 20 m/s2 (c) 5 m/s2

If an object weighs 10 lb, what must the air resistance force be if the object is falling and has reached terminal velocity? (a) 10 lb (b) 32 lb (c) there is no way of telling without knowing what the value of the terminal velocity is