NEWTON’S LAWS OF MOTION

1. NEWTON’S LAWS OF MOTION

2. The space shuttle Endeavor lifts off for an 11-day mission in space. All of Newton’s laws of motion - the law of inertia, action-reaction, and the acceleration produced by a resultant force -are exhibited during this lift-off. Credit: NASA Marshall Space Flight Center (NASA-MSFC). NASA

3. Objectives: Students should be able to: • Write Newton’s second law using appropriate units for mass, force, and acceleration, and use it to solve problems. • Demonstrate your understanding of the distinction between mass and weight. • Draw free-body diagrams for objects at rest and in motion. • Explain Newton’s first and third laws

4. Newton’s First Law (AKA The Law of Inertia) Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force. A glass is placed on a board and the board is jerked quickly to the right. The glass tends to remain at rest while the board is removed.

5. Newton’s First Law (Cont.) Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force. Assume glass and board move together at constant speed. If the board stops suddenly, the glass tends to maintain its constant speed.

6. Discuss what the driver experiences when a car accelerates from rest and then applies the brakes. (a) The driver is forced to move forward. An object at rest tends to remain at rest. Understanding the First Law: (b) Driver must resist the forward motion as brakes are applied. A moving object tends to remain in motion.

7. Newton’s Second Law: • Second Law: Whenever a resultant force acts on an object, it produces an acceleration: an acceleration that is directly proportional to the force and inversely proportional to the mass. Usually written as ∑F = ma

8. Pushing the cart with twice the force produces twice the acceleration. Three times the force triples the acceleration. Acceleration and Force With Zero Friction Forces

9. F F a/2 a Pushing two carts with same force F produces one-half the acceleration. The acceleration varies inversely with the amount of material (the mass). Acceleration and Mass Again With Zero Friction

10. Measuring Mass and Force The SI unit of force is the newton (N) and the unit for mass is the kilogram (kg). One newton is that resultant force which imparts an acceleration of 1m/s2to a mass of1 kg.

11. A 160-lb person weighs about 712 N 1N = 0.225 lb 1 lb 4.45N 1lb = 4.45 N Comparing the Newton to the Pound A 10-N hammer weighs about 2.25 lb

12. a= 2 m/s2 F = ? 6kg Example 1:What resultant force F is required to give a 6 kg block an acceleration of 2 m/s2? F = ma = (6 kg)(2 m/s2) F = 12 N Remember consistent units for force, mass, and acceleration in all problems.

13. First we find the acceleration a of plane. + F = 4.2 x 104 N F = ma m = 3.2 x 104 kg Example 2. A net force of 4.2 x 104 N acts on a 3.2 x 104 kg airplane during takeoff. What is the force on the plane’s 75-kg pilot? a = 1.31 m/s2 To find F on 78-kg pilot, assume same acceleration: F = 98.4 N F = ma = (75 kg)(1.31 m/s2);

14. When we say that the acceptable units for force and mass are the newton and the kilogram, we are referring to their use in physical formulas.( Such as F = m a) The centimeter, the millimeter, the milligram, the mile, and the inch may be useful occasionally in describing quantities. But they should not be used in formulas. A Note Regarding Consistency in Units

15. Problem Solving Strategy(For the Simpler Problems.) • Read problem; draw and label sketch. • List all given quantities and state what is to be found. • Make sure all given units are consistent with Newton’s second law of motion (F = m a). • Determine two of the three parameters in Newton’s law, then solve for the unknown.

16. Example 3.A 54-gtennis ball is in contact with the racket for a distance of 40 cm as it leaves with a velocity of 48 m/s. What is the average force on the ball? First, draw sketch and list given quantities: Given: vo = 0; vf = 48 m/s x = 40 cm; m = 54 g a = ? Consistent units require converting grams to kilograms and centimeters to meters: Given: vo = 0; vf = 48 m/s x = 0.40 m; m = 0.0540 kg; a = ? Cont. . .

17. 0 Example 3 (Cont). A 54-gm tennis ball is in contact with the racket for a distance of 40 cm as it leaves with a velocity of 48 m/s. What is the average force on the ball? Knowing that F = m a, we need first to find acceleration a: F = ma F = 156 N F= (0.054 kg)(2880 m/s2);

18. W g F = m aso that:W = mgand m = Weight and Mass • Weight is the force due to gravity. It is directed downward and it varies from location to location. • Mass is a universal constant which is a measure of the inertia of a body.

19. 10 kg m 9.8 m/s2 W Weight and Mass: Examples • What is the weight of a 10-kg block? W = mg = (10 kg)(9.8 m/s2) W = 98 N

20. 800 lb W = 3200 lb Inconsistent Common Usage In the United States, objects are often referred to by their weight at a point where gravity is equal to 32 ft/s2. You might hear: “An 800-lb force pulls a 3200-lb car.” This car should be called a 100-slug car. Thus, when an object is described as a _?_-lb object, we remember to divide by g to get mass.

21. F 10 kg Inconsistent Usage (Cont.) Even metric units are used inconsistently. Mass in kg is often treated as if it were weight (N). This is sometimes called the kilogram-force. A chemist might be asked to weigh out 200 g of a certain element. Also, you hear about a 10-kg load as if it were weight. The kilogram is a mass - never a force - and it doesn’t have direction or vary with gravity.

22. Always Remember!! In Physics, the use of Newton’s second law and many other applications makes it absolutely necessary to distinguish between mass and weight. Use the correct units! Metric SI units: Mass is in kg; weight is in N. USCU units: Mass is in slugs; weight is in lb. Always give preference to the SI units.

23. F = 40 N a8 m/s2 W=? Example 4.A resultantforce of 40 N gives a block an acceleration of 8 m/s2. What is the weight of the block near the surface of the Earth? To find weight, we must first find the mass of the block: W = mg = (5 kg)(9.8 m/s2) Now find weight of a 5-kg mass on earth. W = 49.0 N

24. Third Law:Forces occur in pairs, which are equal in magnitude and opposite in direction. (You can refer to them as action and reaction forces.) Action Action Reaction Reaction Newton’s Third Law:

25. Use the words by and on to study action/reaction forces below as they relate to the hand and the bar: Action Reaction Acting and Reacting Forces The action force is exerted by the _____ on the _____. bar hands The reaction force is exerted by the _____ on the _____. bar hands

26. Force on Board Force on Runner Example 5:A 60-kg athlete exerts a force on a 10-kg skateboard. If she receives an acceleration of 4 m/s2, what is the acceleration of the skateboard? Force on runner = -(Force on board) mrar = -mbab (60 kg)(4 m/s2) = -(10 kg) ab a = - 24 m/s2

27. Summary Newton’s First Law: An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force. Newton’s Second Law: A resultant force produces an acceleration in the direction of the force that is directly proportional to the force and inversely proportional to the mass, i.e. ∑F = ma Newton’s Third Law:Forces occur in pairs, which are equal in magnitude and opposite in direction.