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## The Laws of Motion

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**The Laws of Motion**Physics 2053 Lecture Notes The Laws of Motion**The Laws of Motion**Topics 4-01 Force 4-02 Newton’s First Law 4-03 Newton’s Second Law 4-04 Newton’s Third Law 4-05 Applications of Newton’s Laws 4-06 Forces of Friction The Laws of Motion**Force**Size 100 106 1020 1035 Types Range Gravitational Unlimited Electromagnetic Unlimited Weak Nuclear 10-12 m Strong Nuclear 10-15 m The Laws of Motion**Newton’s First Law**The magnitude of a force can be measured using a spring scale. A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The Laws of Motion**Newton’s First Law**If no external force acts Newton’s first law is often called the law of inertia. Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. The Laws of Motion**Newton’s First Law**When you sit on a chair, the resultant force on you is A) zero. B) up. C) down. D) depending on your weight. The Laws of Motion**Newton’s Second Law**Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. Force is a vector, so SF = ma is true along each coordinate axis. Units of Force SystemMassAcceleration Force SI kg m/s2 N = kg m/s2 British slug ft/s2 lb = slug ft/s2 The Laws of Motion**Newton’s Second Law**N mg A man stands on a scale inside a stationary elevator. Forces acting on the man Reading on scale The Laws of Motion**Newton’s Second Law**v N mg When Moving Upward With Constant Velocity Forces acting on the man Reading on scale The Laws of Motion**Newton’s Second Law**a N mg When Moving Upward With Constant Acceleration Forces acting on the man Reading on scale The Laws of Motion**Newton’s Second Law**N mg When Moving Downward With Constant Acceleration Forces acting on the man a Reading on scale The Laws of Motion**Newton’s Second Law**A constant net force acts on an object. Describe the motion of the object. A) constant acceleration B) constant speed C) constant velocity D) increasing acceleration The Laws of Motion**Newton’s Second Law**A constant force F acts on a block of mass m. which is initially at rest. Find the velocity of the block after time Dt. vo = 0 Dt = 5 s F = 20 N v= ? F m = 5 kg m The Laws of Motion**Newton’s Second Law (Problem)**F What average force is required to stop an 1100 kg car in 8.0 s if the car is travelling at 95 km/h? Newton’s 2nd Law The Laws of Motion**Newton’s Second Law**A net force F accelerates a mass m with an acceleration a. If the same net force is applied to mass 2m, then the acceleration will be A) 4a. B) 2a. C) a/2 D) a/4 The Laws of Motion**Newton’s Second Law (Problem)**Tmax a m mg The cable supporting a 2,125 kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? Newton’s 2nd Law The Laws of Motion**Newton’s Second Law (Problem)**a How much tension must a rope withstand if it is used to accelerate a 1200 kg car vertically upward at 0.80 m/s2. Newton’s 2nd Law The Laws of Motion**Newton’s Second Law**F F R Universal Gravitational Constant Gravitational Force: Gravitational Force is the mutual force of attraction between any two objects in the Universe. m M The Laws of Motion**Newton’s Second Law**The gravitational force between two objects is proportional to A) the distance between the two objects. B) the square of the distance between the two objects. C) the product of each objects mass. D) the square of the product of each objects mass. The Laws of Motion**Newton’s Second Law**Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force A) is cut to one fourth. B) is cut in half. C) doubles. D) quadruples The Laws of Motion**Newton’s Second Law**Two objects, with masses m1 and m2, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2m1 and 2m2, and the distance is changed to 4r. What is the magnitude of the new gravitational force? A) F/16 B) F/4 C) 16F D) 4F The Laws of Motion**Newton’s Second Law**F F “g” in terms of G g m R M The Laws of Motion**Newton’s Second Law**Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms. Mass is not weight: Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same. Gravitational mass mg mg = mi Inertial mass mi The Laws of Motion**Newton’s Second Law**m Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is: Weight = mg The Laws of Motion**Newton’s Second Law**Mass and weight A) both measure the same thing. B) are exactly equal. C) are two different quantities. D) are both measured in kilograms. The Laws of Motion**Newton’s Second Law**A stone is thrown straight up. At the top of its path, the net force acting on it is A) equal to its weight. B) greater than its weight. C) greater than zero, but less than its weight. D) instantaneously equal to zero. The Laws of Motion**Newton’s Third Law**F1 F2 Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. Action/Reaction Forces The Laws of Motion**Newton’s Third Law**N mg An object at rest must have no net force on it. If it is sitting on a table, the object exerts a downward force mg on the surface of the table. m The surface of the table exerts an upward force on the block, called the normal force. It is exactly as large as needed to balance the force from the object. The Laws of Motion**Newton’s Third Law**F If an upward force F is applied to the block, the magnitude of the normal force is N mg The Laws of Motion**Newton’s Third Law**F If a downward force F is applied to the block, the magnitude of the normal force is N m mg The Laws of Motion**Newton’s Third Law**Action-reaction forces A) sometimes act on the same object. B) always act on the same object. C) may be at right angles. D) always act on different objects. The Laws of Motion**Newton’s Third Law**A 40,000 kg truck collides with a 1500 lb car and causes a lot of damage to the car. A) the force on the truck is greater then the force on the car. B) the force on the truck is equal to the force on the car. C) the force on the truck is smaller than the force on the car. D) the truck did not slow down during the collision. The Laws of Motion**Newton’s Third Law**A golf club hits a golf ball with a force of 2,400 N. The force the golf ball exerts on the club is A) slightly less than 2400 N. B) exactly 2400 N. C) slightly more than 2400 N. D) close to 0 N. The Laws of Motion**Applications of Newton’s Laws**A block of mass m moving with a speed vo is brought to rest by a constant force F. Find the distance the block moves. vo = 20 m/s F = -10 N v= 0 F m = 5 kg m Dx Newton’s 2nd Law The Laws of Motion**Solving Problems with Newton’s Laws**N T T m1g m2g Find the acceleration of the two block system Forces on m1 m1 m2 a Forces on m2 The Laws of Motion**Solving Problems with Newton’s Laws**T T m2g m1g Mass 1 Find the acceleration of the two block system Mass 2 m2 m1 The Laws of Motion**Solving Problems with Newton’s Laws**y N mg sin(q) mg cos(q) x mg q q The Laws of Motion**Problem**A pair of fuzzy dice is hanging by a string from your rear-view mirror. While you are accelerating from a stoplight to 24 m/s in 6.0 s, what angle does the string make with the vertical? The acceleration of the dice a Newton’s 2nd Law The Laws of Motion**Solving Problems with Newton’s Laws**Three mass system - find acceleration T2 T1 F m 2m 3m The Laws of Motion**Solving Problems with Newton’s Laws**Three mass system - find T2 T1 T2 F m 2m 3m The Laws of Motion**Solving Problems with Newton’s Laws**Three mass system - find T1 T1 T2 F m 2m 3m The Laws of Motion**Solving Problems with Newton’s Laws**Three mass system - find T1 Or T2 T1 F m 2m 3m The Laws of Motion**Forces of Friction**You are standing in a moving bus, facing forward, and you suddenly fall forward. You can imply from this that the bus's A) velocity decreased. B) velocity increased. C) speed remained the same, but it's turning to the right. D) speed remained the same, but it's turning to the left. The Laws of Motion**Forces of Friction**N F fs mg Friction: Force of Static Friction m The Laws of Motion**Forces of Friction**N F fk mg Friction: Force of Kinetic Friction v m The Laws of Motion**Forces of Friction**Coefficients of Friction Steel on steel 0.74 0.57 Aluminum on steel 0.61 0.47 Copper on steel 0.53 0.36 Rubber on concrete 1.0 0.8 Wood on wood 0.25-0.5 0.2 Glass on glass 0.94 0.4 Waxed wood on wet snow 0.14 0.1 Waxed wood on dry snow ------ 0.04 Metal on metal (lubricated) 0.15 0.06 Ice on ice 0.1 0.03 Teflon on Teflon 0.04 0.04 The Laws of Motion**Forces of Friction (Problem)**a N mg Suppose that you are standing on a train accelerating at 2.0 m/s2. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? Frictional force Newton’s 2nd Law The Laws of Motion**Forces of Friction**The force that keeps you from sliding on an icy sidewalk is A) weight. B) kinetic friction. C) static friction. D) normal force. The Laws of Motion**Forces of Friction**y N F N mk F q f q f x mg mg Pulling a block with constant speed Pulling a block m The normal force The Laws of Motion**Forces of Friction**Pulling a block with constant speed y N F N mk F q f q m f x mg mg The frictional force The Laws of Motion