Physics 111. Lecture 9 (Walker: 5.1-4) Newton s 2 nd Law: F = ma Newton s 3 rd Law. February 16, 2009

Transcription

1 Physics 111 Lecture 9 (Walker: 5.1-4) Newton s nd Law: F = ma Newton s 3 rd Law February 16, 009 Lecture 9 1/3 Force Force: push or pull. Symbol F (also W and N ) Force is a vector it has magnitude and direction. SI unit of force: Newton (N) Lecture 9 /3

2 The Law of Inertia If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, a moving object will keep moving at a constant speed in a straight line (i.e., will move with constant velocity). This is Newton s 1 st Law, and it is also known as the Law of Inertia. Mass is the measure of how much inertia an object has. Lecture 9 3/3 Motion and Inertial Frames In order to change the velocity of an object (either velocity magnitude or direction), a net force is required. (Newton s 1 st Law) For Newton s Laws to be valid, we must use an inertial coordinate system, or inertial reference frame. An inertial reference frame is one which is not accelerating (can be stationary or moving at constant velocity). Accelerating reference frames are not inertial, and fictitious forces may appear. Lecture 9 4/3

3 Inertia In (a) the plane is flying horizontally at constant speed, and the tennis ball does not move horizontally. Inertial reference frame? In (b) the pilot suddenly opens the throttle and the plane rapidly gains speed, so that the tennis ball accelerates toward the back of the plane. Inertial reference frame? Was there a net force on the tennis ball in case (b)? Lecture 9 5/3 Acceleration vs. Force Using a calibrated force gauge, we can do experiments to see what determines acceleration. 1. Acceleration is proportional to force: F a 1 1 F a 1 1 Lecture 9 6/3

4 Acceleration vs. Mass. Acceleration is inversely proportional to mass: M a 1 M 1 a 1 Lecture 9 7/3 Newton s Second Law of Motion Combining these two observations gives F a, and choosing appropriate units we can make a= m F m Or, more familiarly, This is the mathematical expression of Newton s nd Law of Motion. Units: Mass has SI units of kg, and acceleration has SI units of m/s. We define the SI unit of force as: 1 newton = 1 N = 1kg m/s. Lecture 9 8/3

5 Example: Accelerated Mass m 1 A net force of 3.0 N produces an acceleration of.0 m/s on an object of unknown mass. What is the mass of the object? m F (3.0 N) = = = 1.5 kg (.0 m/s ) 1 a 1 Lecture 9 9/3 Example: A Space Walk You are stranded in space. Fortunately, you have a propulsion unit that provides a constant net force F. You turn it on; after 3.0 s you have moved.5 m. If your mass is 68 kg, find F. x= v t+ at = at x (.5 m) a = = = 0.50 m/s t (3.0 s) r a = (0.50m / s ) r r F = ma = 34N Lecture 9 10/3

6 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: (5-1) Lecture 9 11/3 Combining Forces Forces add vectorially. r r r r F F F F n net = 1+ + L = i= 1 i Lecture 9 1/3

7 Question 1 Two forces are exerted on an object. Which third force would make the net force point to the left? (a) (b) (c) (d) Lecture 9 13/3 Direction of Acceleration a = F net /m where F net = F 1 + F + F 3 + The acceleration is in the same direction as the net force. Lecture 9 14/3

8 Typical Forces Lecture 9 15/3 Question Lecture 9 16/3

9 Example: Three Forces Moe, Larry, and Curley push on a 75 kg boat, each with a 80.5 N force parallel to dock. (a) What is the acceleration of the boat if they all push in the same direction? F1 = FM + FL + FC = 3(80.5 N) = 41.5 N a = F / m= (41.5 N) / (75 kg) = 0.31 N/kg = 0.31 m/s 1 1 Lecture 9 17/3 (b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown? a F = FM FL FC = 80.5 N = F / m= ( 80.5 N)/ (75 kg) = m/s Lecture 9 18/3

10 Newton s Third Law of Motion Forces always come in pairs, acting on different objects: If Object 1 exerts a force F on Object, then Object exerts a force F on Object 1. These forces are called action-reaction pairs. Alternate Wording: For every action there is an equal and opposite reaction. r F A on B r = F B on A Lecture 9 19/3 Newton s 3 rd Law of Motion Some action-reaction pairs: Lecture 9 0/3

11 Example: Pulling a Rope (1) 1 A student pulls horizontally with a force of 100 N on a rope attached to a wall. Two students pulls on opposite ends of a rope with forces of 100 N each. Which tension is larger? a. T 1 >T b. T 1 =T c. T 1 <T Lecture 9 1/3 Question A small car is pushing a larger truck that has a dead battery. The mass of the truck is much larger than the mass of the car. Which of the following statements is true? a. Car exerts a force on the truck, but truck doesn t exert a force on the car. b. Car exerts a larger force on truck than truck exerts on the car. c. Car exerts the same force on truck as truck exerts on the car. d. Truck exerts a larger force on car than car exerts on truck. e. Truck exerts a force on car, but car doesn t exert a force on truck. Lecture 9 /3

12 End of Lecture 9 Before the next lecture, read Walker Chapter Homework Assignments #5a should be submitted using WebAssign by 11:00 PM on Wednesday, Feb. 18. Lecture 9 3/3