Physics 111. Lecture 8 (Walker: 5.1-3) Force (F) Mass (m) Newton s 2 nd Law: F = ma. Summary - 2D Kinematics. = (20.0 m/s)(6.

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1 Physics Lecture 8 (Walker: 5.-3) Force (F) Mass (m) Newton s nd Law: F = ma Example: A Supply Drop Helicopter drops supply package to flood victims on raft. When package is released, helicopter is 00 m directly above raft and flying at velocity 5.0 m/s at angle 36.9 above horizontal. [Neglect air resistance]. (a) How long is package in air? (b) How far from raft does package land? Sept. 8, 009 g Lecture 8 /6 Lecture 8 /6 v = v sin θ = (5.0 m/s)(sin36.9 ) = 5.0 m/s; v = v cos θ = 0.0 m/s 0y 0 0 0x 0 0 yt () = v yt gt = 0-00m = (5.0 m/s)t - (0.5)(9.8 m/s )t t (5.0 m/s) ± (5.0 m/s) (9.8 m/s )( 00 m) (9.8 m/s ) t = 3.4 s and t = 6.30 s x= xh = v0 xt = (0.0 m/s)(6.30 s) = 6 m The package will hit the water 6 m from raft. Lecture 8 3/6 g Summary - D Kinematics Components of motion in the x- and y- directions can be treated independently. In projectile motion, the y-component of acceleration is g; there is no x- acceleration. If the launch angle is zero, the initial velocity has only an x-component. The path followed by a projectile is a parabola. The range is the horizontal distance the projectile travels. Lecture 8 4/6

2 Forces Fundamental Forces Usually think of a force as a push or pull Vector quantity: size & direction May be contact or field force Types Strong Nuclear Force Electromagnetic force Weak nuclear force Gravity Characteristics All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics Lecture 8 5/6 Lecture 8 6/6 Newton s First Law External force any force that results from the interaction between the object and its environment Statement of Newton s st Law: When there is no net external force acting on an object, the acceleration of the object is zero. Inertia and Mass Inertia is the tendency of an object to continue in its original motion Mass (symbol m) is a measure of the inertia, i.e resistance of an object to changes in its motion caused by a force Recall: mass is a scalar quantity SI Unit of mass: kilograms (kg) Lecture 8 7/6 Lecture 8 8/6

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 8 9/6 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 st Law, and it is also known as the Law of Inertia. Mass is the measure of how much inertia an object has. Lecture 8 0/6 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 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 8 /6 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 8 /6

4 Acceleration vs. Force Using a calibrated force gauge, we can do experiments to see what determines acceleration.. Acceleration is proportional to force: F a Acceleration vs. Mass. Acceleration is inversely proportional to mass: M a F a M a Lecture 8 3/6 Lecture 8 4/6 Newton s Second Law of Motion Combining these two observations gives F F a, and choosing appropriate units we can make a = m 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: newton = N = kg m/s. Lecture 8 5/6 Example: Accelerated Mass m A net force of 3.0 N produces an acceleration magnitude of.0 m/s on an object of unknown mass. What is the mass of the object? F (3.0 N) m = = =.5 kg (.0 m/s ) a Lecture 8 6/6

5 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 0 x (.5 m) a = = = 0.50 m/s t (3.0 s) r a = (0.50m / s ) r r F = ma = 34N Lecture 8 7/6 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: (5-) Lecture 8 8/6 Combining Forces Forces add vectorially. Question Two forces are exerted on an object. Which third force would make the net force point to the left? r r r r F F F F n net = + + L = i= i (a) (b) (c) (d) Lecture 8 9/6 Lecture 8 0/6

6 Direction of Acceleration a = F net /m where F net = F + F + F 3 + The acceleration is in the same direction as the net force. Typical Forces Lecture 8 /6 Lecture 8 /6 Question 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? F = FM + FL + FC = 3(80.5 N) = 4.5 N a = F / m= (4.5 N) / (75 kg) = 0.3 N/kg = 0.3 m/s Lecture 8 3/6 Lecture 8 4/6

7 Newton s Third Law of Motion (b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown? F = FM FL FC = 80.5 N a = F / m= ( 80.5 N)/ (75 kg) = 0.07 m/s Lecture 8 5/6 Forces always come in pairs, acting on different objects: If Object exerts a force F on Object, then Object exerts a force F on Object. 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 8 6/6 Newton s 3 rd Law of Motion Some action-reaction pairs: Example: Pulling a Rope () A student pulls horizontally with a force of 00 N on a rope attached to a wall. Two students pulls on opposite ends of a rope with forces of 00 N each. Which tension is larger? a. T >T b. T =T c. T <T Lecture 8 7/6 Lecture 8 8/6

8 Question Small car is pushing a larger truck that has a dead battery. Mass of truck is much larger than mass of car. Which of following statements is true? a. Car exerts force on truck, but truck doesn t exert force on car. b. Car exerts a larger force on truck than truck exerts on car. c. Car exerts the same force on truck as truck exerts on car. d. Truck exerts a larger force on car than car exerts on truck. e. Truck exerts force on car, but car doesn t exert force on truck. Lecture 8 9/6 End of Lecture 8 Before the next lecture, read Walker Chapter Homework Assignments #4a should be submitted using WebAssign by :00 PM on Sunday, Sept. 0. Homework Assignments #5a should be submitted using WebAssign by :00 PM on Tuesday, Sept.. Lecture 8 30/6