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Transcript
© Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang Lecture 2 Newton's laws of motion Momentum When explaining changes in motion, it is necessary to consider the mass of the object as well as the velocity. Imagine an unknown object is moving really fast towards you, say at a speed of 20 m/s or 72 km/h. You probably would choose to get out of the way, but what if it is a mosquito? Imagine again an unknown object is travelling towards you at a slow speed of 5 m/s. You may choose to stay, but you are now told that it is an elephant. Therefore, velocity itself is no longer sufficient to describe the effect of change in motion. P is used to denote momentum and P = mv . The unit of momentum is kg m/s. Momentum is also a vector quantity that has the same direction as that of the velocity. Newton's First Law of Motion (Law of Inertia) Every object continues in its state of rest or uniform motion unless made to change by a non-zero net force The inertia of an object is its tendency to resist changes to motion, mass is the only measure of the inertia of an object. In other words, the greater the mass, the more difficult an object could change its motion. The net force is denoted by Fnet and mathematically, Fnet = 0 implies that the object is stationary or moving at a constant velocity (Note constant velocity means both magnitude and direction are not changed). Example The small triangular block is placed on the big one, the surface between the two blocks is frictional and the top surface of the small triangular block is smooth. A smooth ball is placed on the surface of the small triangular block and the small triangular block is released from rest, what will be the path of the motion of the ball? Newton's Second Law of Motion The rate of change in momentum is directly proportional to the magnitude of the net force and is in the direction of the net force. ∆P m∆v Mathematically Fnet = = = ma , the net force has the same direction as that of the acceleration. ∆t ∆t Drawing diagrams and force analysis are critical to solving problems of Newton's Second Law. Newton's Third Law of Motion Whenever an object applies a force (an action) to a second object, the second object applies an equal and opposite force (a reaction) to the first object distinction similarity Physics A pair of equilibrium forces A pair of action-reaction forces Acting on the same object Acting on two different objects Equal in magnitude and opposite in direction 1 © Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang Example A person standing on the ground is trying to raise an object by pulling down a rope over a pulley as shown in the diagram below. The mass of the person is 70 kg and the mass of the object is 20 kg. The object is accelerating uniformly at 0.5 ms-2. The friction between rope and pulley is negligible. Find the normal reaction force that the ground exerted on the person. Example Two students are conducting an experiment in which a block, m1, of mass 0.40 kg is being pulled by a string across a smooth surface. The string is attached over a smooth pulley to another mass, m2, of 0.10 kg. The second mass, m2, is free to fall vertically. This is shown in the figure below: The block is released from rest. What is the acceleration of the block m1? m1 m2 Example A block of mass 0.20 kg is held at point A against a spring which has been compressed by 10 cm as shown in the diagram below. The block is released, and is pushed by the spring across a smooth surface. When the block leaves contact with the spring at point B the block has a speed of 5.0 ms-1. At point C the block still has a speed of 5.0 ms-1. At point C the block encounters a rough surface that provides a constant friction force that brings it to rest at point D. The distance C to D is 2.0 m. What is the magnitude of the friction force? Physics 2 © Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang A ball hangs in a lift and rest against the smooth wall of the lift as shown in the diagram below. The mass of the ball is 2.0 kg and the angle made between the string and the wall is 37º. If the lift is accelerating upwards uniformly at 2.0 ms-2, what will be the tension in the string? (Assume g = 10 ms-2) θ A tractor, including the driver, has a mass of 500 kg and is towing a trailer of mass 1000 kg as shown in figure below. The tractor and trailer are accelerating at 0.50 ms-2. Ignore any retarding friction forces and the mass of the towing rope. The tractor and trailer start from rest. What is the magnitude of the net force on the system of the tractor and trailer? What is the tension in the rope connecting the tractor and trailer? How far does the tractor move in the first 6.0 s? Physics 3 © Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang Apparent weight The apparent weight is equal to the magnitude of the normal reaction force acting on a person. It can be considered as the perceived weight and in some cases different from the actual weight of a person. The actual weight is the universal gravitational force exerted by a reference planet on the person. Note the difference between apparent weightlessness and actual weightlessness Apparent weightlessness occurs when the normal reaction force acting on the person is ZERO i.e. N = 0 Actual weightlessness occurs when the gravitational weight force acting on the person is ZERO, only possible in deep space. i.e. W = 0 Typical apparent weight problems 1. Free falling Helen is carried up on a platform to the top. At the top, a trapdoor in the platform opens and Helen free falls. Approximately 100 m below the release point, a net catches Helen. Helen has a mass of 60 kg, the platform travels vertically upward at a constant speed of 5.0 ms-1. What is Helen's apparent weight as she travels up? As the platform approaches the top, it slows to a stop at a uniform rate of 3.0 ms-2. What is Helen's apparent weight as the platform slows to a stop? Physics 4 © Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang Helen then drops through the trapdoor and free falls. Ignore the air resistance. During her fall, Helen experiences 'apparent weightlessness'. Explain what is meant by apparent weightlessness by making mention of gravitational weight force and normal reaction force. 2. In an accelerating lift N N Going up Speeding up Going up Slowing down W Since N > W, the person will feel heavier W Since N < W, the person will feel lighter 3. At the top or bottom of a circular track N W N W N W If N = 0, the person will experience apparent weightlessness and maximum safe speed occurs when N = 0. If N = 0, the person will experience apparent weightlessness and minimum safe speed occurs when N = 0. N is always greater than W and the person would feel heavier. NOTE: This type is closely related to circular motion, so must be reviewed after completing circular motion. Physics 5 © Copyright FIRST EDUCATION 2011 0430 860 810 Nick Zhang Inclined plane problems and force analysis Force analysis is critical to finding the net force acting on an object and hence deciding the motion of the object. General steps as below should be followed closely: 1. Choose two perpendicular directions into which minimum number of forces acting on an object need to be resolved. 2. Perform vector addition on each resolved direction and determine the net force acting on the object. 3. According to Newton's Second Law of Motion Fnet = ma , determine the acceleration of the object. 4. Other important physical quantities such as displacement, time interval, initial velocity or final velocity could be found given the motion is of uniform acceleration. N N = W cosθ Fnet = W sinθ - Fr = ma Fr W cosθ W sinθ θ W W is the only force needs to be resolved into two perpendicular directions, one is parallel to the slope and the other is perpendicular to the slope. Example Nick is riding his sled on snow. Nick and the sled have a total mass of 80 kg. He travels downhill from A to B. The sled starts form rest. The angle of the slope is 30� . A is a vertical height of 12.8 m above B. At B he then travels along a horizontal snowfield to point C. From A to C (on snow) there is no friction force. What is the momentum of Nick and his sled at point C? At point C he runs off snow onto grass where there is now a constant friction force and he slows to a stop at D after a time of 6.0 s. What is the magnitude of the friction as he travels from pont C to point D? Physics 6