1.8.1 Isaac Newton. Isaac Newton ( )

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1 1.8.1 Isaac Newton In 164, the year Galileo died, Isaac Newton was born in England on Christmas Day. His father had died three months earlier, and baby Isaac, very premature, was also not expected to survive. When he was three, his mother married a wealthy elderly clergyman from the next village, and went to live there, leaving Isaac behind with his grandmother. The clergyman died, and Isaac's mother came back, after eight years, bringing with her three small children. Two years later, Newton went away to the Grammar School in Grantham, where he lodged with the local apothecary (pharmacist), and was fascinated by the chemicals. The plan was that at age seventeen he would come home and look after the farm. He turned out to be a total failure as a farmer. His mother's brother, a clergyman who had been an undergraduate at Cambridge, persuaded Newton s mother that it would be Page 1 of 1 Isaac Newton ( ) better for Newton to go to university, so in 1661 he went to Trinity College, Cambridge. Newton paid his way through college for the first three years by waiting tables and cleaning rooms for the faculty and wealthier students. In 1664, he was elected a scholar, guaranteeing four years of financial support. Unfortunately, at that time the plague was spreading across Europe, and reached Cambridge in the summer of The university closed, and Newton returned home, where he spent two years concentrating on problems in mathematics and physics. He wrote later that during this time he first understood the theory of gravitation, and the theory of optics (he was the first to realize that white light is made up of the colors of the rainbow), and much mathematics, both integral and differential calculus and infinite series. However, he was always reluctant to publish anything, at least until it appeared someone else might get credit for what he had found earlier. Trinity College, Cambridge

2 Newton's first major public scientific achievement was the invention, design and construction of a reflecting telescope. He ground the mirror, built the tube, and even made his own tools for the job. This was a real advance in telescope technology, and ensured his election to membership in the Royal Society. The mirror gave a sharper image than was possible with a large lens because of chromatic aberration. Three problems intrigued scientists in Newton's time: the laws of motion, the laws of planetary orbits, and the mathematics of continuously varying quantities (now known as calculus). It may be fairly stated that Newton was the first to solve all three Newton s Three Laws of Motion 1.8.a Newton s First Law of Motion Newton summarized some of Galileo s ideas about motion to formulate the first law of motion. Scientists prior to Galileo thought that an object needed a net force to maintain constant velocity. Newton s First Law changed this thinking and is stated as: In the absence of forces, an object at rest will stay at rest, and an object that is moving at a constant velocity in a straight line will continue doing so indefinitely. 1.8.a-1 Implications of Newton s First Law Newton s first law is also known as the law of inertia even though it deals with both inertia and momentum. More specifically, it predicts that: 1. An object that is stationary will remain stationary unless an external applied force causes it to start moving. (the principle of inertia).. An object that is moving uniformly will continue to do so unless an external applied force causes its motion to change. (the principle of momentum). Page of 1

3 1.8.b Newton s Second Law Newton s Second Law of Motion is most often expressed as a formula. This formula relates the acceleration of an object with the net force that acts on the object and its mass. (1.7) It cannot be overstated how important this formula is to this course. A great number of word problems can be solved using Newton s Second Law. Eg.#1 The V- military rocket, used by Germany in 1945, had a mass of about 1,000 kg when loaded with fuel and 3,000 kg when empty. Its rocket engine created a thrust of 40,000 N. what was the acceleration of the V- a) at launch? b) at burn-out, just before it ran out of fuel? 1.8.c Newton s Third Law Newton's 3rd law may be formally stated: Forces always occur in pairs. If object A exerts a force onto object B, then object B exerts an equal and opposite force back onto object A or in slogan style: Every action force has an equal and opposite reaction force Note two important provisions: two objects must be involved and the forces act on different objects! Page 3 of 1

4 1.8.c-1 Applications of Newton s Third Law Some situations that Newton s Third Law help to illustrate its usefulness: 1. When water leaves a water nozzle, the nozzle forces the water forward and the water forces the nozzle backward. The nozzle of a big firehose has handles which firefighters must grasp firmly, because the nozzle is forced back.. When jumping from a boat, your feet push back on the boat and the boat pushes forward on your feet. Before jumping from a boat to the dock, it is wise to tie the boat to the dock first as it will move out from under you as you push on it. 3. When a bat hits a ball, the baseball forces the bat to the right (an action) and the bat forces the ball to the left (the reaction). Note that the nouns in the sentence describing the action force switch places when describing the reaction force Weight and Earth s Gravitational Field The weight of an object is defined as: the force exerted by the earth on that object. We can apply Newton s second law of motion to determine the weight of an object on earth. Recall Newton s Second Law: (1.8) The force that an object experiences due to the Earth s gravity (i.e. its weight) is equal to its mass multiplied with the acceleration that object would experience if it were released. On Earth, any object that is released will accelerate at 9.8 m/s toward the Earth. This number is given the symbol g and is called two things: the acceleration due to gravity the gravitational field strength From Newton s Second Law: Planet g Mercury 3.7 m/s Venus 8.8 m/s Moon 1.6 m/s Mars 3.6 m/s Jupiter 3.1 m/s Saturn 8.9 m/s Uranus 8.7 m/s Neptune 11.0 m/s Pluto 0.6 m/s On other planets, the value of g differs depending on the planet as shown above. Page 4 of 1

5 An interesting implication of this is that all objects will accelerate at the same rate regardless of their mass when undergoing free-fall. Eg.# Two masses are attached by a thin rope and pulled by an applied force of 10.0 N[right]. If the friction forces are 0.50 N[left] on the small mass and 0.70 N[left] on the large mass, a) find the net force acting on the system of masses b) find the acceleration of the masses. c) find the tension in the middle rope. Page 5 of 1

6 Eg.#3 Two masses are shown attached to a massless rope suspended over a frictionless pulley. a) Determine the magnitude and direction of the acceleration of each mass. Taking clockwise rotation of the pulley to be positive: 4.0 kg. mass (m 1) 4.5 kg. mass (m ) Setting these equal to one another, we obtain: The 4.0 kg. block accelerates at 0.58m/s [up] and the 4.5 kg. block accelerates at 0.58m/s [down]. b) Determine the tension in the rope. It is sufficient to find the magnitude of the tension force which we can do by evaluating either of the expressions for tension above: Page 6 of 1

7 Eg.#4 Two masses are shown attached to a massless rope suspended over a frictionless pulley on a frictionless ramp. a) Determine the magnitude and direction of the acceleration of each mass. Taking clockwise rotation of the pulley as positive: 4.5 kg. mass (m 1) 3.0kg. mass (m ) Setting these two expressions equal, The 4.5 kg. mass accelerates up the ramp at 0.55m/s and the 3.0 kg mass accelerates downward at 0.55m/s. b) Determine the tension in the rope. Once again, determining the magnitude of the tension is sufficient. Page 7 of 1

8 Worksheet # You apply a force of 0.35N.[up] to lift a fork. The resulting acceleration of the fork is 0.15m./s. [up]. Determine the mass of the fork.. A hot air balloon experiences an acceleration of 1.10 m./s. [down]. The total mass of the balloon, basket and contents is 315 kg. a) What is the upward buoyant force on the system? Page 8 of 1

9 b) The balloonist wants to change the acceleration to zero. There is no fuel left to heat the air in the balloon. Determine the mass of the ballast that must be discarded overboard. (Neglect air resistance). Therefore 35 kg. must be discarded 3. A tree house has a vertical fire pole of smooth metal, designed for quick exits. A child of mass 35.7 kg. slides down the pole with constant acceleration, starting from rest. The pole is 3.10m. high and the journey to the ground takes.00 seconds. a) What is the acceleration of the child? b) What is the force of friction exerted by the pole onto the child? Page 9 of 1

10 4. When an external net force is applied to a particular mass m, an acceleration of magnitude a results. When the mass is increased by.0 kg. and the same net force is applied, the acceleration is 0.37a. Determine the mass m. 5. A boy pushes a lawnmower (m = 17.9kg.) starting from rest across a horizontal lawn by applying a force of 3.9 N. directly along the handle, which is inclined at an angle of 35.1 degrees below the horizontal. The lawnmower accelerates at 1.37m./s. for 0.58 s. after which the mower moves at a constant velocity. Determine: a) The normal force on the mower Page 10 of 1

11 b) The force of friction on the mower. c) The maximum velocity of the mower. d) The force supplied by the boy in order to keep the mower moving at the same velocity. Page 11 of 1

12 6. Blocks A and B are connected by a string that passes over a frictionless pulley as shown below. When the blocks are moving, block A experiences a friction force of 5.7N.[back]. If m A=.7kg. and m B= 3.7kg. calculate: a) The acceleration of the blocks choosing CW rotation of the pulley as the positive direction: b) The tension in the string. Page 1 of 1

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