a c = v2 F = ma F = Gm 1m 2 r d out RMA = F out r 2 " = Fd sin# IMA = d in eff = RMA F in IMA = W out

Transcription

1 Name: Physics Chapter 7 Study Guide Useful Information: a c = v2 F = ma F = Gm 1m 2 r r 2 " = Fd sin# IMA = d in d out RMA = F out eff = RMA F in IMA = W out W in A Basic Understanding: Chapter 7 Odd Numbered Core Problems Chapter 7 Review Problems:! 2, 9, 14, 19, 24, 35, 39, 45, 50. Pushing to be Better: Chapter 7 Your Try Problems Chapter 7 Even Numbered Core Problems Chapter 7 Review Problems: , 18, 22, 23, 26, 27, 28, 29, 31, 33, 40, 41, 42, 46, 47, 48, 49. Standardized Test Prep Digging Deeper: Chapter 7 Review Problems: 32, 34, 44, 55.. Individual Inquiry Notes on Ch. 7 Equations: a c = v2 This is the equation for Centripetal Acceleration. Centripetal Acceleration r is the velocity squared divided by the radius. F = ma Everybody should be comfortable with F = ma by now. I am putting this in here to remind you that you do not need a separate equation for Centripetal Acceleration and Centripetal Force. You just need an equation for Centripetal Acceleration, and then you remember that to change an acceleration into a force, you multiply by the mass. Physics Ch. 7 Study Guide page 1 of 2

2 F = Gm 1m 2 r 2 This is the equation for the gravitational force between any two masses. Force is still measured in Newtons. m1 and m2 are the two masses. r is the center-to-center distance between the two masses. G is the Universal Gravitational Constant. It s value is given below. Do not confuse this with g = 9.81 m/s2. Little g is only valid as an acceleration near the surface of the earth. Big G is a constant with more complicated units, and it is valid anywhere in the universe (so far as we know). G = 6.67 "10 #11 N "m 2 kg 2 $ = Fd sin% The torque on an object is equal to the Force on an object multiplied by the straight-line distance between where the force is applied, and where the pivot point is on the object. The angle is included because we only want to include the part of the force that is perpendicular to the straight line connecting where the force is applied, and where the pivot point is. The little symbol $ is the greek letter Tau. You make it like a pi with one leg. IMA = d in We touched on this next three very briefly before, and we re not going to d out spend much time with them now either. IMA is the Ideal Mechanical Advantage. It is the break you would get on the force needed to do something because you are using a simple machine like a ramp, pulley or lever. It does not take friction into account. It is the ratio of the distances. RMA = F out RMA is the Real Mechanical Advantage. It takes into account friction. F in It is the ratio of the forces. eff = RMA IMA = W out Efficiency is a ratio of how much you actually changed the energy W in of something, divided by how much work you put into that something. Physics Ch. 7 Study Guide page 2 of 2

3 Name: Chapter 7 Worked Examples Physics 1) A plane, on approach into a city, is flying with a speed of 130 m/s. The pilot puts the plane into a banked turn so that the wings are at an angle of 30 to horizontal, but the passengers still feel a force straight down into their seats. a) What is the radius of the turn? b) How many g s is this turn? Your Try: A 220 g ball is swung in a horizontal circle on the end of a 0.45 m long string. The string makes an angle of 39 with the vertical. a) What is the tension in the string? b) What is the period of rotation of the ball? (time it takes to go once around) Physics Ch. 7 Worked Examples page 1 of 3

4 2) The earth orbits the sun every days at an average radius of 1.5 x m. The Universal Gravitational Constant is 6.67 x Nm 2 /kg 2. From just three numbers calculate the mass of the sun. Your Try: The moon orbits the earth every days at an average radius of 3.84 x 10 8 m. The Universal Gravitational Constant is 6.67 x Nm 2 /kg 2. From just three numbers calculate the mass of the earth. Physics Ch. 7 Worked Examples page 2 of 3

5 3) A uniform bar has a length of 128 cm. When a 1kg mass is added to one end, the balance point of the two objects is now 43 cm from that end. What is the mass of the bar? Your Try: A uniform bar has a mass of 435g and a length of 90 cm. What mass must you add to the end of the bar in order to shift the balance point to a point 21 cm from one end? Physics Ch. 7 Worked Examples page 3 of 3

6 Physics Chapter 7 Your Try Problems (Based on various worked examples.) 4) Video 7e: The coefficient of friction between your tires and a level parking lot is 0.7. What is the tightest radius turn you can make at 40mph without skidding? 5) Video 7h: Assuming a lot of simplifications...if you can squat your own body weight, what is the fastest speed you can ski (and carve) a 15m radius turn? 6) Video 7i: Use the radius and mass of the earth to show that the force on a 1 kg mass at the earth s surface is 9.81N. 7) Video 7L: In the pulley diagram below: a) How much rope do you need to pull in order to raise the mass by 0.75m? b) What is the Ideal Mechanical Advantage of this system? c) Assuming that the system is 85% efficient, what is the Real Mechanical Advantage of the system? d) Given that RMA, how much force would you need to apply to P in order to lift a mass of 20 kg?

7 Answers to Chapter 7 Your Try Problems Worked Example 1: A 220 g ball is swung in a horizontal circle... a) Tension = 2.8 N b) Period = 1.2 s Worked Example 2: The moon orbits the earth every days... Mass of Earth = 5.97E24 kg. Worked Example 2: A uniform bar has a mass of 435g grams. 4) Video 7e: The coefficient of friction between your tires and the road is Radius = 47 m 5) Video 7h: Assuming a lot of simplifications...if you can... max speed = 16 m/s 6) Video 7i: Use the radius and mass of the earth to show... Plug the correct data into the correct formula. 7) Video 7L: In the pulley diagram below... a) 3 meters b) IMA = 4 c) RMA = 3.4 d) Force at P = 57.6 N

8 Name: Physics Chapter 7 Core Problems 1) Choose the statement that is INCORRECT. a) A good road bike typically has a Real Mechanical Advantage less than one. b) In real pulley systems, adding pulleys increases the IMA but decreases the Efficiency. c) A ramp always has an Ideal Mechanical Advantage greater than one. d) A wrench with a longer handle will have a higher RMA than a short wrench. e) A lever without friction has a Real Mechanical Advantage equal to it s Efficiency. 2) A ball is attached to a string and you are swinging it horizontally over your head (in a circle). In order to make the ball fly straight forward, you should: a) Release the ball when it is directly in front of you. b) You can t make the ball fly straight forward, it will always curve a bit. c) Release the ball when it is even with your shoulder. d) It depends on the speed with which you are swinging the ball. e) Release the ball when it 45 forward of your shoulder. 3) Water in a bucket is swung in a vertical circle with a radius of 1.12 meters. The bucket is swung just fast enough so that the water just barely stays in the bottom of the bucket at the top of the swing. How long does it take for the bucket to be swung once around the circle? 4) A uniform bar has a mass of 375 g and a length of 0.86 m. When a block of wood is attached to one end of the bar, the balance point of the combination is 0.18 m from the block of wood. What is the mass of the block of wood? 5) The mass of the Sun is 1.99 x 1030kg, and the mass of Mars is 6.42 x 1023kg. The distance between them is 2.28 x 1011m. Find the gravitational force between the Sun and Mars. 6) What is the tangential velocity of a satellite that orbits 1000 km above the surface of the earth? (The mass of earth is 5.98 x kg. The radius of the earth is 6.38 x 10 6 m.) 7) A plane, on approach into a city, is flying with a speed of 150 m/s. The pilot puts the plane into a banked turn so that the wings are at an angle of 25 to horizontal, but the passengers still feel a force straight down into their seats. What is the radius of the turn? 8) An brick has a weight of 14.5N. It takes 10.0N to slide the brick 1.00m up a 25 incline. a) What is the Ideal Mechanical Advantage of this incline? b) What is the Real Mechanical Advantage of this incline? c) What is the efficiency of this incline? Physics Ch. 7 Core Problems page 1 of 1