Honors Physics Second Quarter Test Review Name _______________________________________________________________ Date ___________________ Force and Newton’s Laws 1. Define force: something that causes acceleration 2. List the four basic forces: gravitational, electromagnetic, strong nuclear, weak nuclear 3. a. b. c. State Newton's three laws of motion: An object at rest will stay at rest and an object in uniform motion will stay in uniform motion unless acted on by an outside force. ΣF=ma For every action, there is an equal and opposite reaction. 4. What is inertia? The tendency of an object to resist changes in motion 5. What is mass? A measure of inertia. 6. What is weight? The force of gravity on an object 7. How do you relate mass to weight? Weight is mass multiplied times the acceleration due to gravity. 8. What is Hooke's law and what does it mean in words? F=-kx The force of a spring is proportional to the displacement and in the opposite direction. 9. What simplifying assumption do we make about the tension in a rope? The rope has no mass and the tension is the same throughout the rope. 10. What is the force acting on a 10.0 kg mass that causes a 2.0 m/s2 acceleration? ∑ F = ma = (10.0kg ) (2.0m / s ) = 20.N 2 11. What is the weight of a 5.5 kg mass? mg=(5.5kg)(9.8m/s2)=54N 12. What is the mass of an object weighing 89 N on earth? m = 89 N = 9.1kg 9.8m / s 2 13. What is the weight of a 5.5 slug mass? mg=(5.5slugs)(32ft/s2)=180lb. 14. What is the mass of an object weighing 89 pounds on earth? m= 89lb = 2.8slugs 32m / s 2 15. If the acceleration due to gravity is 1.67 m/s2 on the moon, what is the weight of the object in #42 on the moon? mg=(5.5kg)(1.67m/s2)=9.2N 16. What is another name for Newton's first law? law of inertia 17. What is another name for Newton's third law? conservation of momentum 18. An object is suspended from a spring scale. What happens to the scale reading if the scale and object are accelerated upward? increases accelerated downward? decreases_ dropped in a vacuum? equals zero 19. How would you break Sting A in the picture below? How would you break string B? Why does this work in either case? Pull gently on the loop; pull quickly on the loop; inertia. String A Weight String B Loop 20. Is it necessary to have an atmosphere on a planet to launch a rocket there? yes or no (circle one) 21. Which one of Newton's laws explains the recoil of a gun? 3rd 22. There are three forces acting on a 30.0 kg mass: 20.0 N, 90.0º; 10.0 N, 0º, and 35.0N, 45.0º. Find the magnitude of the resultant force and the resulting acceleration. Express your first answer in Newtons and your second answer in m/s2. F 20N Theta 90º x 0 y 20 10N 0 10 0 35N 45º 24.7 24.7 34.7 34.7 R = Fx2 + Fy2 = (34.7 N ) 2 + ( 44.7 N ) = 56.7 N 2 Fy Fx θ = tan −1 56.7 N , 52.2 −1 44.7 N = tan = 52.2 N 34.7 23. A 20.0 kg object and a 5.0 kg object are suspended from Atwood's machine. What is the tension in the rope and the acceleration of each object when the system is released from rest? (5kg)(9.8m/s2)=49N 5 kg (20kg)(9.8m/s2)=196N for the whole system: ∑ F = ma (20kg )(9.8m / s 2 ) − (5kg )(9.8m / s 2 ) = (25kg )a 20 kg 5 kg a = 5.88m / s 2 for the 5 kg mass: ∑ F = ma T − mg = ma T = mg + ma = (5kg ) 9.8m / s 2 + 5.88m / s 2 T = 78.4 N 24. Find the tension in the ropes shown below: T1 = mg = (10kg )(9.8m / s 2 = 98 N ∑F ∑F rref x = 0 = T2 cos80 − T3 cos 35 y = 0 = T2 sin 80 + T3 sin 35 − 98 N −1 35.0º 80.0º cos80 − cos 35 0 sin 80 sin 35 98 T2 = 88.6 N T3 = 18.8 N 10.0 kg 25. Why do rockets use multiple stages? More efficient use of fuel. 26. Why do satellites orbit outside of the Earth’s atmosphere? So they aren’t burned to a crisp by friction. 27. Define microgravity. Microgravity is when there are few gravitational effects because something is in free fall. This is experience on objects orbiting the Earth or things like the Vomit Comet. 28. Explain the differences (or lack of difference) in the Earth behavior and the microgravity behavior of the following toys: flapping bird The bird only flies by soaring in space. The flapping wings cause it to rotate, not fly in space. spring jumpers There are no differences. klackers It is only possible to do the round and round clacker in space. Astronauts couldn’t do the up and down motion. Applications of Newton’s Laws 29. What factors affect friction between solid objects? types of materials smoothness lubrication magnitude of the normal force 30. What is kinetic friction? friction between two surfaces that are moving with respect to each other 31. What is static friction? friction between two surfaces that are stationary with respect to each other 32. How do static and kinetic friction compare? static is greater 33. Define normal force. a force exerted by one object on another that is perpendicular to the surface boundaries 34. If the coefficient of friction between a wall and a picture frame is 0.30 and the frame has a mass of 10.0 kg, what horizontal force is required to keep the frame on the wall? ∑F y = 0 = f − mg f f = mg = (10kg )(9.8m / s ) = 98 N f = µN f 98 N = 327 N N= = µ .3 2 ∑F x N N =0= N −P mg P = N = 330 N 35. If a horizontal push of 3.00 N is required to push a 20.0 kg carton across a floor at constant velocity, what is the coefficient of kinetic friction between the floor and the carton? ∑F y = 0 = N − mg P N = mg = (20kg )(9.8m / s 2 ) = 196 N f k = µk N = µ k (196 N ) ∑F x = 0 = fk − P f k = P = 3 N = µk (196 N ) 3N = 0.0153 µk = 196 N f P=3.0N mg 36. A skier starts at the top of a 200.0 m long incline that has a slope of 10º. If she starts from rest and has a mass of 50 kg, how long will it take her to reach the bottom? What will her final velocity be? Assume a kinetic friction coefficient of 0.09 and that the air resistance is a constant force of 20 N. ∑F y =0 N = mg cos θ f k = µk N = µ k mg cos θ = 0.09(50kg )(9.8m / s 2 ) cos10 = 43.43 N ∑F x = ma = mg sin θ − f k − FAR (50kg )a = (50kg )(9.8m / s ) sin10 − 43.43 N k − 20 N 2 a = 0.433m / s FAR N fk 2 v 2f = vi2 + 2a∆x mg v f = 2(0.433m / s 2 )(200m) = 13m / s 1 x f = xi + vi t + at 2 2 1 200m = 0 + 0 + (0.433m / s 2 )t 2 2 t = 30 sec 37. What is special about the motion of the center of mass of an object? it is a point in an object that behaves the same as if the entire mass was a particle located at that point 38. What is the difference between center of mass and center of gravity? Center of mass is independent of the gravitational field. If you have a really big object, like Mt. Everest, a kg at the top weighs less than a kg at the bottom. So, the center of gravity is actually below the center of mass for such a large object. 39. When are center of mass and center of gravity the same? For really small objects or objects that far from gravitational fields. 40. Who usually has a higher center of mass, males or females? (circle one) 41. A 50.0 kg dog is separated by 2.5 meters from a 7.0 kg cat. How far is the center of mass from the cat? xcm = 7 kg (0) + 50kg (2.5m) = 2.2m 7 kg + 50kg 42. In the previous problem, how far is the center of mass from the dog? 2.5 m – 2.2 m = 0.3 m 43. Find the center of mass of the following system of four particles: 2.5 kg 4.3 kg 4.2 kg 1.2 kg (2.1, 8.0 ) m (5.3, 4.0 ) m (2.1, 8.5 ) m (9.1, 4.7 ) m 2.5kg (2.2m) + 4.3kg (5.3m) + 4.2kg (2.1m) + 1.2kg (9.1m) = 3.9m 2.5kg + 4.3kg + 4.2kg + 1.2kg 2.5kg (8.0m) + 4.3kg (4.0m) + 4.2kg (8.5m) + 1.2kg (4.7 m) = = 6.4m 2.5kg + 4.3kg + 4.2kg + 1.2kg xcm = ycm 44. Find the center of mass of the four bricks shown below. Each brick is 2" by 6 ". m(1") + m(0) + m(3") + m(5") = 2.25" 4m m(7") + m(3") + m(1") + m(−3") = = 2" 4m xcm = ycm Lab Work 45. Describe methods to .... (also discuss any relevant advantages of your method) determine whether an object is in uniform motion -object travels equal distances in equal times determine mass without using the object’s weight -describe use of inertial pendulum determine the initial velocity of a gun or arrow leaving a bow -shoot straight up, measure maximum height, use 4th kinematics equation Gravity & Kepler’s Laws 46. State the contribution of each of the following scientist to the development of Newtons' Universal Law of Gravitation: Ptolemy: Alexandrian astronomer who thought the Earth was the center of the Universe Copernicus: Polish astronomer that first proposed a heliocentric Universe in the Middle Ages Galileo: developed kinematics, discovered sunspots and the moons of Jupiter’s disproving a geocentric Universe, invented a thermometer Kepler: developed 3 laws of planetary motion Brahe: supplied Kepler with the observational data he used to determine his 3 laws of planetary motion 47. State Kepler's laws of planetary motion: 1: The planets travel around the Sun with elliptical orbits with the Sun as one focus. 2: A line connecting a planet to the Sun sweeps out equal areas in equal times. 3: The period of a planet’s orbit squared is proportional to the radius of the orbit cubed. (T2 α r3) 48. State Newton's law of universal gravitation: F= Gm1m2 r2 49. What would happen if you fell into a tunnel that passed through the center of the earth and went to the other side and why? • • • As you first fall in, you accelerate toward the center of the Earth. But the rate of your acceleration decreases as you fall toward the center and your velocity increases. This is because as you fall more and more of the Earth’s mass is above you canceling out the gravitational pull of the mass below you. You would reach the maximum velocity at the center of the Earth, but your acceleration would be zero because the force of all the mass around you would cancel out. You would keep moving, though. You would start decelerating because more of the Earth’s mass would be above you and pulling you back that way. At the other side of the Earth, your velocity would be zero. You would begin accelerating back toward the center. This would continue forever if there was no friction. (It’s a form of simple harmonic oscillation.) 50. What would your weight be on a planet with the same mass as Earth, but a radius 1/10th the radius of the earth? mg = GMm GMm 2 = 100 r2 r 10 It would be 100 times greater. 51. What would your weight be on the same planet as the previous question if you climbed to the top of a ladder that made your distance from the center of that planet the same as the Earth's radius? The same. 52. What would the acceleration due to gravity at the surface of a planet with twice the mass of the Earth and 5 times the radius of the Earth? g= G2M 2 GM 2 = (5r) 25 r2 It would be 2/25th of Earth's g. 53. What velocity would be required to maintain a lunar orbit of 69 miles? Radius of moon = 1.74 x 106 m Mass of the moon = 7.36 x 1022 kg GM (6.67x10−11 Nm 2 / kg 2 )(7.36x10 22kg) v= = = 1629m /s 1610m r (1.74 x10 6 m + 69mi • mi 54. Three masses are placed at the corners of the isosceles triangle shown below. Find the net gravitational force on the 1.0 kg 1 Θ 2 = Θ3 = sin −1 = 20.9 2.8 G (1kg )(3kg ) F3 = , 20.9 + 270 = 2.55 x10−11 N , 291 (2.8m)2 G (1kg )(2kg ) F2 = , −20.9 + 270 = 1.70 x10 −11 N , 249 2 (2.8m) 1.0 kg 2.8 mmass. θ2 θ3 2.0 kg 3.0 kg 2.0 m F 2.55x10-11N 1.70x10-11N θ 291° 249° x 9.14x10-12N -6.09x10-12N 3.05x10-12N y -2.38x10-11N -1.59x10-11N -3.97x10-11N F = (3.05x10-12i – 3.97x10-11j) N 55. The planet Venus has a diameter of 12,103.6 km and a mass of 4.869 x 1024 kg. It takes Venus an unusually long time to rotate on its axis and it rotates in the opposite direction of all of the other planets. If it rotates on its axis once every 243 Earth days, what altitude would be required for a synchronous satellite? 86400 sec 7 T = (243days ) = 2.1x10 sec day 2π r GM = T r 2 2 4π r GM = 2 T r 1 2 3 24 7 GMT 2 G (4.869 x10 kg ) ( 2.1x10 sec ) = = 1.54 x109 m r = 2 2 4π 4π 12,103, 600m = 1.53 x109 m h = r − rv = 1.54 x109 m − 2 1 3 Units 56. Complete the table with as many different units as possible: mass length time speed velocity acceleration period of rotation frequency of rotation force weight tension friction coefficient of static friction coefficient of kinetic friction spring constant kg, g, slugs meters (and all the prefixes), miles, Astronomical Units, feet seconds m/s, ft./sec, mph m/s, ft./sec, mph m/s2, ft/sec2, mi/hr2 seconds revolutions per second, sec-1, Hertz Newtons (kgm/s2) dynes (gcm/s2) pounds (slugft/s2) Newtons (kgm/s2) dynes (gcm/s2) pounds (slugft/s2) Newtons (kgm/s2) dynes (gcm/s2) pounds (slugft/s2) Newtons (kgm/s2) dynes (gcm/s2) pounds (slugft/s2) unitless unitless N/m lb./ft.