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AP1 – 100 Questions Solutions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. The two entities that comprise a vector are directions and magnitude. For any vector that is not on the x or y axis or must find the x and y components of that vector. The adjacent component is always related to the cosine of the angle. The opposite component is always related to the sine of the angle. Vectors can be added using tip to tail method for two or more vectors or by using parallelogram method with only two vectors. Velocity is a vector and how fast something is going and in what direction. Speed is a scalar and only indicates how fast an object is going. The slope of the distance – time graph is the velocity. Acceleration is the rate of change of velocity (a change in velocity over time). The area under a velocity-time graph is the change in position (or displacement). The slope of the velocity time graph is acceleration. The y intercept on a velocity time graph is the initial velocity (vo). The area under the acceleration-time graph is the velocity. The horizontal acceleration of a projectile is zero. The vertical acceleration of a projectile is 9.8 m/s2. The vertical velocity of the projectile decreases as a projectile rises to its highest point and increases as the projectile falls back down to the ground. The horizontal velocity of the projectile remains constant (because the horizontal acceleration is zero). The initial vertical velocity is zero. The dropped object and the horizontally launched object land on the ground at the same time. 𝑦 = −12𝑔𝑡 2 or 𝑦𝑜 = 12𝑔𝑡 2 depending on the reference frame you choose and which variable y or yo is zero. 𝑥 = 𝑣𝑜𝑥 𝑡 𝑣𝑦 = 𝑣𝑜𝑦 − 𝑔𝑡 => 𝑣𝑦 = −𝑔𝑡 The speed of a projectile t seconds after it starts moving is the same as is the initial horizontal speed. 𝑣𝑦 = 𝑣𝑜𝑦 − 𝑔𝑡 The projectile has the same speed at points B & D. The horizontal velocity is the same for the all points. The direction of the acceleration at all points is down. The vertical velocity is zero and thus has no velocity at point C. The implication of an object not horizontally accelerating is that the horizontal speed will be constant and that the net force (horizontally) is zero. The implication of an object not vertically accelerating is that the vertical speed will be constant and that the net force (vertically) is zero. Inertia is the resistance to an objects change in motion. There is a direct relationship between an object’s mass and it’s inertia. The bigger an object is, the more it will resist its current state of motion….and vice versa. Inertial mass refers to a mass’s resistance to acceleration. Gravitational mass refers to the strength of the gravitation force experienced by the mass. N1L: Objects in Motion stay in motion, objects at rest stay at rest…unless a net force changes that motion. N2L: Net forces cause masses to accelerate 𝛴𝐹 = 𝑚𝑎 N3L: Objects push on each other with equal and opposite force. The sum of forces are zero when an object does not accelerate (at rest or constant speed). The sum of forces are not zero when an object does accelerate. The force of gravity (weight) is always present. => 𝑤 = 𝑚𝑔 37. Net force is depicted by showing all forces acting horizontally and vertically. Together they describe any horizontal or vertical net force. 38. 𝛴𝐹 = 𝑚𝑎 or 𝐹𝑐𝑎𝑢𝑠𝑖𝑛𝑔 − 𝐹𝑜𝑝𝑝𝑜𝑠𝑖𝑛𝑔 = 𝑚𝑎 39. 𝛴𝐹 = Σ𝑚𝑎 or 𝐹𝑐𝑎𝑢𝑠𝑖𝑛𝑔 − 𝐹𝑜𝑝𝑝𝑜𝑠𝑖𝑛𝑔 = Σ𝑚𝑎 40. A normal force is a force applied from a surface onto an object. It is ALWAYS applied perpendicular from the surface onto the object. 41. The component of Fg that points down the slope is mgsinθ. 42. The normal force = weight, because the opposing forces equal each other…because an object placed on a horizontal surface does not accelerate…therefore opposite forces are equal. 43. When pulling up on a mass at some angle above the horizontal, there will be three vertical forces. Normal force (n) and Fsinθ will both point up. Weight (𝑤 = 𝑚𝑔) will point down. Therefore 𝑛 + 𝐹𝑠𝑖𝑛𝜃 = 𝑚𝑔 … solve for n and we get 𝑛 = 𝑚𝑔 − 𝐹𝑠𝑖𝑛𝜃. 44. When pushing down on a mass at some angle below the horizontal, there will be two forces that point down (weight and Fsinθ) and one that points up (normal force) 𝑛 = 𝑚𝑔 + 𝐹𝑠𝑖𝑛𝜃. 45. Terminal velocity is when air resistance and weight are balanced. 46. Terminal velocity is reached when the downward pull of gravity (weight) is equal the air resistance from below. The acceleration due to gravity (9.8 m/s2) drops to zero. 47. Air resistance (R) is equal to weight below. 𝑅 = 𝑚𝑔 48. Tangential velocity is calculated by taking the circumference (2πr) and dividing that by the time for one revolution (the period T). 49. A centripetal force is a center seeking force….and object moving in circular motion will experience a center pointing acceleration. Centripetal acceleration is not a change of speed but rather a change in direction. 50. Right, up, and left 51. Down, right, and up 52. Fc FBDs are depicted as forces pointed toward (or away) from the center of the circle. 𝑣2 53. Fc is the centripetal force => 𝐹𝑐 = 𝑚 𝑟 54. Force vectors that point toward the center of a circle are considered positive. Force vectors that point away from the center of the circle are negative. 55. Possible centripetal forces include friction, weight, normal force, and tension. 56. The work done on an object moving in a circle is zero….because the displacement (and velocity) are perpendicular to the centripetal force which causes the object to stay in a circle. 57. 𝐹𝑔 𝛼 𝑚1 ∗𝑚2 𝑟2 𝑚 => 𝐹𝑔 𝛼 (2)(3) (2)2 => 𝐹𝑔 𝛼 6 4 => 𝐹𝑔 𝛼 6 4 => 𝐹𝑔 𝑖𝑠 1.5 𝑡𝑖𝑚𝑒𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 58. 𝑔 = 𝐺 2 where G is the gravitational constant (6.67 x 10-11) 𝑟 59. Linear momentum is mass times velocity 60. Elastic collisions usually separate the two objects after collision. A perfect elastic collision also conserves kinetic energy as well as momentum. Inelastic collision stick together after colliding. Elastic collision => Inelastic collision => m1v1i m2v2i m1v1 f m2v2 f m1v1i m2 v2i (m1 m2 )v f 61. Impulse is an impact force caused over a small period of time and it will result in an object’s change in momentum. It is also the area under a force vs time graph. 62. Work can only be done by a parallel (or antiparallel) force applied over a certain distance. 63. Work is the area under a Force vs. Distance graph. 64. Work energy theorem states that the net work equals the change in kinetic energy. It links force and distance (the work) with a change in velocity. 65. Conservation of energy states that the total mechanical energy (Kinetic and Potential) remains constant. This means that energy (kinetic and potential) changes form. The general formula is 𝐸𝑖 = 𝐸𝑓 66. 𝐸𝑖 = 𝐸𝑓 + 𝑊𝑓 67. Kinetic energy lost is the loss of energy due to friction. 𝐾𝑙𝑜𝑠𝑠 = 𝐾𝑖 − 𝐾𝑓 68. 𝐾𝑙𝑜𝑠𝑡 = 𝑄 = 𝑚𝑐Δ𝑇 => this relates frictional heat loss to the heat transfer (Q) and the change in temperature (Δ𝑇). m is the mass and c is the specific heat capacity (individual ability to retain heat) 69. 𝑊𝑓 = 𝐾𝑙𝑜𝑠𝑡 = 𝑄 = 𝑚𝑐Δ𝑇 => 𝑓𝑑 = 𝑚𝑐Δ𝑇 70. Power is the rate of work done. It can be found by taking work divided by time. 71. At the equilibrium, the displacement is zero, velocity is a maximum, potential energy is zero (min), acceleration is zero (min), and kinetic energy is a maximum. 72. At the amplitude or maximum displacement, the displacement is maximum, the velocity is zero, potential energy is a maximum, acceleration is a maximum, and kinetic energy are zero,. 73. Horizontal oscillator => position vs time (position function) => 𝑥(𝑡) = 𝐴𝑐𝑜𝑠(𝜔𝑡) Velocity vs time (velocity function) => 𝑣(𝑡) = −𝐴𝜔cos(𝜔𝑡) Acc vs time (acceleration function)=> 𝑎(𝑡) = −𝐴𝜔2sin(𝜔𝑡) Vertical oscillator => position vs time (position function) => 𝑦(𝑡) = 𝐴𝑠𝑖𝑛(𝜔𝑡) Velocity vs time (velocity function) => 𝑣(𝑡) = 𝐴𝜔cos(𝜔𝑡) Acc vs time (acceleration function)=> 𝑎(𝑡) = -Aω2sin(ωt) 74. The period of simple pendulums depend on the length of the pendulum and gravity. T 2 L g period of oscillating masses on springs depend on the mass and the spring constant. T 2 m k . The 75. Angular position is theta (θ - rad), angular velocity (ω – rad/s), angular acceleration (α – rad/s2) v r a r 76. s r 77. The rotational inertia is a resistance of an object ability to rotate about some point on itself or about some other point (for particles). The quantities involved in rotational inertia are mass and the radial distance to the point of rotation. 78. Torque is the tendency to rotate because of an applied perpendicular force. It is calculated by multiplying the perpendicular component of force by the distance of lever arm (distance from force to point of rotation). 79. L I 80. L mvr 81. Angular momentum is conserved when there is no net torque acting on the object. 82. Angular momentum is conserved in this case of a diver trying to do three somersaults before hitting the water. As the diver tucks in their legs, they reduce their “radius” and thus their rotational inertia is smaller, making their angular velocity larger…which means they are able to spin more times before hitting the water. 83. Electric force occurs between two CHARGES separated by a distance, while gravitational forces occur between two MASSES separated by a distance. Electric forces can be attractive (opposite charges) or repulsive (like charges), while gravitational forces are ONLY attractive. 84. q (charge) and E (electric field) take the place of m and g. 85. 𝐹𝑒 𝛼 𝑚1 ∗𝑚2 𝑟2 => 𝐹𝑒 𝛼 (2)(3) (2)2 => 𝐹𝑒 𝛼 6 4 => 𝐹𝑒 𝛼 6 4 => 𝐹𝑔 𝑖𝑠 1.5 𝑡𝑖𝑚𝑒𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟. Electric force is an inverse square law just like gravitational force. 86. E kq r2 87. Use q when dealing with point charges the resulting forces, electric field, or electric potential (voltage). Use Q when dealing with the charge stored on a capacitor. 88. An electric field is what forces a charge to move. 89. The ease with which charges can be moved is voltage. Voltage is the work done to move an individual charge in an electric field. 90. The actual movement of charges along a conductor is known as current. Current can be measure by finding the amount of current passing a point in a certain amount of time. V P IV , P I R , P R 2 91. V IR (Ohm’s Law), 92. In a series circuit, current stays the same and voltage adds. 93. In a parallel circuit, voltage stays the same and current adds. 94. Both transverse and longitudinal waves carry energy. However longitudinal waves vibrate parallel to the direction of the wave energy and transverse waves vibrate perpendicular to the direction of wave energy. An example of a longitudinal wave is a sound wave. An example of a transverse wave is any electromagnetic wave. 2 95. v f …. Wave speed is directly proportional to both wavelength and frequency. Wavelength is inversely proportional to the frequency. 96. Energy is directly related to frequency and inversely proportional to wavelength. 97. On a sinusoidal wave (transverse wave), the wavelength is found by measuring to the same point on the next wave. The amplitude is the maximum displacement from the equilibrium position (midline on the graph)…i.e. it is the height or depth of the wave from the midline. 98. For string and open tubes, the wavelength is twice the length ( = 2L). For tubes closed at one end, the wavelength is four times the length ( = 4L). 99. Aim High!!!!! 100. You need to be IN CONTROL!!!