Grade 12 University Physics. Tutorial 1

Transcription

1 Grade 12 University Physics Tutorial 1 1 Wyle Coyote is initially 15 m behind the Roadrunner and steps into a VIPER GTS (Roadrunner Edition). The Viper (initially stationary) can accelerate at 7m/s 2. The Roadrunner (initially stationary) accelerates at 4 m/s 2. However, the Viper s top speed is only 120 km/hr and once the car reaches this speed it can no longer accelerate. a) Determine the time it takes for the Viper to catch the Roadrunner. b) Determine the speed of the Roadrunner when the Viper catches it c) Determine the speed of the Viper when it catches the Roadrunner d) Is the speed calculated in c greater then 120 km/hr. If so, does the Viper ever catch the Roadrunner? 2 A car travels 400 m [E20N] in 40 seconds, then turns [N] and travels 800 m in 85 seconds. The car then stops for 60 seconds and then travels 1000 m [W30S] in 120 seconds. Calculate a) the components for each displacement vector b) the resultant displacement for the x direction c) the resultant displacement for the y direction d) the resultant displacement (angle and magnitude) e) the total time of the trip f) the average speed g) the average velocity

2 Tutorial 2 1. A 5 kg box, initially at rest is dragged across a level floor with a force of 70 N (applied at an angle of 30 degrees relative to the horizontal). The box moves 10 m in 4 seconds. Determine a) normal force acting on the box (Ans: 14 N) b) the force due to friction (Ans: N) 2. A car is rounding a curve with a velocity of 72 km/hr. The coefficient of static friction between the tires of the car and the road is Determine the minimum turning radius required so that the car can turn without sliding if the curve is banked at an angle of 8 degrees. 3. Centripetal Motion A helicopter maintains a constant altitude and begins to travel in a circular pattern. In 3 minutes, the helicopter completes 2 cycles of motion. The centripetal acceleration of the helicopter is 2.2 m/s2. Determine the speed of the helicopter (Ans: 31.5 m/s). 4. Determine the coefficient of friction, if the acceleration of the system is 5 m/s/s. 5. A sled is traveling down a hill (whose surface is at a 25 degree angle relative to the horizontal), and the coefficient of friction between the sled and the surface of the hill is Determine the acceleration of the sled. (Ans: m/s/s) 6. A satellite has a speed of 7151 m/s above the earth s surface (mass is 5.98x1024 kg). The radius of the earth is 6.38x106 m. Calculate (Law of Gravitation, Centripetal force) a) the altitude of the satellite above the earth s surface b) the period of revolution around the earth 1.42x106 m 6853 seconds

3 Tutorial 3 A ping pong ball (mass is 15 grams) has an initial velocity of -0.5 m/s. As it makes contact with a racket, the force the ball experiences is 0.2 N for 250 milliseconds. Determine the final velocity of the ball (impulse). (2.833 m/s) A particle (mass is 2x10-27 kg, initially stationary) decays into 3 particles. Particle A (mass is 1x10-27kg) has a velocity of 1m/s [N30W]. Particle B (mass is 0.25x10-27 kg) has a velocity of 3 m/s [S]. What is the velocity of the 3rd particle (conservation of momentum)? Two asteroids (mass is 1000 kg and 100 kg) are moving towards each other. The heavier asteroid has a speed of 5000 km/hr. The lighter asteroid has a speed of 500 km/hr. After the collision, the heavier asteroid has a speed of 4400 km/hr. Determine the velocity of the lighter asteroid (conservation of momentum). (5500 km/hr) A head on elastic collision occurs between objects A (mass is 5 kg) and B (mass is 2 kg). Object B is initially stationary. After the collision, B is moving with a velocity of 3 m/s. Determine the speed of object A after the collision. A spring is initially compressed by 0.15 m and has a spring constant of 1000 N/m. A 1 kg block is placed next to the spring. The angle the incline makes with the horizontal is 15 degrees. The coefficient of friction along the incline is 0.4. a) Calculate the initial energy of the block b) Calculate the initial force acting on the block c) Calculate the normal force acting on the block while it is on the incline d) Calculate the force due to friction acting on the block while on the incline e) Calculate the maximum distance the block travels along the incline An arrow is fired at a styrofoam (mass is 2 kg) block (acting like a pendulum). The mass of the arrow is 15 grams, and travels with a velocity of 30 m/s prior to hitting the block. a) Calculate the velocity of the arrow block combination right after collision b) Calculate the kinetic energy of the arrow block combination right after the collision c) Calculate the maximum height the arrow block combination swings to (when the speed is 0) d) Calculate the change in kinetic energy of the arrow block e) Calculate the change in GPE of the arrow block

4 Tutorial 4 To increase its altitude from 600 km, a rocket ship (mass is kg) fires it rockets, and the rocket motor converts J of energy from chemical potential energy into mechanical energy. Determine a) the initial amount of mechanical energy the ship had at an altitude of 600 km (ET1) b) the total amount of mechanical energy the ship has after the rocket has been fired (ET2) c) the new altitude that the shuttle will orbit at d) the binding energy of the shuttle at the new altitude ( a) x1011 J b) -5.69x1011 J c) 610 km d) 5.69x1011 J) 1. Two charges are separated by 1 mm. Charge A has more electrons than protons. Charge B has 3000 more protons than electrons. Determine a) the charge of A and B b) the magnitude of the electric force acting between the charges c) the electric potential energy a) charge A is 2.4x10-15 C, charge B is 4.8x10-16 C b) 1.037x10-14 N c) 1.037x10-17 J

5 2. Determine the net electric force acting on charge D due to the presence of the other 3 charges 3. An electron (mass is 9.11x10-31 kg) enters a magnetic field (0.5 Tesla) whose orientation is out of the page. The speed of the electron is 2x106 m/s. Determine the magnetic force and radius of the circular path of the electron. (answers: 1.6x10-13 N, 2.278x10-5 m) 4. To create the appropriate character, an inkjet printer uses charge placed on small ink drops to deflect the drops (mass is 2x10-10 kg) appropriately. The oil drops have an initial speed of 25 m/s when they enter the parallel plate. The drops are deflected downward by m. The drops have a negative charge. The distance between the plates is 2 cm, and the potential difference is 120 volts. Determine the charge on the drops. (answer: 8.3x10-11 Coulombs)

6 Tutorial 5 Two point sources in phase are oscillating in water 20 times every 3 seconds. The water waves move at a speed of 30 cm/s. The distance between source 1 and a point where destructive interference occurs is 45 cm. The point of destructive interference is on the second nodal line. a) Calculate the frequency of the wave b) Calculate the possible distance that is separating the point of destructive interference and source 2. c) If the two sources are out of phase, how does your answer in b change? A double slit experiment is conducted using a red laser and a blue laser. The wavelength of the blue laser (440 nm) is incident on the double slits. An interference pattern occurs on a screen located 1 m from the slit, and the distance between successive minimas is measured to be 8.8 mm. When the red light is incident, the distance between successive minimas is measured to be 13.6 mm. Calculate the wavelength of the red light. A layer of oil (n = 1.2) is floating on top of a layer of water (n = 1.33). A wavelength of blue light (wavelength is 440 nm) is seen brightly reflecting off of the oil. The oil is at least 500 nm thick. Calculate the minimum thickness (greater than 500 nm) of the oil drop. Why do you see different colours coming from different parts of the oil drop? Answers: 1. a) 6.67 Hz = 7 Hz b) cm, cm OR 5x102 cm, 4x102 cm c) 54 cm, 36 cm OR 5x102 cm, 4x102 cm nm OR 6.8x10-7 m nm, 487 nm OR 4.2x10-7m, 4.9x10-7m OR 4.2x102 nm, 4.9x102 nm nm OR 5.5x102 nm or 5.5x10-7 m

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