170 Test example problems CH1,2,3

Transcription

1 170 Test example problems CH1,2,3 WARNING: these are simply examples that showed up in previous semesters test. It does NOT mean that similar problems will be present in THIS semester s test. Hence, you are suggested to use these problems to deepen your understanding on the CONCEPTS involved in these problems. Please do not waste your time memorize them.

2 (8 points) Q1: Obtain x vs t (4 points) and a vs t (4 points) diagram to scale based on the provided v vs t. The initial conditions are: at t=0, the initial position is -2 m. (feel free to answer directly on the graphs below).

3 (8 points) Q2: You are on the roof of the physics building, 50 meters above the ground (your personal height is negligible). You are dropping (zero initial velocity) an egg from the edge of the roof. a) How long is it going to take for the egg to hit the floor? (2 points) Now you are throwing another egg straight up with an initial velocity of v=15m/s above your head. As the egg falls back down, it misses the edge of the building and hits the floor as well. b) What is the maximum height the egg will reach? (2 points) c) How long will take the egg to reach this height? (2 points) You would like to drop (zero initial velocity) a third egg after the second one, such that both eggs hit the floor at the same time. d) How long after throwing the second egg do you need to drop the third one? (2 points) (10 points) Q3: Given the two fundamental definitions of acceleration velocity v dr dt dv a and dt, derive the following for the case of a 2 dimensional projectile motion where the plane is horizontal, the initial speed and angle are known, and the initial position is set to zero.: a) The functional form of v x (t) b) The functional form of x (t) c) The functional form of v y (t) d) The functional form of y (t) e) The functional form of y (x) (2 points) f) The functional form of x ( ) (2 points) g) needed for the maximum range (2 points)

4 (9 points) Q4: A snowball rolls off a barn roof that slopes downward at an angle of 30 o. The edge of the roof is 20m above the ground, and the snowball has a speed of 10m/s as it rolls off the roof. If we ignore air resistance, a) How long does it take for the snowball to strike to ground? (2 points) b) How far from the edge of the barn does the snowball strike anything else while falling? (2 points) c) What is the speed of the snowball right before it strikes the ground? (2 points) d) Based on the coordinate system you have chosen in a), b) and c), draw the x vs t, v vs t, and a vs t to scale for this motion. (3 points) 7 points) Q5: The radius of the earth s orbit (assumed to be circular) around the sun is 10 8 km, and the earth travels around this orbit in 365 days. a) What is the magnitude of the orbital velocity of the earth in m/s? (3 points) b) What is the radial acceleration of the earth toward the sun in m/s 2? (3 points) c) Sketch this motion, and indicate clearly the velocity and acceleration vectors 8 points) Q6: Given the vectors below such that W=90, T=120, and N=100; using the fact that T N, and that the direction L is defined by an angle of 45 degree with respect to the x axis, obtain the following: a) Component notation of W in the (x,y) coordinate system b) Component notation of T in the (x,y) coordinate system c) Component notation of N in the (x,y) coordinate system d) Component notation of W in the (x,y ) coordinate system e) Component notation of T in the (x,y ) coordinate system f) Component notation of N in the (x,y ) coordinate system g) Component notation of T parallel to the direction L, and expressed in the (x,y) coordinate system h) Component notation of T perpendicular to the direction L, and expressed in the (x,y) coordinate system

5 (7 points) Q2: You are on the edge of the roof of the physics building, 60 meters above the ground (your personal height is negligible). You are dropping (zero initial velocity) a kg egg from the edge of the roof. Use g 9.8ms. a) How long is it going to take for the egg to hit the floor? Now you are throwing another egg straight up with an initial velocity of v=10m/s above your head. As the egg falls back down, it misses the edge of the building and hits the floor as well. b) What is the maximum height the egg will reach? c) How long will take the egg to reach this height? You would like to drop (zero initial velocity) a third egg after the second one, such that both eggs hit the floor at the same time. d) How long after throwing the second egg do you need to drop the third one? (2 points) e) Now you see me walking on the ground level towards the building with a set of homework in my hands. With great wisdom, you decide to try to stop me so I never climb the stairs to assign this evil set which most likely will give you headache. The best way is to drop a fourth egg on my head so that I have to turn around to take a shower, cursing my bad luck in the process (coz I haven t seen you yet!). If I am walking at a constant speed of 2 m/s towards the entrance of the building (located straight below your position), how far from it should I be for you to release the egg so that it reaches its target (me!...) (2 points)?

6 Make sure that you show me clearly which part you are working on ( a), b),..), and circle your final answer. 5 points) Q5: A baseball is given an initial velocity with magnitude v o at an angle above the surface of the incline, which is in turn inclined at an angle above the horizontal. a) Calculate the distance, measured along the incline, from the launch point where the baseball strikes the incline. Your answer will be in terms of v o, g, and. (3 points) b) What angle gives the maximum range, measured along the incline? (2 points) 8 points) Q6: Given the vectors below such that W=150, T=20, and N=80; using the fact that T N, and that the direction L goes through two points A(0,3), and B(2,0), obtain the following: Use: iˆ, ˆj for the (x,y) coordinate system, and use: i ˆ', ˆj ' for the (x,y ) coordinate system. You will also need: F ( F eˆ) eˆ // i) Component notation of W in the (x,y) coordinate system j) Component notation of T in the (x,y) coordinate system k) Component notation of N in the (x,y) coordinate system l) Component notation of W in the (x,y ) coordinate system m) Component notation of T in the (x,y ) coordinate system n) Component notation of N in the (x,y ) coordinate system o) Component notation of T parallel to the direction L, and expressed in the (x,y) coordinate system p) Component notation of T perpendicular to the direction L, and expressed in the (x,y) coordinate system

7 4 points) Q8: As a ship approaching the dock at 45 cm/s, an important piece of landing equipment needs to be thrown to it before it can dock. This equipment is thrown at 15m/s at 60 degrees above the horizontal from the top of a tower at the edge of the water, 8.75m above the ship s deck. For this equipment to land at the front of the ship, at what distance D from the dock should the ship be when the equipment is thrown? 6 points) Q7: Beer pong has always been your favorite game to watch. You notice that the table top is however inclined at an angle of 10 degrees below the x axis (the lower side is where the cup is). The cup is sitting on one edge of the table, and the player

8 throws the ball at a height of 0.5 meter above the table top from the other side of the table. If the initial velocity of the ball is 5 m/s at an angle of 30 degrees above the horizontal, calculate (ignore air resistance, ignore the height of the cup, and use 2 g 9.8ms ): a) The maximum height above the table top that the ball is going to reach. b) How long the ball takes to reach its highest position. c) The velocity magnitude and direction of the ball at its highest position. d) The velocity magnitude and direction of the ball after 0.7 seconds. e) How long is the table for the ball to make it into the cup. f) The velocity of the ball right before hitting the cup. Make sure to draw a diagram of the process including a coordinate system to get credits. Make sure that you show me clearly which part you are working on ( a), b),..), and circle your final answer. 4 points) Q8: You are paddling across the Molokai s channel in the east direction with a speed of 2 m/s. The current is strong and is directed south with a magnitude of 1 m/s. a) What is your velocity? (2 points) You paddle with the above velocity for 6 hours (steady current). But then, the current suddenly switches, and is now pushing you full west with a magnitude of 0.5m/s for the rest of the trip! b) How long is it going to take you to reach Molokai? (2 points)

9 (14 points) Q3: Given the vectors below such that W=50, T=30, and N=40; using the fact that T N, and that the direction L is defined by a line going through two points A and B, such as A ( 4,0), and B ( 0, 2), CALCULATE THE FOLLOWING : a) T N (3 points) b) Component notation of W T N in the (x,y ) coordinate system (3 points) c) Component notation of W N in the (x,y) coordinate system (3 points) d) Component notation of T parallel to the direction L, and expressed in the (x,y) coordinate system (3 points) e) Component notation of T perpendicular to the direction L, and expressed in the (x,y) coordinate system (2 points)

10 (15 points) Q5: You are throwing a ball with an initial speed of 30 m/s and an angle of 60 degrees with respect to the horizontal. The field you are playing on is not horizontal, but is inclined by an angle of 10 degrees with respect to the horizontal. a) How far does the ball land? (3 points) b) How long was it in the air? (3 points) c) What is its final velocity right before impact? (3 points) d) What is its final acceleration right before impact? e) What is the maximum height (measured with respect to the horizontal) that the ball reaches? (2 points) f) Sketch the y vs t, x vs t, vy vs t, vx vs t, ax vs t, and ay vs t based on your coordinate system (3 points)