Spring 2010 Physics 141 Practice Exam II Phy141_mt1b.pdf

Transcription

1 1. (15 points) You are given two vectors: A has length 10. and an angle of 60. o (with respect to the +x axis). B has length 10. and an angle of 200. o (with respect to the +x axis). a) Calculate the components of both vectors, and write them in the blank lines below (4 pts). A = î + ĵ y 10 B = î + ĵ x 10 b) Construct and clearly present the resulting vector from the addition of A plus B (i.e., R A B ) on the coordinate system above and give the values of the components in terms of unit vectors î and ĵ in the blank lines below. (5 pts.) R = î + ĵ c) Find the scalar (dot) product A B. (3 pts.) d) Find the vector (cross) product A B. (3 pts.) 15 3 Page 1/7

2 2. (18 points) A model rocket with a parachute recovery system is launched (from rest on the ground) straight up. The rocket first accelerates at 4.00 m/s 2 directly upwards for 3.00 s. Then the engine shuts off and the rocket moves in free fall for 2.00 s. At this point a parachute comes out and the rocket quickly (you may assume immediately) slows down to a terminal speed of 4.48 m/s. a) How high above the ground (in meters) is the rocket when its engine shuts off? (3 pts.) b) What is the maximum height above the ground reached by the rocket (in meters)? (4 pts.). c) How high above the ground is the rocket when its parachute opens? (4 pts.) d) How long does it take the rocket to float to the ground after its parachute opens? (4 pts.) e) Sketch the velocity of the rocket for each of the three phases of flight below. (3 pts) v t Accelerates Upwards Engine off Parachute out 18 4 Page 2/7

3 3. (14 points) You want to throw a (puffy harmless) snowball at a friend and hit her/him in the shoulder. Your friend is standing 1.50 m below you a distance of 10.0 m away, as marked with the X on the figure to the right. You throw the snowball horizontally with an initial velocity of v o. You can ignore air resistance. a) Calculate the time the ball is in the air. (5 pts) 1.50 m v o 10 m g X b) Calculate the needed initial velocity, v o, for the ball to exactly hit the person in the shoulder. (5 pts.) c) Using your chosen coordinate system (must clearly mark on figure above), sketch the x and y position of the ball versus time during its motion in the air. (4 pts.) x y t t 14 5 Page 3/7

4 4. (15 points) You are a pilot who takes a small airplane out for a flight. Your airplane travels at 190 km/h in still air and you decide to fly (in the air) in a direction exactly south-east (i.e., at an angle of 45 o south of east). The wind is blowing due north at 50 km/h. a) Draw the complete velocity vector diagram (below) for this situation, including the velocity of the airplane with respect to the ground. Clearly label and identify each velocity vector. (3 pts.) N (or +y) W E (or +x) S b) What is your velocity vector with respect to the ground (in component form)? (6 pts.) c) After one hour of flying, what distance and direction, did you travel with respect to the ground? (6 pts.) 15 6 Page 4/7

5 5. (22 points) A block of mass m 1, on an incline with angle is attached to another block of mass m 2, on a flat surface, with a massless rope that passes over a frictionless ring. A large horizontal force, F, pulls mass m 2 to the right, as shown in the figure. The coefficient of kinetic friction, k, between the blocks and surfaces is the same everywhere. m 1 m 2 F g a) Draw the free body diagrams (i.e. indicate all forces acting on each block) and write the corresponding Newton s Force equations-of-motion for that block. Clearly indicate your choice of axes on the free body diagrams. (13 pts.) m 1 m 2 Problem 5 continues on the next page. 7 Page 5/7

6 Problem 5 continued. b) Solve for the acceleration of the system in terms of the horizontal force F, m 1, m 2, k,, and g. (5 pts.) c) Calculate the minimum horizontal force F needed to pull both blocks to the right at constant speed given the following values: m 1 =10.0 kg, m 2 =20.0 kg, k =0.200, = 25 o and g = 9.8 m/s 2. (4 pts.) 22 8 Page 6/7

7 6. (16 points) You attach a mass, m = kg, to a L =1.0 m long rope and swing it around your head. The rope (which you can assume is massless) makes an angle of with respect to the horizontal, as shown in the figure. Top View Side View v m L m a) In the Side View figure above, clearly show all the forces acting on the mass. Include the acceleration vector in the figure. (3 pts.) b) Calculate the speed of the mass (in m/s) for the given quantities. (6 pts.) c) What is the period of this motion? (3 pts.) d) What is the tension in the rope? (4 pts.) 16 9 Page 7/7