Physics I (Navitas) FINAL EXAM Fall 2015

Transcription

1 Physics I (Navitas) FINAL EXAM Fall 2015 Name, Last Name First Name Student Identification Number: Write your name at the top of each page in the space provided. Answer all questions, beginning each new question in the space provided. Show all work. Show all formulas used for each problem prior to substitution of numbers. Label diagrams and include appropriate units for your answers. You may use an alphanumeric calculator (one which exhibits physical formulas) during the exam as long as you do not program any formulas into memory. By using an alphanumeric calculator you agree to allow us to check its memory during the exam. Simple scientific calculators are always OK! Score on each part Part 1 (16) Part 2 (14) Part 3 (20) Part 4 (20) Part 5 (25) Part 6 (25) Part 7 (15) Part 8 (15) Total Score (out of 150 pts) Total Score (scaled up to 200 pts)

2 2 Problem 1: (16 points) - 2 pts each -- No partial credit on this problem only. Put a circle around the letter that you think is the best answer. 1-1 A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height? A) The heavy object, because it has greater kinetic energy. B) The lightweight object, because it has smaller kinetic energy. C) The lightweight object, because it weighs less. D) The heavy object, because it weighs more. E) They both slide to the same height. I-2 Which of the following quantities does NOT have units of enery? (m is mass, g is the acceleration due to gravity, h and d are distances, F is a force, v is a speed, a is an acceleration, P is power, and t is time). A) mgh B) Fd C) (1/2) mv 2 D) ma E) Pt I-3 Two identical satellites A and B are doing around Earth in circular orbits. The distances of satellite B from Earth s center is twice that of satellite A. The ratio of the centripetal forces acting on B compared to that acting on A is: A) 1:8 B) 1: 4 C) 1:2 D) 2:1 E) the same

3 3 I-4 A 2-kg ball dropped vertically undergoes a collision with a horizontal floor and bounces up. The instant before it hits the floor, the speed of the ball is 2 m/s. The instant after the bounce, the speed of the ball is 1 m/s. The change in the momentum of the ball is: A) 2 N.s upward B) 2 N.s downward C) 6 N.s upward D) 6 N.s downward E) zero I-5 An object with mass m is located halfway between an object of mass M and an object of mass 3M that are separated by a distance d. What is the magnitude of the force on the object with mass m? A) 4GMm/ d 2 B) 2GMm/d 2 C) 8GMm/d 2 D) GMm/(2 d 2 ) E) GMm/(4 d 2 ) I-6 A merry-go-round spins freely when Janice moves quickly to the center along a radius of the merry-go-round. It is true to say that A) the moment of inertia of the system decreases and the angular speed increases. B) the moment of inertia of the system decreases and the angular speed decreases. C) the moment of inertia of the system decreases and the angular speed remains the same. D) the moment of inertia of the system increases and the angular speed increases. E) the moment of inertia of the system increases and the angular speed decreases.

4 4 I-7 Identical forces act for the same length of time on two different masses. The change in momentum of the smaller mass is A) smaller than the change in the momentum of the larger mass, but not zero. B) larger than the change in momentum of the larger mass. C) equal to the change in momentum of the larger mass. D) zero. E) There is not enough information to answer the question. I-8 An object of mass M oscillates on the end of a spring. To double the period, replace the object with one of mass: A) 2M B) M/2 C) 4M D) M/4 E) None of the above.

5 Problem 2 short problems 2-1 (6) The figure below shows two SHM, labeled A and B 5 For each of them, determine - A) The amplitude of A and B B) The frequency of A and B C) The period of A and B D) The angular frequency of A and B 2-2 A solid sphere of radius, R and mass, M starts from rest at the top of an smooth inclined plane (no friction) an rolls down the inclined plane. The height of the inclined plane is h. Given moment of inertia of solid sphere = I sphere = 2 5 MR2 A) (7) Determine its linear velocity at the bottom of the incline express this in terms of g and h. B) (1) If R = 30cm, M = 1kg, and h = 1.2m, calculate the linear velocity.

6 For problems 3 to 8 NO credit will be given for just correct answer without appropriate formulae/logic. Circle your numerical answers. 6

7 Problem 3: ( 20 points) 7 A stone is launched at t = 0 with a speed of 15 m/s from ground level at an angle of 50 degrees above the horizontal (with respect to ground) and aimed at a building. The stone hits the building when it is at its maximum height. (Assume that there is no air resistance.) A) (3) Draw a labeled diagram ; include the path of the stone. B) (3) Express the initial velocity vector (use numerical values) of the stone in unit vector notation. C) (4) Express the velocity (use numerical values) of the stone when it hits the building in unit vector notation. D) (5) Determine the horizontal distance that the stone travels before it hits the building. E) (5) Determine the vertical height of the stone when it hits the building.

8 Problem 4: ( 20 points) 8 A 3.0-kg rifle shoots a kg bullet at a speed of 180 m/s. A) (4) Calculate the velocity of the rifle show all the steps clearly. The bullet collides with wooden block of mass 3.6 kg (which is suspended by a thin massless rod) and the bullet gets embedded into the wood. B) (5) Determine the speed of the (wood + bullet) just after the collision. As a result of collision, the (wood + bullet) swing to a height, h. C) (5) Determine the height, h. D) (6) What quantities are conserved in part (A) and part (B) and part (C)?

9 Problem 5: ( 25 points) 9 NOTE: Use work-energy methods to solve the following problem. (No points will be given if you use another method.) A skier of mass M starts from rest and skis down a incline (length = L) with a slope angle of θ (having a coefficient of kinetic friction of µ k ). A) (4) Draw the free-body diagram. B) (8) Write down the expressions (in terms of the parameters given) that will enable you to determine the work done by each of the forces that acts on the skier during the descent. C) (8) Determine the speed of the skier at the bottom of the incline if M = 78 kg, θ = 24 degrees, L = 100 m, and µ k = 0.07 D) (5) At the bottom of the incline the ground is level and has a coefficient of kinetic friction of 0.13, determine the distance the skier will travel on the level ground before coming to a stop.

10 Problem 6: ( 25 points) 10 The figure shows two masses (M 1 and M 2 ) connected by a massless cord that passes over a pulley of radius R o, mass M P, and moment of inertia I. One surface is at an angle θ and both surfaces are frictionless. A) (5) Draw the free-body diagram for each of the masses on the figure above. B) (5) Use Newton s II law to write the equation that describes the linear acceleration of M 1. C) (5) Use Newton s II law to write the equation that describes the linear acceleration of M 2. D) (5) Write down the equation that describes the angular acceleration of the pulley. E) (5) Solve the above equations to determine the linear acceleration of the system.

11 Problem 7: ( 15 points) 11 A figure skater can decrease her spin rotation rate from an initial rate of 2.5 rev/s to a final rate of 1.0 rev every 1.5 s. Her initial moment of inertia is 1.2 kg.m 2. A) (7) What is her final moment of inertia? B) (4) She continues to slow down and comes to a stop in 10 s. Calculate her angular acceleration? B) (4) How many number of revolutions did she make in this time?

12 Problem 8: ( 15 points) 12 G = 6.67 x Nm 2 /kg 2 M E = 5.98 x kg R E = 6.37 x 10 6 m (Earth s mass) (Earth s radius) Planet X has a mass of 5 times that of Earth and a free-fall acceleration at the surface of 2/3 (two thirds) that of Earth s. A) (8) Determine the ratio of the radii (planet X / planet Earth). B) (7) Determine the ratio of the escape velocity (planet X / planet Earth).