TEST 4 THE EXAM IS DUE NEXT FRIDAY

1. (30 POINTS)  THIS PROBLEM INVOLVES A SHORT TUTORIAL PROVIDED IN LECTURE  based on section 10.3; see examples 10.4 and especially 10.5.  Also review projectile motion !!

We look at  concepts of both kinetic energy of rotation about a moving axis in Chapter 10 and also projectile motion in a previous chapter. (That’s a hint.).   I leave it to you to break the problem up appropriately to find answers to questions below: In a small town just north of Bend Oregon, a solid uniform   ball in the shape of a sphere rolls without slipping up a hill. It’s part of an outdoor high school physics experiment. AT THE BOTTOM OF THE HILL THE LINEAR SPEED OF THE CENTER OF MASS IS  V_cm = 25.0 m/s . At the top of the hill  the ball  is moving horizontally, then  it goes over the vertical cliff and undergoes projectile motion with negligible  air resistance to the best approximation.

(a)   (27 points)  What distance D from the foot of the cliff does the ball land and what is the speed V_cm of the center of mass just before it lands?

(b)   (3 points) Notice that when the ball lands, it has a larger translational speed V_cm  than it had at the bottom of the hill at the start of problem.  Does it mean the ball somehow gained energy by going up the hill? Explain in as clear a way as you can. Use clean, concise sentences, diagrams and  other deviceS you may write  on your paper to convey your explanation.

2. (30 POINTS) CHAPTER 10.  This problem “maps” into #16, 17, 70, 73, 68, at the very least!  See online lecture notes related to these problems ! A thin,  light horizontal string is wrapped  around the rim of a 4.00-kg solid uniform disk that is 30.0 cm in diameter.  A box is connected  to the right end of the string and moves to the right along the ground horizontally with no friction. The box has mass m = 1.00 kg. The box is subjected to a horizontal force of magnitude F =100. 0 N parallel to the ground.  The disk is rotates clockwise about a fixed axis attached to a steel structure bolted to the ground:

(a) (15 points) What is a, the linear acceleration magnitude the box?

(b) (10 points) What is the tension T in the string? 

(c) (5 points) If the disk is replaced with a hollow thin walled cylinder of the same mass, and diameter, what will be the acceleration in part (a)? 

3.  (30 points)  STATICS  CH. 11:  A beam is attached to a wall,  and at the other end is held in place by a cable of tension T. Also,  a block of mass M =  3.0 kg is attached to the beam end. Check out the diagram. The beam has mass 1.0 kg.  As you can see,  the beam makes an angle of 60 degrees with the horizontal.

(a) (26) What is the tension T ? HINT: CHOOSE THE AXIS OF ROTATION TO BE THE POINT WHERE THE BEAM AND WALL MEET. SEE CLASS NOTES INVOLVING THE HORIZONTAL AND NON-HORIZONTAL BEAM PROBLEMS AND MAKE ADJUSTMENTS.

(b) (2) What is the horizontal  component of force F_h exerted on the beam by the wall ?

(c)  (2) What is the vertical  component of force F_v exerted on the beam by the wall ?

4.   (26  points) CHAPTER 13. Gravity problem mapped to #15, 16 AND 17 UNDER THE HEADING “ GRAVITATIONAL POTENTIAL  ENERGY.”   THE 2D VECTOR PROBLEMS  WILL BE ON FINAL EXAM  PART 2.
(a) (13) See Figure 1. A rocket is fired from the surface of the earth with initial velocity Vo = escape velocity.  What is the escape velocity?  You must show all steps leading to  your answer.  M_E = 5.97x10²⁴ kg and R_E = 6.38x10⁶ m. 

(b) (13) See Figure 2. A rocket is fired from the surface of the earth with initial velocity Vo =2·V_{ESC  .} What is the velocity V when the rocket reaches r = ∞?

5. CHAPTER 14 OSCILLATIONS OF ALL SORTS  INCLUDING A PENDULUM ( SEE QUIZ 15)  WHICH WILL APPEAR ON THE FINAL EXAMINATION PART 2.  
(26 POINTS) A block of mass 4.00 kg is attached to a horizontal spring. No friction! At t = 0, the mass has position x_o = 0.400 m and velocity v_o = -5.00 m/s. The force constant of the spring is k = 300 N/m.
(a) (13)What is the amplitude A ?
(b) (13)What is the phase constant  ?
Assume the position obeys the equation: