Real Test 4:  AN EXTRA CREDIT PROBLEM FROM CHAPTER 12 WILL BE ADDED LATER SO KEEP ON CHECKING BACK; WILL ALERT YOU BY EMAIL TO THIS FACT WHEN THE TIME COMES. THE TEST DUE DATE HAS BEEN EXTENDED TO NEXT FRIDAY. 

1.  (40 POINTS)  This problem involves concepts of both kinetic energy of rotation about a moving axis in Chapter 9 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  Vcm = 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)   (37 points)  What distance D from the foot of the cliff does the ball land and what is the speed Vcm of the center of mass just before it lands?

(b)   (3 points) Notice that when the ball lands, it has a larger translational speed Vcm  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 device you may write  on your paper to convey your explanation.

 

 

 

 

 

2. (40 POINTS) CHAPTER 10. 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 is subjected to a horizontal force of magnitude F =100. 0 N parallel to the ground. The box has mass m = 1.00 kg.  The disk is rotates clockwise about a fixed axis attached to a steel structure bolted to the ground:

(a) (20 points) What is a, the linear acceleration magnitude the box?

(b) (15 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.  (40 points)  CHAPTER 10. A 9.0 m uniform beam is hinged to a vertical wall and held horizontally by a 5.0 m cable attached to the wall 4.0 m above the hinge, as shown below. The metal of the cable has test strength of 1.00 KN (kilo-Newton), which is the maximum tension magnitude T the cable can support. That means  the cable  will break if  T is greater than this value.

(a) (4 points) What is the angel θ ?

 

(b) (2 points) What is the distance along the bean between the hinge and where the cable is attached to the beam?

 

(c) (32 points) What is the largest  beam mass m (corresponding to the test strength) the cable can support with the given configuration shown?

(d) (4 points) Find the horizontal and vertical components of the force the hinge  exerts on the beam,

 

 

4.   (40  points) CH. 11: A 2.00 kg frictionless block is attached to a horizontal spring as shown. Spring constant k = 200.00 N/m. At t = 0, the position x = 0.225 m,  and the velocity is 4.25 m/s toward the right in the positive x direction. Position x as a function of t  is:  x = 
A*cos(ωt + theta) , where A is the amplitude of motion and ω is the angular frequency discussed Chapter 11 and the notes. Theta is called the phase constant that will be addressed for extra credit below. 

(a) (28 points) Use conservation of energy to compute amplitude A.
(b) (5 points)  How much farther from the point shown will the block move before it momentarily comes to rest before turning around?

(c) (4 points)  What is the period T of the motion?

(d) (3 points)  If the mass of this problem was doubled to 4.00 kg, how would your answer to part (c ) change?
(e) (4 points) EXTRA CREDIT: Use your trigonometry background to find phase constant theta.