TEST 2 SP’11

1. ( 40 points) Block 1 , Block 2 and Block 3 are in contact on a table inclined by θ= 30 degrees with the horizontal. Starting from rest, you apply a  force to Block 1 of magnitude F = 101.25 N and direction parallel to incline. As shown below, we represent the force’s   application point  with a tail at Block 1’s left end. The coefficient of kinetic friction between surface and blocks is µ =  0.15. The block’s masses are m1 = 4.00 kg, m2 = 2.00 kg  and m3 = 1.00 kg, respectively.   To  most clearly  show your  thinking, try to use these and possibly other well established symbols  until the last step before your numerical answer, which you should box.

 

For parts (a), (b) and (c) label all vector components with symbols.

(a) (3 points)     Draw a force diagram  for Block 1.

(b) (3 points)     Draw a force diagram  for Block 2.

(c)  (3 points)     Draw a force diagram  for Block 3.

(d) (11 points)   What is the magnitude F12 of the  force of contact  between  Block 1 and Block 2.  

(e)  (11 points)   What is the magnitude F23  of the force of contact between Block 2 and Block 3.

(f)   (5 points)    What is the common  acceleration of the three  blocks?

(g) (3 points)    What is the common velocity of the three blocks after 3.00 seconds? 

 



2. (40 points)  This problem deals with a game at an urban  golf park.  At t = 0, a golf  ball is launched from  the base of a ramp making a 45 degree angle with the horizontal.  The golf ball is launched at speed  20.00 m/s at an angle of 68.0 degrees with the horizontal.
 

(a) (30 points) How far away does the ball land,  measured along the ramp,  from the base ? In other words,  what is the distance from the base along the ramp?
(b) (10 points) What is the ball’s speed just before impact with ramp?

 

3.  (40 points)  Below is an  engineer’s diagram  of a “Rotor-ride” at a carnival.   People rotate in a vertical cylindrically walled room. A typical person is represented by the grey box. When the floor drops out from under her feet,  the person is pinned against the  wall and does not slide down as she rotates.   Let the coefficient of static friction between person and  wall be µ = 0.400.

(a)  (4   points) Draw a free body diagram for the  person at the moment shown.   

(b) (30 points) Find the minimum linear speed V  of the person that keeps her from slipping down.  

(c) (6 points) Suppose a  typical teenager has mass m =  70.00 kg. What would be the magnitude N of the normal force acting on her if she rotated at the speed you computed in part (b)? Does this seem reasonable?  Explain.