ANSWERS
Quiz 1 - Chapter 4, 1
CH 4 : Multiple Choice Questions-1, 2, 15
exercises/problems -1, 2, 3, 5;  If  Ch. 4 problems seems difficult, skip to the Ch. 1 exercises/problems below then return to finish  these later.
CH 1: exercises/problems-34, 37, 38 (see exercise #4, Ch 4) for comparison and practice),  42, 44, 48, 50
DISCUSSIONS
CH. 4

Multiple Choice Questions 1, 2, 15 each deal with Newton's first Law, which says if the net force is ZERO, the object undergoes uniform motion  or remains at rest. 
exercises problems.
1. Fx = 10*cos45 and Fy = - 10*sin 45 assuming the positive y directions is UP.

2. Let the 270 N-force be along the positive x axis, and the 300 N-force be 60 degrees above the positive x axis.  The components  of the resultant are  Rx = 300*cos 60 + 270 and Ry = 300*sin60 + 0 = 300*sin 60. Find the magnitude and angle using class notes. 
Below is another way of seeing the problem:

 

Solve:            

 makes an angle of 31.8° with the rope of dog A.


3. Fx = F*cos50 and Fy = F*sin 50 assuming the positive y directions is UP.
4.  The net force is vertically up with magnitude 5 = 2*T*sin 52.5. Solve for T = magnitude of tension force.
5. Fx = 985*cos 31- 788*cos58 - 411*cos53  
and Fy = 985*sin 31  +  788*sin58 - 411*sin53  
Find the magnitude and angle using class notes. 
CH. 1
34.  (a) quadrant 1  (b) quadrant 3  (c) quadrant 2  (d) quadrant 4

Below is another way of seeing the problem:
37.  (a) The resultant  is in the first quadrant. 
(b) the difference is in the third quadrant.  Use tail to tail method
(c) the resultant  is in the opposite direction as the vector in part (a).  
(d) the difference is in the opposite direction as the vector in part (b).  Use tail to tail method.
38.  See hint to #4, Ch. 4. Same problem, different numbers>
Below is another way of seeing the problem:

 
. 
(b) Careful measurement of the length of  and  gives
42.  Fx = 20*cos37 and Fy = 20*sin 37

Below is another way of seeing the problem:

 

 (b)

44. Starting with vector-A and going counter-clockwise: Here are the x components:
12 cos 53, - 6cos60, 15cos40 . And here are the y components
12sin 53, -6sin 60, -15sin 40. 
Below is another way of seeing the problem:

For each vector, use the relations  and

Solve:  For vector    

For vector      For vector    

48. Resolve the components as we did in problem 44.  Add up the x-components to get Rx.  Add up the y components  to get Ry.   Use the Pythagorean Theorem to get the magnitude. See class notes for the quadrant and angle.

Below is another way of seeing the problem:

The counterclockwise angles each vector makes with the +x axis are:      and  The components of each vector are shown in Figure (a) below.

 

 

 

 

Solve:  (a)    

(b)  is the resultant pull.

(c)    and  are shown in Figure (b) above.

 and  so

(d) The vector addition diagram is given in Figure (c) above. Careful measurement gives an  value that agrees with our results using components.

50. There are three vectors we want to add:
The first vector has zero x-component, the second vector has zero y component, and the third vector has components  given by Fx = 3.1*cos45 and Fy = 3.1*sin 45 (in the first quadrant.)  See guidelines in #48.
Below is another way of seeing the problem:

         38º north of east. This result is confirmed by the figure below.

 

`