VECTORS Name:_______________________________       

Partners:____________________________________   Course:________________

 Visit the following site and get an understanding of vectors and scalars.

 Purpose: To determine
(a) the resultant and equilibrant of two or more vectors                
(b) the components of a vector 
analytically and to verify the results using a force table and a PC.

Apparatus: force table with pulleys, mass hangers, mass set, string, level, and PC.

Theory: a) analytical method

Let's say two forces F₁ (making an angle θ₁ with the x-axis) and F ₂ (making an angle θ₂ with the x-axis) are acting on an object. To find the resultant force we will do the following: 

Force	X-component	Y-component
F1	F1 Cos θ1	F1 Sin θ1
F2	F2 Cos θ2	F2 Sin θ2
F1 + F2	Fx = F1 Cos θ1+ F2 Cosθ2	Fy = F1 Sin θ1 + F2 Sin θ2

Magnitude of the resultant (F_R) is given by;    F_R ^{2 =} F_x ²  + F_y ²

Direction of the resultant, θ_R, measured from the X - axis depends on the signs of Fx and Fy. 

When Fx > 0 and  Fy >0; θ_R = tan^-1(F_y/F_x).

When the components are negative go the appropriate quadrants and determine θ_R.

The equilibrant is given by:

magnitude = magnitude of the resultant.

direction = θ_E = 180 + θ_R.

Procedure

A) Use of a PC:

1. Click "Short cut to Phys". 

2. Type 1(one) and Enter.

3. Type P and put in the magnitude of the first vector and Enter.

4. Put in the angle of the first vector and Enter.

5. Type P and put in the magnitude of the second vector and Enter.

6. Put in the angle of the second vector and Enter.

7. Push Esc for vector data list or continue with third and fourth vectors.

8. Obtain F_R (=R) and θ_R (=A) for the first 4 cases and Fx and Fy for the last case. 

9. Type "system" and enter and then type "exit" to get to windows. 

B) Analytical Method 

Use the analytical method and find the magnitude and the direction of the resultant. Estimate the direction of the equilibrant.

C) Force Table Check

Addition of two vectors:

1) Use a level to make sure the force table is leveled.

2) Mount a pulley on the 0 degree mark and suspend a 50 gram mass hanger. Mount a second pulley on the 90 degree mark and suspend a 100 gram mass (hanger and a 50 gram mass).

3) Set up the equilibrant on the force table and test the system for equilibrium.

4) Remove all the masses from the force table.

5) Mount a pulley on the 20 degree mark and suspend a 50 gram mass. Mount a second pulley on the 120 degree mark and suspend a 250 gram mass.

6) Set up the equilibrant on the force table and test the system for equilibrium. 

7) Remove the equilibrant mass.  

Addition of three vectors:

1) Mount a pulley on the 300 degree mark and suspend a 300 gram mass (masses 50 gram and 250 gram are already there).

2) Set up the equilibrant on the force table and test the system for equilibrium.

3) Remove all the masses from the force table.

Addition of four vectors:

1) Mount a pulley on the 30 degree mark and suspend a 100 gram mass. Mount a second pulley on the 140 degree mark and suspend a 150 gram mass. Mount a third pulley on the 200 degree mark and suspend a 125 gram mass. Mount a fourth pulley on the 300 degree mark and suspend a 200 gram mass.

2) Set up the equilibrant on the force table and test the system for equilibrium.

3) Remove all the masses from the force table.

Vector resolution:

1) Mount a pulley on the 30 degree mark and suspend a 300 gram mass over it.

2) Find the magnitudes of the components along the 0 degree (X- axis) and 90 degree (Y-axis) directions. 

3) Set up the above components as they have been determined. Move the 300 gram mass to, 30 + 180 = 210 degrees, which is the direction of the equilibrant. Test the system for equilibrium.

DATA 

Addition	Resultant Vector		Force Table Check
	From computer	Analytical method
50 g @ 0^0 and 100 g @ 90^0	FR=R= θR =A=	FR= θR= θE=	________
50 g @ 20^0 and 250 g @ 120^0	FR=R= θR =A=	FR= θR = θE=	________
50 g @ 20^0 250 g @ 120^0 300 g @ 300^0	FR=R= θR =A=	FR= θR = θE =	________
100 g @ 30^0 150 g @ 140^0 125 g @ 200^0 200 g @ 300^0	FR=R= θR =A=	FR= θR = θE =	_________
Resolution	XXXXXXXXXXXX	XXXXXXXXXXX	XXXXXXXXXXXX
300 g @ 30^0	Fx= Fy=	Fx= Fy=	_________

Exercise: Use the graphical method to find the magnitude (F_R) & direction (θ_R) of the resultant for the case of addition of four vectors. Here you need to draw a vector diagram, using a protractor and ruler, following the tail-to-tip method, to scale. Show the direction of the vectors and identify F_R & θ_R in the drawing.

F_R = ____________ θ_R = _________________

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