Force Table Vectors
Force Table Vectors
In front of you, you should see three spring scales attached together by strings. The three strings represent the force vectors pulling the knot in 3 different directions. What do the three force vectors add up to on your table, and how do you know?
Zero Reading:
Disconnect a string from one of the scales. Look at your scale readings­are they exactly at zero? If not, you need to calibrate the spring scales by turning the plastic screw at the top of the spring scale until the scale pointer is aligned to zero with no mass attached to the scale.
These are physics' graduated cylinders...
...because they're cylinders...
...with graduations on them!!!
TOO
MUCH!!!
NOT
ENOUGH!!!
N
0
N
N
0
0
JUST
RIGHT!!!
0
0
0
2
2
2
2
2
2
4
4
4
4
4
4
6
6
6
6
6
6
8
8
8
8
10
8
8
10
10
10
10
10
12
12
12
12
12
12
14
14
14
16
16
16
18
20
14
16
14
16
14
16
18
18
18
18
18
20
20
20
20
20
Force Table Vectors
Next, reconnect the strings and slide a piece of paper underneath the central knot. Check central knot.
Check to see that your spring scales show forces between 2 and 20 Newtons, if and 20 Newtons,
if not, call over your instructor to adjust the positions of your spring scales. your spring scales. A = _
_ N
B = __ N
Mark spots under each string near the knot and near the edge of the paper. Make sure the paper does NOT move! Record the pull value in Newtons (N) from each scale next to the marks for each string.
C=
__
N
A = _
_ N
B = __ N
Now turn your marks into full lines (force vectors radiating away from the central knot), and record the angle between each line (string). If you add the three angles together, what should they equal and why?
C=
__
N
Now turn your marks into full lines (force vectors radiating away from the central knot), and record the angle between each line (string). If you add the three angles together, what should they equal and why?
B
θ1 θ2
A
θ3
C
On big paper, you need a scale so your smallest line is at least 10cm long. Your colors count too!
.8
7
=
B = 9.6N
θ1
θ2
A θ3
N
N
0
4.
C=
On big paper, you need a scale so your smallest line is at least 10cm long. Your colors count too!
N
.8
7
=
B = 9.6N
θ1
θ2
A
θ3
C=
N
0
4.
This is my smallest force, so this line needs to be at least 10 cm. What would be a good scale for my paper?
SAMPLE ONLY!
Factor Unit Labeling:
Scale: 3 cm = 1 N
3 cm
A = 4.0 N X
= 12 cm
1 N
CHOOSE YOUR OWN SCALE!!
LONGER FORCE VECTORS MEAN LESS ERROR!!!
On big paper, you need a scale so your smallest line is at least 10cm long. Your colors count too!
N
8
7.
=
B = 9.6N
(28.8 cm)
θ1
.
3
(2
θ3
m)
2 c
0 N
4.
C=
(1
θ2
A )
cm
8
Scale: 1 N = 3 cm
On big paper, you need a scale so your smallest line is at least 10cm long. Your colors count too!
.
B = 9.6N
θ1
θ2
A 7
= N
8
θ3
0 N
4.
C=
Scale: 1 N = 3 cm
On big paper, you need a scale so your smallest line is at least 10cm long. Your colors count too!
7
= B = 9.6N
θ1
θ2
N
8
.
A θ3
0 N
4.
C=
θ3
Scale: 1 N = 3 cm
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
N
8
7.
B = 9.6N
θ1
= A
θ2
0 N
4.
C=
Scale: 1 N = 3 cm
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
N
8
7.
B = 9.6N
θ1
= A
You should get this:
θ2
0 N
4.
C=
Scale: 1 N = 3 cm
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
θT
B = 9.6N
N
8
7.
= A
You should get this:
θ1 θR
θ2
0 N
4.
C=
Theoretically:
θT = θ1 + θR = ???
Scale: 1 N = 3 cm
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
N
8 .
7
B = 9.6N
θ1
=
A
You'll probably get this:
.0
4
C=
θ2
N
Scale: 1 N = 3 cm
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
N
8 .
7
B = 9.6N
θ1
=
A
You'll probably get this:
N
Your scale will allow you to determine the magnitude of your Resultant's force.
.0
4
C=
θ2
Scale: 1 N = 3 cm
.8
= 7
A θA
N
Then, add the two smaller vectors together graphically (hint: tip to tail). Draw the resultant in another color. Using your scale, determine how big the resultant is.
B = 9.6N
You'll probably get this:
θR
θ1
N
Use your protractor to determine your actual angle.
.0
4
C=
θ2
Actually:
θA = θ1 + θR
Scale: 1 N = 3 cm
Finally, compare the resultant and the original large vector. Do these vectors cancel out? If not, how much are they off? (in Newtons & percent) Are they in the same direction (are they along the same line)? How much off are they? (in degrees & percent)
Force:
% Diff =
θ:
Measured ­ Calculated
(Avg of Meas & Calc)
% Error =
Theoretical ­ Actual
Theoretical
X 100
X 100