Addition
of Vectors
Procedure:
1) Using the force table and spring scales provided set up a tug-of-war using three different forces. DO NOT situate the forces in a highly symmetrical configuration. When establishing an equilibrium configuration make sure the circular ring is centered on the pin, and that you are keeping the spring scales horizontal.
2) When you have arrived at a situation of equilibrium
record the readings on the spring scales and the angles the cords make with one
another (you can use the angle markings on the force table as a reference). Also
provide an estimate of the uncertainty of each of your recorded forces (for
example, magnitude of 12.5 ± 0.5 N, angle 120 ± 5 degrees ).
| Magnitude and uncertainty | Angle and uncertainty | |
| Force 1 | ||
| Force 2 | ||
| Force 3 |
3) On a separate page, make a sketch of the forces acting on the ring taking
care to label the magnitudes of each of the forces along with their respective
angles.
4) Repeat steps 1-3 using four different forces
acting on the ring.
| Magnitude and uncertainty | Angle and uncertainty | |
| Force 1 | ||
| Force 2 | ||
| Force 3 | ||
| Force 4 |
Analysis/Questions
1) Is force a
vector or scalar? Explain your reasoning. If several forces act on an object
what procedure would allow one to determine the total force acting on
that object?
2) Determine the net force acting on the
ring for the
situation involving three forces by adding the forces graphically
on the page where you have already drawn the forces. Using a protractor and ruler
find the net force (direction and magnitude) acting
on the ring.
| Magnitude and uncertainty | Angle and uncertainty | |
| Net force (3 forces) |
3) Repeat step
(2) for the case of four forces acting on the ring.
| Magnitude and uncertainty | Angle and uncertainty | |
| Net force (4 forces) |
4) For the
case of three forces acting on the ring add the forces algebraically.
To accomplish this resolve each of the three forces into x and y components.
Determine the total x and y
for the sum of the three forces. From these components Fx
and Fy determine the
magnitude and direction of the sum of the three forces. Compare these results
with those found in (2) above.
| x -component | y-component | |
| Force 1 | ||
| Force 2 | ||
| Force 3 | ||
| Net force | ||
| Net force | Magnitude: | Angle: |
5) Ideally you should have found that no net force acts on
the ring. Due to your errors, however, this will not be the case. Can you come
up with a rough measure of how to quantify your error?
6) To what extent is the quantitative estimate of your
percentage error you proposed in part (5) in agreement with the uncertainties in
your measurements of the forces acting on the ring?