Lab 1: Determination of the weight of a suspended mass using force vectors
Purpose:
To determine the weight of a suspended mass and a circular protractor using the vector components two
supporting forces when the system is in a state of static equilibrium.
Theory
When a system is in static equilibrium, there is no net force in any direction and no movement of the
objects in the system. The forces of the two supporting forces must balance each other and the weight of
the suspended mass and the protractor. Therefore, the two horizontal (x) components should have equal
and opposite values and nullify each other while the two vertical (y) components of the upward forces
must equal the downward force of the weight of the protractor-mass.
It is reasonable to assume there will be a small absolute error between the actual (experimental) values of
the equilibrium components and the expected (calculated) value. The amount of error can be measured by
the total of the horizontal forces and by the difference between the sum of the upward forces and the
weight downward.
Materials
equilibrium apparatus: spring scales (2) with protractor (360°) and loops of string (3)
unknown mass
ring stands (2) with clamps
Procedure

Slide the metal rings at the end of two spring scales down each
of the two ring stands until they are stopped by a ring or other
clamp attached to the ring stand.

Attach the suspended mass to the third loop of string and allow to hang.

Adjust the heights of the clamps and/or the distance between
the ring stands until the suspended mass is suspended above the table.

For convenience turn the protractor so that “0” and “180” run horizontally
and “270” is at the bottom in line with the string connected to the
suspended mass (plumb line). The spring scale on the LEFT (0) will have a positive (+) horizontal component.

Measure and record the magnitude of the force F (in newtons, N - not grams!) and the corresponding angle for each
spring scale.

Draw a scale diagram on graph paper of the two supporting spring scales attached to the ring stands and add them
graphically. Label each vector clearly as well as the resultant.

Calculate the horizontal (x) and vertical (y) components of each spring scale and determine the resultant
mathematically. Show one sample calculation for each type using the data your group collected.

Determine and record the weight of the protractor and the suspended mass.
Discussion of Results and Conclusions

Describe the resultant vector of the diagram (graphical addition of supporting spring scales).

State the sum of the horizontal components and the vertical components of the supporting spring scales as well as the
weight of the suspended mass and protractor.

Evaluate the accuracy of the experiment – how close were the results to the expectations.

Identify significant sources of error in the procedure and materials and provide reasonable ways to reduce these errors.
Group Members: ___________________________________________________________________________
Physics 12 – 10.1
Date of Data Collection: __________________
Results
RAW DATA
CALCULATED DATA
Spring Scale
Magnitude of
Force Fr (N)
Direction of
Force – θ
Horizontal Force,
Fx (N)
Vertical Force,
Fy (N)
supporting spring scale A
supporting spring scale B
resultant
RAW DATA
CALCULATED DATA
Spring Scale
Magnitude of
Force Fr (N)
Direction of
Force – θ
Horizontal Force,
Fx (N)
Vertical Force,
Fy (N)
supporting spring scale A
supporting spring scale B
resultant
RAW DATA
CALCULATED DATA
Spring Scale
Magnitude of
Force Fr (N)
Direction of
Force – θ
Horizontal Force,
Fx (N)
supporting spring scale A
supporting spring scale B
resultant
Measured weight of the suspended mass and protractor: _________________
Vertical Force,
Fy (N)