Experiment 4 Addition of Forces and Vectors
OBJECTIVE: The purpose of this experiment is to practice the addition of vectors graphically and analytically and to compare the results obtained by these two methods.
APPARATUS:
Cenco force table with pulleys. Metal ring, strings, weight hangers and weights. Rulers and protractors.
The force table provides a means for applying known forces at one or more points and in various directions in the horizontal place. The forces are the tensions in strings which pass over pulleys attaches to the rim of the circular table and from which weights are hung.
PRINCIPLES AND EQUATIONS: If several forces act on a body, the vector sum of these forces governs the motion of the body. According to Newton’s 1st Law of Motion the body will remain at rest (if originally at rest) or will move with a constant velocity (if originally in motion) if the vector sum of all forces acting on it is zero (the vector sum is called the resultant force). The body is then said to be in translational equilibrium. In this experiment we consider forces acting on a small body (a metal ring), arranging them so that the body is in translational equilibrium, and we determine how nearly these forces satisfy the translational equilibrium condition that their vector sum is zero. Forces will be measured in units called “gram-weight” (gmwt). One gmwt is the force of gravity on one gram of mass. Therefore a mass of M grams will correspond to a force of M gmwt.
DATA AND GRAPHS: See attached
CALCULATIONS:
Sample Point 2:
Since the hanger mass is 50g, it is to be added to the mass of the weight.
For example, Point 2 was 26 g, so: 26g + 50g = 76g
Angle of P2 = 135° x (π/180°) = 2.36 radians x-axis coordinate = sin135° = 0.71cm y-axis coordinate = cos135° = -0.71cm
Resultant vector 2 x-coordinate was (P2+P3) x-coordinates = (-0.71cm) + (-0.17cm) = -0.88cm
Resultant vector 2 y-coordinate was (P2+P3) y-coordinates = (0.71cm) + (-0.98cm)
APPARATUS:
Cenco force table with pulleys. Metal ring, strings, weight hangers and weights. Rulers and protractors.
The force table provides a means for applying known forces at one or more points and in various directions in the horizontal place. The forces are the tensions in strings which pass over pulleys attaches to the rim of the circular table and from which weights are hung.
PRINCIPLES AND EQUATIONS: If several forces act on a body, the vector sum of these forces governs the motion of the body. According to Newton’s 1st Law of Motion the body will remain at rest (if originally at rest) or will move with a constant velocity (if originally in motion) if the vector sum of all forces acting on it is zero (the vector sum is called the resultant force). The body is then said to be in translational equilibrium. In this experiment we consider forces acting on a small body (a metal ring), arranging them so that the body is in translational equilibrium, and we determine how nearly these forces satisfy the translational equilibrium condition that their vector sum is zero. Forces will be measured in units called “gram-weight” (gmwt). One gmwt is the force of gravity on one gram of mass. Therefore a mass of M grams will correspond to a force of M gmwt.
DATA AND GRAPHS: See attached
CALCULATIONS:
Sample Point 2:
Since the hanger mass is 50g, it is to be added to the mass of the weight.
For example, Point 2 was 26 g, so: 26g + 50g = 76g
Angle of P2 = 135° x (π/180°) = 2.36 radians x-axis coordinate = sin135° = 0.71cm y-axis coordinate = cos135° = -0.71cm
Resultant vector 2 x-coordinate was (P2+P3) x-coordinates = (-0.71cm) + (-0.17cm) = -0.88cm
Resultant vector 2 y-coordinate was (P2+P3) y-coordinates = (0.71cm) + (-0.98cm)