PURPOSE

To prove that forces add the same way as vectors do.

EQUIPMENT

Force table, weights, weight hangers,protractor,compasses and ruler.

METHOD

Suppose we add two vectors A and B and obtain the resultant R as it is shown in Fig l. In addition, at point O we construct the vector R' (antiresultant of R) which is equal in magnitude but opposite in direction to the vector R. If we add the vectors A, B, and R' then the final result must be equal to zero.

Our apparatus consists the large circular disk calibrated in degrees and the pulleys. The pulleys are attached to the disk and weights can be hang over them as it is shown in the Fig 2.

Now if we apply to the pulleys such weights that the forces acting on the point O add up to zero we may keep our system in equilibrium. Having already two such forces fixed it is possible to find the third force which will keep this system in equilibrium using the method of trials and errors.

However this method is hardly practical because it takes a lot of time. Therefore let us assume that forces add the same way as vectors do, and use this assumption to find out the third force.

EXPERIMENTAL

All the forces involved in the following cases are defined by their magnitudes in newtons and relative directions expressed in degrees with help of angle . Solve these cases adding forces graphically and check your theoretical results experimentally.

(l) Force addition

        A = 0.2 x 9.80 N                 _A = 30^o

        B = 0.2 x 9.80 N                _B = l20^o

where 9.80 is the value of gravity acceleration. Notice that the force 0.2 x 9.80 N is created by a mass of .2 kg.

(2) Force addition

        A = 0.2 x 9.80 N                _A = 20^o

        B = 0.l5 x 9.80 N                _B = 80^o

(3) Force addition

        A = 0.2 x 9.80 N                _A = 0^o

        B = 0.l5 x 9,80 N                _B = 90^o

(4) Force resolution

        A = 0.3 x 9.80 N                _A = 60^o

find the coordinates A_x and A_y if the x-axis is associated with the angle = 0^o and the y-axis is associated with the angle = 90^o.

(5) Force addition

        A = 0.2 x 9.80 N                _A = 30^o

        B = 0.l x 9.80 N                 _B = 90^o

        C = 0.05 x 9.80 N              _C = 300^o