Three beads are placed along a thin rod. the first bead, of mass m1 = 22 g, is placed a distance d1 = 1.5 cm from the left end of the rod. the second bead, of mass m2 = 12 g, is placed a distance d2 = 2.4 cm to the right of the first bead. the third bead, of mass m3 = 53 g, is placed a distance d3 = 3.6 cm to the right of the second bead. assume an x-axis that points to the right. a) write a symbolic equation for the location of the center of mass of the three beads relative to the left end of the rod, in terms of the variables given in the problem statement.
b) find the center of mass in centimeters relative to the left end of the rod
c) write a symbolic equation for the location of the center of mass of the three beads relative to the center bead in terms of the variables given in the statement problem
d) find the center of mass in centimeters relative to the middle bead.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.