As a pendulum swings , the angle (theta) that it makes with the vertical changes through its swing. the force of gravity pulling on the bob is given by f=mg sin (theta), where g is equal to 9.8m/s^2. if the mass of the pendulum is 0.01 kg, what is the force pulling on the pendulum when it makes a 22.5 degree angle with the vertical?

For this case what we should do is use the given equation:
 F = mg sin (theta)
 And replace the following values:
 m = 0.01 kg
 g = 9.8m / s ^ 2
 theta = 22.5 degrees
 Substituting we have:
 F = (0.01) * (9.8) * sin (22.5)
 F = 0.037502976 N
 
 The force pulling on the pendulum when it makes a 22.5 degree angle with the vertical is:
 F = 0.037502976 N