Question

The center of gravity of the meter stick is 49 cm. mass of meter stick 50 g . mass of hanger #1 =5 g. mass of hanger #2 = 5 g. 1.Place the fulcrum at 51 cm. Attach a 200 g mass, plus hanger #1, at 17 cm on the meter stick and calculate where to attach a 200 g mass, plus hanger #2, to balance it. 2.Balance the stick with the fulcrum at its center of gravity. Attach a 500 g mass, plus hanger #1, at 32 cm on the meter stick and calculate where to attach a 200 g mass, plus hanger #2, to balance it. 3.Balance the stick with the fulcrum at its center of gravity. Attach a 50 g mass, plus hanger #1, at 8 cm on the meter stick and calculate where to attach a 200 g mass, plus hanger #2, to balance it. Round to the nearest millimeter. Include units (cm).

Answer 1

Solution:

Given, mass of meter stick = 50 g

Centre of gravity of meter stick is at 49 cm mark.

Mass of hanger #1 = mass of hanger #2 = 5gm

Solution:1

See diagram based on data given in part 1

To balance Hanger #2 and 200gm mass is attached at x cm mark. So net torque of all forces about fulcrum must be zero about any axis.

Net Torque About Fulcrum = 0

(Here Torque in outward direction is written with positive sign, and that in inward direction is written with nigative sign)

205 * 34 + 50 * 2 = 205 * (x - 51)

41 * 34 + 10 * 2 + 41 * 51 = 41 * x

x = 85 + 20/41 cm = 85.5 cm

Solution:2

See diagram based on data given in part 2

To balance Hanger #2 and 200gm mass is attached at x cm mark. So net torque of all forces about fulcrum must be zero about any axis.

Net Torque About Fulcrum = 0

(Here Torque in outward direction is written with positive sign, and that in inward direction is written with nigative sign)

505 * 17  = 205 * (x - 49)

101 * 17 + 41 * 49 = 41 * x

x = 41 + 1717/41 cm = 82.8 cm

Solution:3

See diagram based on data given in part 3

To balance Hanger #2 and 200gm mass is attached at x cm mark. So net torque of all forces about fulcrum must be zero about any axis.

Net Torque About Fulcrum = 0

(Here Torque in outward direction is written with positive sign, and that in inward direction is written with nigative sign)

55 * 41 = 205 * (x - 49)

11 = x - 49

x = 60 cm