Question

Torque and equilibrium – Lab 07

You have already learned that an unbalanced or net force F accelerate an object, but it is also possible for a balanced set of forces to cause motion. To understand this condition it is necessary to realize that when we deal with real objects they have size and the location of where the force is applied matters. To analyze this motion you must not deal only with the size and direction of F but also where it acts on the object. An object will rotate or change it’s orientation when a net torque is applied to it. A torque t is the description of a force acting at a distance and is the cause of rotation motion. Torque is defined in terms of the distance from the center of rotation and the point of application of the force F as follows:

1. From the center of rotation draw a line to the point of application of the force. This line is usually symbolized by r and referred to as the lever arm or moment arm.
2. The force F may or not be parallel to the moment arm. In either case, the force F may be resolved into its two components, one parallel (F_||) to r and the other perpendicular (F_^) to r.
3. The torque t is defined as the product of r and F_^. These concepts are illustrated below.

Definition of torque t.

F_||

                                                        

                                                                 F

                          r                           F_^                                                                                                                                        F

                                                                                                                             r

Center of rotation

             or

    Rotation axis

                                            Torque = t = Force ´ lever arm = F_^ ´ r

Procedure

         The equipment in the experiment consists of a meter stick balanced at its center of gravity as shown below and various arrangements of weight holders attached at various positions. Make sure the meter stick is oriented so that 0 starts on your left as you view the cm scale. In is necessary to include the mass of the holders since they contribute to the weight at the point they are located. Weigh the mass of the holders and make sure they are very close to the same. Do not start by assuming the center of gravity is at the 50 cm mark; the center of gravity was found by balancing the ruler without masses or mass holders. This value will be given to you.

If we were still on campus, our static equilibrium lab would look rather like this. We would use our classroom meter sticks, with a heavy stand and a fulcrum apparatus attached to the stick so it can be balanced upon a wire. We would have hangers that clamp to hold a hanging mass centered at any point along the meter stick. This lab gave excellent results: you could easily see if nature agreed with your calculations.

the center of gravity of our lab meter sticks was not generally at the 50 cm mark.

We have assigned the following data:

mass of the meter stick (including attached fulcrum apparatus)	Center of gravity of meter stick	Mass of hanger #1	Mass of hanger #2	Location A	Location B	Location C
250. grams	49.5 cm	10.0 grams	10.0 grams	37.5 cm	45.0 cm	52.5 cm

PART 1

You have three tasks.

Trial I:   Balance the stick with the fulcrum at its center of gravity. Attach a 200 g mass, plus hanger #1, at Location A on the meter stick and calculate where to attach a 200 g mass, plus hanger #2, to balance it.

Trial II:    Balance the stick with the fulcrum at its center of gravity. Attach a 500 g mass, plus hanger #1, at Location B and determine where to attach a 200 g mass, plus hanger #2, to balance it.

Trail III:     Move the fulcrum to Location C, even though the meter stick does not balance. Attach a 200 g mass with hanger #1 at Location A and calculate where to place a 200 g mass with hanger #2 to make it all balance.

DATA

Center of gravity: ______ cm

Mass of stick (including attached fulcrum):______ g

Mass of hanger #1: ______ g

Mass of hanger #2: _______ g

Let the 0 cm mark on the meter stick be on the left, 100 cm mark on the right.

Any mass hung at location A or B gives ccw torque.

Let “Mass 1” be the mass of hanger #1 plus the mass attached to it.

Let “Location 1” be the location (cm marked on the meter stick) of hanger #1.

Let “Mass 2” be the mass of hanger #2 plus the mass attached to it.

Let “Location 2” be the location (cm marked on the meter stick) of hanger #2.

                                                τ = r⊥ * F = r⊥ * m * g

ANALYSIS:

	Mass 1	Location 1	Lever Arm from fulcrum to Location 1	CCW Torque From Mass 1 at Location 1	Torque from off-balance weight of the meter stick	CW Torque Needed from Mass 2 to balance	Mass 2	Location 2 From fulcrum to Location 2	Lever Arm
I
II
III

Answer 1

Trial	Mass 1(g)	Location 1(cm)	Lever Arm from fulcrum to Location 1	CCW Torque From Mass 1 at Location 1(Ncm)	Torque from off-balance weight of the meter stick	CW Torque Needed from Mass 2 to balance	mass 2	Location 2 From fulcrum to Location 2	Lever Arm
1	210	37.5	49.5-37.5=12	(12*210*9.8)*10^-3=24.696		-24.696	210	24.696/(.210*9.8)=12cm	49.5+12=67.5
2	510	45	4	19.992		-19.992	210	9.714	59.21
3	210	37.5	52.5-37.5=15	38.22(including the torque created by scale)		-38.22	210	18.57	71.071

Note:Rough work sheet is attached . The mass of the scale is taken to be the mass of the scale along with the fulcrum