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Static Equilibrium Lab: Finding Torques and Moment Arms, Study notes of Advanced Physics

Australian College of Kuwait (ACK)Advanced Physics

A lab experiment aimed at testing the condition of static equilibrium by summing torques. Students will learn how to find the moment arm and torque on an object, and understand the conditions for an object to be in static equilibrium. Equipment includes a meter stick with different masses attached, and the procedure involves finding the center of mass, moment arm of a force, and force produced using torques. Calculations are required to compare experimental and expected values.

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2021/2022

Uploaded on 08/01/2022

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1"
"
Torques and Equilibrium
Goal: To test the condition of static equilibrium by summing torques.
Lab Preparation
There are two main things to review for this lab.
First, understanding how to find the magnitude of the torque on an object,
τ
= F
l
,
and knowing how to find the moment arm l is very important. Remember, the
moment arm is the shortest distance between the axis of rotation and the line of
action (Figure 1). If
θ
= 90o then the moment arm is equal to r, the distance from
the axis to where F is applied.
Figure 1
Second, the conditions for an object to be in static equilibrium are:
ΣF = 0
Σ
τ
= 0
For this lab these conditions will be met. When Σ
τ
= 0 this means that the
counterclockwise torques (positive) must balance the clockwise torques
(negative). Reviewing problems of this type will be helpful for this lab.
Equipment
A meter stick with different masses attached to it will be the main equipment for
this lab.
F"
l
Line"of"action"
axis"of"rotation""
θ
r"
pf3
pf4
pf5

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Torques and Equilibrium

Goal: To test the condition of static equilibrium by summing torques. Lab Preparation There are two main things to review for this lab. First, understanding how to find the magnitude of the torque on an object, τ = F l, and knowing how to find the moment arm l is very important. Remember, the moment arm is the shortest distance between the axis of rotation and the line of action (Figure 1). If θ = 90o^ then the moment arm is equal to r , the distance from the axis to where F is applied. Figure 1 Second, the conditions for an object to be in static equilibrium are: Σ F = 0 Σ τ = 0 For this lab these conditions will be met. When Σ τ = 0 this means that the counterclockwise torques (positive) must balance the clockwise torques (negative). Reviewing problems of this type will be helpful for this lab. Equipment A meter stick with different masses attached to it will be the main equipment for this lab.

F

l Line of action axis of rotation θ r

Procedure I. Center of mass of a meter stick Support the meter stick with its sliding ‘knife-edge’ attachment on the metal stand. Slide the meter stick through the knife-edge until it balances. Clamp the knife-edge to the meter stick and leave it there for the rest of the lab. The center of mass is at the knife-edge. Record the meter stick reading at this point. II. Finding the mass of the meter stick by using torques Insert a nail through the meter stick at the 75 cm point and rest the meter stick in the stand at this point. Find experimentally where a mass m = 300 g should be hung by a loop of thread from the meter stick to make it balance (see Figure 2 ). Figure 2 By placing m in this position you are balancing the torques on the meter stick. Thus, the meter stick is put into a condition of static equilibrium. If the axis of rotation is chosen to be at the 75 cm position then the clockwise torque produced by m must balance out the counterclockwise torque produced by the meter stick (here we are taking the mass of the meter stick and knife edge to act at its center of mass with a mass = Ms ). Measure and record the distances a and b shown in Figure 2. Find Ms by summing torques around the axis of rotation. Now find the mass ( M ) of the meter stick (with knife edge) directly on a scale and record. Find the % difference between this value (the expected value) and Ms (the experimental value) using: !"!"#$%"&'() !!"#$%&$' !"#$%&$' x 100%. STAND m = 300 g nail pivot knife edge attachment W = M gs 75 cm a b

Hang m 1 = 400 g exactly at the 60 cm point. Adjust the meter stick so it is nearly horizontal. You may need to raise the scale or stand by placing a book or two underneath it. Record the scale reading. Measure the mass of the small wooden prism and subtract this from the scale reading to find the experimental value of Fb in grams. Once again take the axis of rotation to be the 75 cm point. Sum torques and calculate the expected value of Fb and also find the % difference between the expected and experimental values. V. Finding moment arm for forces at an angle Hang the meter stick at the 1 cm point on a nail (in a wooden dowel) on a tall stand. Another string hangs vertically downward from the nail to serve as a plumb line. Arrange a pulley and mass m = 100 g as shown in Figure 5 to apply a force at right angles to the meter stick at the 60 cm point. Use the edges of a sheet of paper to test that you have a right angle between the string going to the pulley and the meter stick. Figure 5 Measure x , the moment arm due to the weight of the meter stick, from the plumb line to the center of mass of the meter stick. Letting the axis of rotation be at the 1 cm point, the torque produced by the string (attached at the 60 cm point) must be balanced out by the torque produced by the weight of the meter stick. Sum torques about this axis and calculate the expected value of x. Find the % difference between expected and experimental values of x. 60 90 a nail pivot at 1 cm m =100 g Plumb Line x W Pulley

VI. Finding the angle for a force As in part V hang the meter stick by the nail at the 1 cm point. Put a string through the hole at the 99 cm point and lead the string around the pulley on the other stand as shown in Figure 6. Figure 6 Place a 100 g mass at the end of the string over the pulley and adjust the position of the pulley to place the meter stick in a horizontal position. One way to determine when the meter stick is in the horizontal position is to use the top or bottom line of the blackboard as a horizontal reference line and stand back a meter or more from the meter stick and align the meter stick with the blackboard line. Position the protractor mounted on a separate stand (use another dowel- mounted nail to hold the protractor) to measure the angle θ of the string with respect to the horizontal. Record the value of θ. To calculate the expected value of θ you once again will want to apply the conditions for static equilibrium. A free body diagram of the meter stick is shown in Figure 6. Selecting the axis of rotation at the 1 cm mark will eliminate any torques produced by the pivot (force P ) and thus, the torque produced by the weight of the meter stick must be balanced out by the torque produced by the string attached at the 99 cm point. Use this information to help calculate the expected value of θ. Check to see if this is close to your measured value of θ. When finished with your lab please make sure your lab station is cleaned up. Homework

  1. For part VI draw a picture showing where the moment arm is located for the tension T and then calculate this moment arm value.
  2. For part VI calculate the predicted values of Px and Py in grams. e 1 99 Protractor on separate nail pivot and stand Nail Pivot a b W P (^) Py T Px Ty Tx Freebody diagram of meter stick e m =100 g