Phys 244 Torque Online 2022

George Mason University Physics 244 (Online) Torque Learning Goals: 1. The goal of this lab is to investigate and understand static equilibrium for a horizontally suspended meter stick. 2. After completing this lab, students will understand the basic concept of torque 3. You will perform am error analysis and determine the uncertainties of your measurements. Materials: Meter stick apparatus, string, force sensors, Capstone, masses, Excel References: Giancoli, Physics 7th Edition: chapter 8, sections 4, 5 OpenStax, College Physics, chapter 9 Background Theory: When forces act on an extended body, torques, or rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components: F net = F 1 + F 2 + F 3 + … = 0 (1) Torques may be calculated about the axis of your choosing and because a meter stick is our body, the length of the lever arm can be conveniently determined without resolving components. ❑ net = ❑ 1 + ❑ 2 + ❑ 3 + … = 0 (2) Each torque is specified by the equation: 1 Figure : Equilibrium

τ = Fdsinθ (3) where  is taken as the angle between the force vector and the lever arm vector. In today’s experiment this angle will be 90  and thus sin(90  ) = 1. Normally, up is "+" and down is "-" for forces. For torques, the convention is to define clockwise as "-" and counterclockwise as "+". As stated above if the system is in static equilibrium, the sum of the torques and forces at any pivot point will equal zero. Today you will sum the forces and torques at two distinct pivot points on a suspended meterstick to demonstrate that the system is in static equilibrium. Experiment: The goal of today’s experiment is to “discover” the concept of equilibrium. You will use a meter stick and measure the forces acting on the meter stick after hanging different weights onto it. The force sensors interface with the PASCO data acquisition box and you will use Capstone (choose the digital display) to measure the forces, and MS Excel to record your results. This experiment requires you to record your measurements in a table similar to the sample table in this handout. Once you have completed your measurements, calculate the torques and discuss the equality of force and torque equations. Data Collection and Analysis: The ruler is suspended by two force sensors at either end of the ruler as shown in the figure below. This allows the system to be in static equilibrium since the force sensors hold up the meterstick and mass system. The readings on the force sensors may not be equal depending upon the distribution of the masses on the meterstick and the location of the sensors. 2

s F = √ s Fleft 2 + s Fright 2 = √ ( 0.05 ) 2 +( 0.05 ) 2 = 0.07 N Table 2: Sum of Forces for meterstick system Mass (kg) F # F (N) x (cm) x (m) m 1 +hanger F1 m 2 +hanger F2 m 3 +hanger F3 m 4 (meterstick) F4 Left F sensor - hanger F5  0.05 Right F sensor - hanger F6  0.05 Sum of Positive Forces  0.05 Sum of Negative Forces  0.05 Sum of all Forces  5. Using the zero position ( x = 0 m) of the meter stick as the axis of rotation and counterclockwise torques as positive, determine the sum of the torques acting in both directions and record them on the data sheet (Create table 3 in Excel). Check for equality between positive and negative sums within the calculated uncertainties. If we assume the uncertainty in the measurement of the position is very small, the percentage uncertainty of the force measurements will equal the percentage uncertainty in the torque measurements. Use the force uncertainties provided in the previous table to compute the associated uncertainties of the torque measurements. %s F = s F F = %s T = s T T thus s T = %s F ∗ T 6. Repeat the calculation with the lever arm located at the axis point in the middle of the meter stick ( x = 0.50 m) and recalculate torques. Check for equality between positive and negative results, within calculated uncertainties. 7. Discuss your results. Is the sum of all forces zero within the uncertainty? Is the sum of all torques zero within the uncertainty? Was the meterstick in equilibrium? Table 3: Torque Calculation Table (be sure to include signs on torques) 4

Lever Arm (m) Axis at x = 0 m Torque (N-m) Axis at x = 0 m Lever Arm (m) Axis at x = 0.5 m Torque (N-m) Axis at x = 0.5 m F1   F2   F3   F4   F5   F6   Sum of Positive Torques   Sum of Negative Torques   Sum of all Torques   Note: The uncertainty of the force sensor is provided as 0.05 N. References: Image credit: http://philschatz.com/physics-book/contents/m42171.html 5