Module 8 Lab 7 Torque and equilibrium

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School

Virginia Commonwealth University *

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Course

201

Subject

Mechanical Engineering

Date

Dec 6, 2023

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NOL PHY 201 Lab - Torque and Equilibrium Name In this lab you will determine the mass of two objects (one of your choices and a blank printed page) using a ruler. There are three activities. There are six pages in this lab worksheet. Please make sure to get all the information and complete all activities. Each lab counts for 20 points and is about 1.42% of the total grade. Lab Goals This lab will help you learn the following: ● How to perform an experiment independently ● How to take measurements, obtain results, and interpret them correctly ● How to estimate the accuracy of experimental results. Introduction The two conditions for mechanical equilibrium of a rigid body are: the sum of the forces must be equal to zero Σ ⃗ F = 0 and the sum of the torques must be equal to zero Σ ⃗ τ = 0 The first condition ensures that the rigid body is not moving linearly or that it is moving with constant linear velocity (Newton’s First Law of Motion). In this experiment, the rigid body (the ruler) is restricted from linear motion and the condition is automatically satisfied. If the sum of the torques is zero, the object is in rotational equilibrium, and either it does not rotate, or it rotates with a constant angular velocity. Page 1 of 6

NOL PHY 201 A torque results from the application of force acting at a distance from an axis of rotation. If the angle between the vector force ⃗ F and the vector distance ⃗ r is called θ the magnitude of the torque is equal to τ = Frsin ( θ ) . The unit of torque is the meter times Newton (mN). In this lab, the angle between the vector ⃗ F and the vector ⃗ r is 90 o . Activity 1 Material and formulae Material Ruler, Scotch tape, one coin, string (like dental floss, sewing thread, etc.) Object 1: one page of printed paper, Object 2: a small object of your choice (like an eraser, a ring) Build the formulae Please look at the image of the setup below and answer the following questions. ● What is the force that the coin exerts on the ruler? Highlight the correct answer. (Assume zero the force due to the string). Page 2 of 6

NOL PHY 201 a) Its weight mg b) Its mass m c) no force is acting on the ruler ● In the images above, which distance r should be used in the torque formula for the coin? (The distances are from the lateral threads to the ruler center of equilibrium). a) Distance marked as A b) Distance marked as B ● Write here the torque due to the coin, in formula (no numbers): ● Write here the torque due to the object placed on the ruler, in formula (no numbers): ● Write here the condition of equilibrium. The left torque equal to the right torque: Activity 2 Experiment and results Set up 1. Using the scotch tape and a string secure the ruler hanging free from a table. You want to suspend it through its center. The ruler should be in balance. 2. Cut two equal pieces of a string and attach them to the coin and to the object. 3. Make two loops that hang on the ruler. 4. Place the coin and the object (use one object at the time) on the opposite side of the ruler center until you find the perfect equilibrium. 5. Search for the value of the mass of the coin on the Internet. 6. Comparing the left torque with the right torque, find a relation between the coin's mass and the mass of the object. Page 3 of 6

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NOL PHY 201 Object 1: One page of printed paper Complete the table below: Mass of the coin (grams) r distance for the coin (cm) r distance for the paper page (cm) 1. Solve the torque equation for the mass of the paper. Write here the equation, no numbers, just the formula: paper 's mass= 2. Now, please plug the data from your experiment and find the mass of the paper. Show all your work. 3. Take a picture of your ruler in equilibrium with the coin and the paper and add it here below. Object 2: One object of your choice Complete the table below: Mass of the coin (grams) r distance for the coin (cm) r distance for the object (cm) Page 4 of 6

NOL PHY 201 1. Solve the torque equation for the mass of the object. Write here the equation, no numbers, just the formula: paper 's mass= 2. Now, please plug the data from your experiment and find the mass of the paper. Show all your work. 3. Take a picture of your ruler in equilibrium with the coin and the paper and add it here below. Activity 3 Make a prediction and test it. Page 5 of 6 Paper and object in equilibrium

NOL PHY 201 Physics formulae can be used to make predictions. Place the object at a fixed distance from the Ruler canter of equilibrium and then predict where you should place the paper in order for the system to be in balance. Include a picture of your set up. 1) Distance in centimeters from the object's thread to the center of equilibrium of the ruler, r object = ¿ ______________________ 2) Using the torque equations, predict the distance from the ruler equilibrium' s point where you should place the paper. r paper = ¿ ______________________ 3) Show here the calculations on how you predict this value. 4) Balance, now, the paper on the ruler with the object. Was your prediction correct? Where did you place the paper? actualr paper = ¿ ______________________ 5) Determine the percent error with your predicted value. % error = 100 ∗ | ( Actualvalue − Predicted value Predicted value ) | = ______________________ Page 6 of 6

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