# Physics 106P: Lecture 1 Notes Exam II Physics 101: Lecture 14 Torque and Equilibrium Todays lecture will cover Textbook Chapter 8.2-8.4 Physics 101: Lecture 14, Pg 1 Review Rotational Kinetic Energy Krot = I 2 Rotational Inertia I = miri2 Energy Still Conserved!

Today Torque Physics 101: Lecture 14, Pg 2 You Know Torque! A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it? A) x = 25 B) x=50 C) x=75 D) x=100 E) 1 kg cant balance a 2 kg weight. 0 25 10050 cm 1 kg

50 75 2kg Balance Demo Physics 101: Lecture 14, Pg 3 Torque Rotational effect of force. Tells how effective force is at twisting or rotating an object. = +- r Fperpendicular = r F sin Units N m Sign: CCW rotation is positive

Physics 101: Lecture 14, Pg 4 ACT The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which of the cases is the torque on the nut the biggest? A. Case 1 B. Case 2 C. Case 3 CORRECT Physics 101: Lecture 14, Pg 5 ACT 2 The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case.

In which of the cases is the torque on the nut the smallest? A. Case 1 B. Case 2 C. Case 3 CORRECT Physics 101: Lecture 14, Pg 6 Torque Example and ACT A person raises one leg to an angle of 30 degrees. An ankle weight (89 N) attached a distance of 0.84 m from her hip. What is the torque due to this weight? 1) Draw Diagram 2) = F r sin F r sin(90 =30) 65 N m 4 8

. 0 r = 30 m F=89 N If she raises her leg higher, the torque due to the weight will A) Increase B) Same C) Decrease Physics 101: Lecture 14, Pg 7 Equilibrium Acts A rod is lying on a table and has two equal but opposite forces acting on it. What is the net force on the rod? A) Up

B) Down C) Zero Y direction: Fy = may +F F = 0 Will the rod move? A) Yes B) No y Yes, it rotates! F x F Physics 101: Lecture 14, Pg 8 Equilibrium

Conditions F=0 =0 for Equilibrium Translational EQ (Center of Mass) Rotational EQ (True for any axis!) Choose axis of rotation wisely! A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it? A) x = 25 B) x=50 C) x=75 D) x=100 E) 1 kg cant balance a 2 kg weight. 50

cm 9.8 N d Balance Demo = 0 19.6 N 9.8 (0.5) (19.6)d = 0 d = 25 Physics 101: Lecture 14, Pg 9 Static Equilibrium and Center of Mass Gravitational Force Weight = mg

rm Acts as force at center of mass rcm i i mi Torque about pivot due to gravity = mgd Object not in static equilibrium pivot d Center of mass W=mg Physics 101: Lecture 14, Pg 10 ot Static Equilibrium Not in equilibrium

Equilibrium pivot d Center of mass W=mg Center of mass Torque about pivot 0 Torque about pivot = 0 A method to find center of mass of an irregular object Physics 101: Lecture 14, Pg 11 Preflight The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight?

1. The person on the left is supporting the greatest weight CORRECT 2. The person on the right is supporting the greatest weight 3. They are supporting the same weight 66% assume r for F1(person on the left to the log) is 1/4R, then after calculation i get F1=2F2 24% 10% 0% 20% 40%

60% 80% The guy on the left has to support more weight because he is further in and has to support more of the board. Physics 101: Lecture 14, Pg 12 Preflight The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight? 1. The person on the left is supporting the greatest weight CORRECT 2. The person on the right is supporting the greatest weight 3. They are supporting the same weight Look at torque about center: FR L FL L/2 = 0 FR= FL

FL L/2 FR mg L Physics 101: Lecture 14, Pg 13 Preflight Most difficult concepts: deciding where to make your point of origin or axis difference betweenforce and torque [demo] how to find the signs when putting into the equation studying biochem while completing these physics assignments torque Torque sounds so ominous all the equations Physics 101: Lecture 14, Pg 14

Homework 8 Hints A 75 kg painter stands at the center of a 50 kg, 3 meter plank. The supports are 1 meter in from each edge. Calculate the force on support A. 1 meter 1 meter B A 1) Draw FBD 2) F = 0 1 meter FA + FB mg Mg = 0

3) Choose pivot 4) = 0 FA FB 0.5meter mg Mg -FA (1) sin(90)+ FB (0) sin(90) + mg (0.5)sin(90) + Mg(0.5) sin(90) =0 Physics 101: Lecture 14, Pg 15 Homework 8 Hints If the painter moves to the right, the force exerted by support A A) Increases B) Unchanged C) Decreases

1 meter 1 meter A B Physics 101: Lecture 14, Pg 16 Homework 8 Hints How far to the right of support B can the painter stand before the plank tips? 1 meter 1 meter A

B Just before board tips, force from A becomes zero FB 1) Draw FBD 2) F = 0 FB mg Mg = 0 3) Choose pivot 4) = 0 0.5meter x mg FB (0) sin(90) + mg (0.5)sin(90) Mg(x) sin(90) = 0 0.5 m = x M

Physics 101: Lecture 14, Pg 17 Mg Sign Problem There is no hinge attaching the black rod to the wall, what is the minimum coefficient of friction necessary to keep the sign from falling? Physics 101: Lecture 14, Pg 18 Equilibrium Example A 50 kg diver stands at the end of a 4.6 m diving board. Neglecting the weight of the board, what is the force on the pivot 1.2 meters from the end? 1) Draw FBD 2) Choose Axis of rotation 3) = 0

Rotational EQ F1 (1.2) mg (4.6) = 0 F1 = 4.6 (50 *9.8) / 1.2 F1 = 1880 N 4) F = 0 Translational EQ F1 F2 mg = 0 F2 = F1 mg = 1390 N F1 F2 mg Physics 101: Lecture 14, Pg 19 Homework 8 Hints Bar & Weights m1g

Using FTOT = 0: Mg T Mg m2g T = m1g + m2g + allows you to solve for m1 Physics 101: Lecture 14, Pg 20 Find net torque around this (or any other) place

(m1g) = 0 since lever arm is 0 T x m1g Mg m2g Physics 101: Lecture 14, Pg 21 T L/2 (m1g) = 0 since lever arm is 0 m1g

Mg m2g (Mg ) = -Mg L/2 Physics 101: Lecture 14, Pg 22 T x (m1g) = 0 since lever arm is 0 m1g Mg m2g

(Mg ) = -Mg L/2 (T ) = T x Physics 101: Lecture 14, Pg 23 Work Done by Torque Recall For W = F d cos a wheel Work: W = Ftangential d = Ftangential 2 r / (2 ) ( in radians) = Ftangential r = Power: P = W/t = /t Physics 101: Lecture 14, Pg 24

Summary Torque = Force that causes rotation = F r sin Work done by torque W = Equilibrium F=0 = 0 Can choose any axis. Physics 101: Lecture 14, Pg 25