1. Home
  2. College physics for ap® courses
  3. Statics and torque
  4. The second condition for

9.2 The second condition for equilibrium  (Page 5/9)

<< Chapter < Page
  College physics for ap® courses     Page 5 / 9
Chapter >> Page >

Section summary

  • The second condition assures those torques are also balanced. Torque is the rotational equivalent of a force in producing a rotation and is defined to be
    τ = rF sin θ size 12{τ= ital "rF""sin"θ} {}

    where τ size 12{τ} {} is torque, r size 12{r} {} is the distance from the pivot point to the point where the force is applied, F size 12{F} {} is the magnitude of the force, and θ size 12{θ} {} is the angle between F size 12{F} {} and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm r ⊥ size 12{r rSub { size 8{ ortho } } } {} is defined to be

    r ⊥ = r sin θ size 12{r rSub { size 8{ ortho } } =r"sin"θ} {}

    so that

    τ = r ⊥ F . size 12{τ=r rSub { size 8{ ortho } } F} {}
  • The perpendicular lever arm r ⊥ size 12{r rSub { size 8{ ortho } } } {} is the shortest distance from the pivot point to the line along which F size 12{F} {} acts. The SI unit for torque is newton-meter (N·m) . The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero:
    net τ = 0 size 12{"net "τ=0} {}

    By convention, counterclockwise torques are positive, and clockwise torques are negative.

Conceptual questions

What three factors affect the torque created by a force relative to a specific pivot point?

Got questions? Get instant answers now!

A wrecking ball is being used to knock down a building. One tall unsupported concrete wall remains standing. If the wrecking ball hits the wall near the top, is the wall more likely to fall over by rotating at its base or by falling straight down? Explain your answer. How is it most likely to fall if it is struck with the same force at its base? Note that this depends on how firmly the wall is attached at its base.

Got questions? Get instant answers now!

Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this help? (It is also hazardous since it can break the bolt.)

Got questions? Get instant answers now!

Problems&Exercises

(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?

a) 46.8 N·m

b) It does not matter at what height you push. The torque depends on only the magnitude of the force applied and the perpendicular distance of the force's application from the hinges. (Children don't have a tougher time opening a door because they push lower than adults, they have a tougher time because they don't push far enough from the hinges.)

Got questions? Get instant answers now!

When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. (a) How much torque are you exerting in newton × meters (relative to the center of the bolt)? (b) Convert this torque to footpounds.

Got questions? Get instant answers now!

Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.

23.3 N

Got questions? Get instant answers now!

Use the second condition for equilibrium (net τ = 0) to calculate F p in [link] , employing any data given or solved for in part (a) of the example.

Got questions? Get instant answers now!

Repeat the seesaw problem in [link] with the center of mass of the seesaw 0.160 m to the left of the pivot (on the side of the lighter child) and assuming a mass of 12.0 kg for the seesaw. The other data given in the example remain unchanged. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium.

Given:

m 1 = 26.0 kg, m 2 = 32.0 kg, m s = 12.0 kg, r 1 = 1.60 m, r s = 0.160 m, find (a) r 2 , (b) F p

a) Since children are balancing:

net τ cw = – net τ ccw ⇒ w 1 r 1 + m s gr s = w 2 r 2 alignl { stack { size 12{"net "τ rSub { size 8{"cw"} } =" net "τ rSub { size 8{"ccw"} } } {} #drarrow w rSub { size 8{1} } r rSub { size 8{1} } +m rSub { size 8{s} } ital "gr" rSub { size 8{s} } =w rSub { size 8{2} } r rSub { size 8{2} } {} # {}} } {}

So, solving for r 2 size 12{r rSub { size 8{2} } } {} gives:

r 2 = w 1 r 1 + m s gr s w 2 = m 1 gr 1 + m s gr s m 2 g = m 1 r 1 + m s r s m 2 = ( 26.0 kg ) ( 1.60 m ) + ( 12.0 kg ) ( 0.160 m ) 32.0 kg = 1.36 m

b) Since the children are not moving:

net F = 0 = F p – w 1 – w 2 – w s ⇒ F p = w 1 + w 2 + w s alignl { stack { size 12{"net "F=0=F rSub { size 8{p} } - w rSub { size 8{1} } - w rSub { size 8{2} } - w rSub { size 8{s} } } {} #drarrow F rSub { size 8{p} } =w rSub { size 8{1} } +w rSub { size 8{2} } +w rSub { size 8{3} } {} } } {}

So that

F p = ( 26.0 kg + 32.0 kg + 12.0 kg ) ( 9.80 m / s 2 ) = 686 N alignl { stack { size 12{F rSub { size 8{p} } = left ("26" cdot 0" kg "+" 32" cdot "0 kg "+"12" cdot "0 kg" right ) left (9 cdot "8 " {m} slash {s rSup { size 8{2} } } right )} {} #= {underline {"686"" N"}} {} } } {}

Got questions? Get instant answers now!

Test prep for ap courses

Which of the following is not an example of an object undergoing a torque?

  1. A car is rounding a bend at a constant speed.
  2. A merry-go-round increases from rest to a constant rotational speed.
  3. A pendulum swings back and forth.
  4. A bowling ball rolls down a bowling alley.

(a)

Got questions? Get instant answers now!

Five forces of equal magnitude, labeled A – E , are applied to the object shown below. If the object is anchored at point P , which force will provide the greatest torque?

The diagram shows a gray that is a rounded shape of a shoe. Slightly to the right of center is a black dot labeled P. There are 5 red arrows nearly perpendicular to the curved line representing the edge of the object. Arrow A is pointing straight down toward where the line curves around the top. Arrow B is a horizontal line pointing away from the object as the edge curves slightly in an almost vertical line. Arrow C is pointing directly below the P from the edge down. At this point the object begins to curve up from the horizontal. Arrow D is pointing toward straight up toward the object's edge where the object is curving upward more than point C. Arrow E is pointing toward the left edge at around a 45 degree angle toward the object and is approximately perpendicular to the object again.
Five forces acting on an object.
  1. Force A
  2. Force B
  3. Force C
  4. Force D
  5. Force E
Got questions? Get instant answers now!

Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 4

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask