<< Chapter < Page Chapter >> Page >
net τ = 0 size 12{"net "τ=0} {}

where net means total. Torques, which are in opposite directions are assigned opposite signs. A common convention is to call counterclockwise (ccw) torques positive and clockwise (cw) torques negative.

When two children balance a seesaw as shown in [link] , they satisfy the two conditions for equilibrium. Most people have perfect intuition about seesaws, knowing that the lighter child must sit farther from the pivot and that a heavier child can keep a lighter one off the ground indefinitely.

Two children are sitting on a seesaw. On the left side, a lighter child is sitting and on the right, a heavier one. The distance of the lighter child from the fulcrum is more than that of heavier child. At the fulcrum, an upward force vector labeled as F-p is shown. The weights of the two children, w-one and w-two, are shown as vectors in the downward direction, and the force at the fulcrum, F-p, is shown as a vector in the upward direction.
Two children balancing a seesaw satisfy both conditions for equilibrium. The lighter child sits farther from the pivot to create a torque equal in magnitude to that of the heavier child.

She saw torques on a seesaw

The two children shown in [link] are balanced on a seesaw of negligible mass. (This assumption is made to keep the example simple—more involved examples will follow.) The first child has a mass of 26.0 kg and sits 1.60 m from the pivot.(a) If the second child has a mass of 32.0 kg, how far is she from the pivot? (b) What is F p , the supporting force exerted by the pivot?

Strategy

Both conditions for equilibrium must be satisfied. In part (a), we are asked for a distance; thus, the second condition (regarding torques) must be used, since the first (regarding only forces) has no distances in it. To apply the second condition for equilibrium, we first identify the system of interest to be the seesaw plus the two children. We take the supporting pivot to be the point about which the torques are calculated. We then identify all external forces acting on the system.

Solution (a)

The three external forces acting on the system are the weights of the two children and the supporting force of the pivot. Let us examine the torque produced by each. Torque is defined to be

τ = rF sin θ . size 12{τ= ital "rF""sin"θ} {}

Here θ = 90º , so that sin θ = 1 for all three forces. That means r = r size 12{r rSub { size 8{ ortho } } =r} {} for all three. The torques exerted by the three forces are first,

τ 1 = r 1 w 1

second,

τ 2 = r 2 w 2

and third,

τ p = r p F p = 0 F p = 0.

Note that a minus sign has been inserted into the second equation because this torque is clockwise and is therefore negative by convention. Since F p acts directly on the pivot point, the distance r p is zero. A force acting on the pivot cannot cause a rotation, just as pushing directly on the hinges of a door will not cause it to rotate. Now, the second condition for equilibrium is that the sum of the torques on both children is zero. Therefore

τ 2 = τ 1 , size 12{τ rSub { size 8{2} } =τ rSub { size 8{1} } } {}

or

r 2 w 2 = r 1 w 1 . size 12{r rSub { size 8{2} } w rSub { size 8{2} } =r rSub { size 8{1} } w rSub { size 8{1} } } {}

Weight is mass times the acceleration due to gravity. Entering mg for w , we get

r 2 m 2 g = r 1 m 1 g .

Solve this for the unknown r 2 size 12{r rSub { size 8{2} } } {} :

r 2 = r 1 m 1 m 2 . size 12{r rSub { size 8{2} } =r rSub { size 8{1} } { {m rSub { size 8{1} } } over {m rSub { size 8{2} } } } } {}

The quantities on the right side of the equation are known; thus, r 2 size 12{r rSub { size 8{2} } } {} is

r 2 = 1.60 m 26.0 kg 32.0 kg = 1.30 m . size 12{r rSub { size 8{2} } = left (1 "." "60"" m" right ) { {"26" "." 0" kg"} over {"32" "." " 0 kg"} } =1 "." "30"" m"} {}

As expected, the heavier child must sit closer to the pivot (1.30 m versus 1.60 m) to balance the seesaw.

Solution (b)

This part asks for a force F p . The easiest way to find it is to use the first condition for equilibrium, which is

net F = 0 .

The forces are all vertical, so that we are dealing with a one-dimensional problem along the vertical axis; hence, the condition can be written as

Questions & Answers

What does mean ohms law imply
Victoria Reply
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
Vineeta Reply
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
Abubakar Reply
What is a molecule
Samuel Reply
Is a unit of a compound that has two or more atoms either of the same or different atoms
Justice
A molecule is the smallest indivisible unit of a compound, Just like the atom is the smallest indivisible unit of an element.
Rachel
what is a molecule?
Vineeta
what is a vector
smith Reply
A quantity that has both a magnitude AND a direction. E.g velocity, acceleration, force are all vector quantities. Hope this helps :)
deage
what is the difference between velocity and relative velocity?
Mackson
Velocity is the rate of change of displacement with time. Relative velocity on the other hand is the velocity observed by an observer with respect to a reference point.
Chuks
what do u understand by Ultraviolet catastrophe?
Rufai
A certain freely falling object, released from rest, requires 1.5seconds to travel the last 30metres before it hits the ground. (a) Find the velocity of the object when it is 30metres above the ground.
Mackson
A vector is a quantity that has both magnitude and direction
Rufus
the velocity Is 20m/s-2
Rufus
derivation of electric potential
Rugunda Reply
V = Er = (kq/r^2)×r V = kq/r Where V: electric potential.
Chuks
what is the difference between simple motion and simple harmonic motion ?
syed
hi
Peace
hi
Rufus
hi
Chip
simple harmonic motion is a motion of tro and fro of simple pendulum and the likes while simple motion is a linear motion on a straight line.
Muinat
a body acceleration uniform from rest a 6m/s -2 for 8sec and decelerate uniformly to rest in the next 5sec,the magnitude of the deceleration is ?
Patricia Reply
The wording not very clear kindly
Moses
6
Leo
9.6m/s2
Jolly
the magnitude of deceleration =-9.8ms-2. first find the final velocity using the known acceleration and time. next use the calculated velocity to find the size of deceleration.
Mackson
wrong
Peace
-3.4m/s-2
Justice
Hi
Abj
Firstly, calculate final velocity of the body and then the deceleration. The final ans is,-9.6ms-2
Muinat
8x6= 48m/-2 use v=u + at 48÷5=9.6
Lawrence
can i define motion like this motion can be define as the continuous change of an object or position
Shuaib Reply
Any object in motion will come to rest after a time duration. Different objects may cover equal distance in different time duration. Therefore, motion is defined as a change in position depending on time.
Chuks
Practice Key Terms 4

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask