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Similar observations can be made using a meter stick held at different locations along its length.

A pole vaulter is standing on the ground holding a pole with his two hands. The center of gravity of the pole is between the hands of the pole vaulter and is near the right hand of the man. The weight W is shown as an arrow downward toward center of gravity. The reactions F sub R and F sub L of the hands of the man are shown with vectors in upward direction. A free body diagram of the situation is shown on the top right side of the figure.
A pole vaulter holds a pole horizontally with both hands.

A pole vaulter is standing on the ground holding a pole with his two hands. The center of gravity of the pole is between the hands of the pole vaulter and is near the right hand of the man. The weight W is shown as an arrow downward toward center of gravity. The reactions F sub R and F sub L of the hands of the man are shown with vectors in upward direction. A free body diagram of the situation is shown on the top right side of the figure.
A pole vaulter is holding a pole horizontally with both hands. The center of gravity is near his right hand.

A pole vaulter is standing on the ground holding a pole from one side with his two hands. The centre of gravity of the pole is to the left of the pole vaulter. The weight W is shown as an arrow downward at center of gravity. The reaction F sub R is shown with a vector pointing downward from the man’s right hand and F sub L is shown with a vector in upward direction at the location of the man’s left hand. A free body diagram of the situation is shown on the top right side of the figure.
A pole vaulter is holding a pole horizontally with both hands. The center of gravity is to the left side of the vaulter.

If the pole vaulter holds the pole as shown in [link] , the situation is not as simple. The total force he exerts is still equal to the weight of the pole, but it is not evenly divided between his hands. (If F L = F R size 12{F rSub { size 8{L} } =F rSub { size 8{R} } } {} , then the torques about the cg would not be equal since the lever arms are different.) Logically, the right hand should support more weight, since it is closer to the cg. In fact, if the right hand is moved directly under the cg, it will support all the weight. This situation is exactly analogous to two people carrying a load; the one closer to the cg carries more of its weight. Finding the forces F L size 12{F rSub { size 8{L} } } {} and F R size 12{F rSub { size 8{R} } } {} is straightforward, as the next example shows.

If the pole vaulter holds the pole from near the end of the pole ( [link] ), the direction of the force applied by the right hand of the vaulter reverses its direction.

What force is needed to support a weight held near its cg?

For the situation shown in [link] , calculate: (a) F R size 12{F rSub { size 8{R} } } {} , the force exerted by the right hand, and (b) F L size 12{F rSub { size 8{L} } } {} , the force exerted by the left hand. The hands are 0.900 m apart, and the cg of the pole is 0.600 m from the left hand.

Strategy

[link] includes a free body diagram for the pole, the system of interest. There is not enough information to use the first condition for equilibrium (net F = 0 size 12{F=0} {} ), since two of the three forces are unknown and the hand forces cannot be assumed to be equal in this case. There is enough information to use the second condition for equilibrium (net τ = 0 ) size 12{ ital "net"`τ=0} {} if the pivot point is chosen to be at either hand, thereby making the torque from that hand zero. We choose to locate the pivot at the left hand in this part of the problem, to eliminate the torque from the left hand.

Solution for (a)

There are now only two nonzero torques, those from the gravitational force ( τ w size 12{τ rSub { size 8{W} } } {} ) and from the push or pull of the right hand ( τ R size 12{τ rSub { size 8{R} } } {} ). Stating the second condition in terms of clockwise and counterclockwise torques,

net τ cw = –net τ ccw . size 12{"net "τ rSub { size 8{"cw"} } ="net"τ rSub { size 8{"ccw"} } } {}

or the algebraic sum of the torques is zero.

Here this is

τ R = –τ w

since the weight of the pole creates a counterclockwise torque and the right hand counters with a clockwise torque. Using the definition of torque, τ = rF sin θ size 12{τ= ital "rF""sin"θ} {} , noting that θ = 90º size 12{θ} {} , and substituting known values, we obtain

0 . 900 m F R = 0 .600 m mg . size 12{ left (0 "." "900"" m" right ) left (F rSub { size 8{R} } right )= left (0 "." "600"" m" right ) left ( ital "mg" right )} {}

Thus,

F R = 0.667 5.00 kg 9.80 m/s 2 = 32.7 N.

Solution for (b)

The first condition for equilibrium is based on the free body diagram in the figure. This implies that by Newton’s second law:

F L + F R mg = 0 size 12{F rSub { size 8{L} } +F rSub { size 8{R} } - ital "mg"=0} {}

From this we can conclude:

F L + F R = w = mg size 12{F rSub { size 8{L} } +F rSub { size 8{R} } =w= ital "mg"} {}

Solving for F L size 12{F rSub { size 8{L} } } {} , we obtain

F L = mg F R = mg 32 . 7 N = 5.00 kg 9.80 m/s 2 32.7 N = 16.3 N alignl { stack { size 12{F rSub { size 8{L} } = ital "mg" - F rSub { size 8{R} } } {} #= ital "mg" - "32" "." 7 {} # =0 "." "333" ital "mg" {} #= left (0 "." "333" right ) left (5 "." "00"" kg" right ) left (9 "." "80"" m/s" rSup { size 8{2} } right ) {} # ="16" "." 3" N" {}} } {}

Discussion

F L size 12{F rSub { size 8{L} } } {} is seen to be exactly half of F R size 12{F rSub { size 8{R} } } {} , as we might have guessed, since F L is applied twice as far from the cg as F R .

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If the pole vaulter holds the pole as he might at the start of a run, shown in [link] , the forces change again. Both are considerably greater, and one force reverses direction.

Take-home experiment

This is an experiment to perform while standing in a bus or a train. Stand facing sideways. How do you move your body to readjust the distribution of your mass as the bus accelerates and decelerates? Now stand facing forward. How do you move your body to readjust the distribution of your mass as the bus accelerates and decelerates? Why is it easier and safer to stand facing sideways rather than forward? Note: For your safety (and those around you), make sure you are holding onto something while you carry out this activity!

Phet explorations: balancing act

Play with objects on a teeter totter to learn about balance. Test what you've learned by trying the Balance Challenge game.

Balancing Act

Summary

  • Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain. We have discussed the problem-solving strategies specifically useful for statics. Statics is a special case of Newton’s laws, both the general problem-solving strategies and the special strategies for Newton’s laws, discussed in Problem-Solving Strategies , still apply.

Conceptual questions

When visiting some countries, you may see a person balancing a load on the head. Explain why the center of mass of the load needs to be directly above the person’s neck vertebrae.

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Problems&Exercises

To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. What are the magnitudes of the forces on the ladder at the top and bottom?

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In [link] , the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the hands are 0.700 m apart. Calculate the force exerted by (a) his right hand and (b) his left hand. (c) If each hand supports half the weight of the pole in [link] , show that the second condition for equilibrium (net τ = 0) is satisfied for a pivot other than the one located at the center of gravity of the pole. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium described above.

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Questions & Answers

if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
Declan Reply
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flow rate is the volume of fluid which passes per unit time;
Rev
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
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When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
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nehemiah
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i don't know
Adah
y
nehemiah
what are the relationship between distance and displacement
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They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
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I have not try that experiment but I think it will magnet....
Rev Reply
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Jeff
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If a magnet is in a pool of water, would it be able to have a magnetic field?.
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Fokoua
I=q/t
saifullahi
Current is the flow of electric charge per unit time.
saifullahi
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saifullahi
materials that allows charge to flow at varying conditions, temperature for instance.
Mokua
these are materials which have electrical conductivity greater than the insulators but less than metal, in these materials energy band Gap is very narrow as compared to insulators
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materials that allows charge to flow at varying conditions, temperature for instance.
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it is branch of science that deal with interaction matter and energy is called physics . and physics is based in experiential observation and quentative measurement.
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to briefly understand the concept of physics start with history and a brief history of time by Stephen hawkings is what made me have interest in physics
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physics is a branch of science which deals with the study of matter, in relation to energy.
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physics is a natural science that involve the study of matter and it's motion through space and time, along with related concept such as energy and force
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Physics is the science of natural things. for instance, take classical laws which describe the principles of working of the macro realm and then take the quantum laws which describe the quantum realm. It relates everything in this universe –e. g when you see anything, actually photons penetrate.
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the time rate of flow of electric charge, inthe direction that a positive moving chargewould take and having magnitude equal tothe quantity of charge per unit time:measured in amperes.
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Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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