Unit 4 Statics - Centre for Distance Learning and … 4 Statics.pdf · Unit 4 Statics Physics...

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Unit 4 Statics Static Equilibrium

Translational Forces

Torque

Dynamics vs Statics ___________ is the study of ________ and _________.

We study ____ objects ________.

_________ is the study of _______ and ___________.

We study _____ objects __________________.

Recall Newton’s First Law

All objects remain at _______, or continue to move at a

__________________ unless acted upon by an

___________________________.

Thus, an object will stay at _____ if all of the forces acting on the

object __________ each other.

We say that the object is in a state of ____________________

if it is at __________.

An object ________________________ ___________ is in a

state of _______________________________

In Static Equilibrium

We must consider:

_________________________

Forces that make objects ______ from one

__________________________.

_________________________

Forces that make an object _________ about a

_________.


Translation Forces Activity

Draw a free body diagram.

What is the mass of the object?

Find the tensions in the ropes below.


OR

Why do the vectors connect together?

We can find the tensions using the Law of

Sines

Find T1

Find T2

Find the mass of the snowflake


Torques

(Rotational Forces)

Archimedes said "Give me a lever long enough and a fulcrum on

which to place it, and I shall move the world."

Centre of Mass

(Gravity Spot)

The __________ is a single point in a body at which its entire

mass is considered to be concentrated.

An object can balance on a point only if its center of mass is

directly _________ the point.

Alternatively, if you hang an object from a string, the object's

center of mass will be directly __________ the string.

It is usually located near the more __________ part of an object.

The centre of mass is also called the _______________, which is

the point at which the force of ________ acts. The force of

gravity is equal on both sides of the object’s centre of

_________.

The center of mass is an important point on an aircraft, as it

defines the amount of ______ forward or behind the center of

gravity that needs to be moved in order to pitch the plane up or

down without applying any external forces


Location of Centre of Mass

For ____________ shaped objects the centre of mass is at the

_______________________.

For example the centre of mass of a ball (sphere) is located at

the ________ of the ball.

For __________ shaped objects, the centre of mass is located at

its _______ point in a gravitational field.

Example:

Find the centre of mass of the following:

1. A uniform 10 m log?

2. A uniform 15 m extension ladder?

3. A broom?

4. A Triangle

5. A boomerang?

Note: In the case of a boomerang the centre of mass is

________________________________________________

A male versus A female

A person's center of mass is slightly below his/her

_____________, which is nearly the __________ center of a

person.

Males and females have ________ centers of mass


Females' centers of mass are ______ than those of males.

The average ratio of center of mass to height in females is

approximately 0.543 and the average ratio of center of mass to

height in males is approximately 0.560.

Where is the centre of mass of a hammer?

When a force is not directed through an object’s centre of mass,

the force will cause the object to ________

Example:

Look in text pages 233 – 238

Torque

Torque: The __________ force caused by a _______ acting

at a distance from a ___________

Examples:

_________________________________

_________________________________

_________________________________

_________________________________

Equation for Torque

where

is Torque

is the distance a Force is applied from a pivot point (aka

point of rotation)


is the component of the force that acts perpendicular

to the surface.

What are the units for Torque?

Is Torque a vector quantity?

Examples of Torque

1. Find the torque supplied to a 75 cm wide door by the following

forces applied at the edge of the door:

A) 20N

B) 30 N at 30o to the perpendicular to the door

2. Suppose a bolt requires 65 Nm to be properly tightened. What force

is required if the wrench is 15 cm long?


Not tested on public, but useful info in real life!! 3. In the old British system (and in the US) torque is measured in ft-

lbs. How many Nm is one ft-lb?

One foot is 0.305 m.

One kilogram is 2.2 pounds

Static Equilbrium

Consists of 2 Parts

First Part

Translation Forces

where ______is the sum of ALL of the

forces acting on an object ________________

________________________

Second Part

Torques (or Moments of Force)

where _____ is the sum of ALL of the

(____________________) acting on an object.

NOTE: These forces are NOT acting _________

______________________________________

______________________________________

______________________________________


Static Problems Torque

(we did translational forces in unit 2)

_______________________________

_______________________________

_______________________________

_______________________________

Torque Questions

Seesaw problems:

1. Pat and Tyler are playing on a 4 m long seesaw that is supported at

the centre. If Pat has a mass of 30 kg and sits at one end of the

seesaw, where should Tyler (mass = 35 kg) sit so that the seesaw

balances?


2. A playground seesaw with a total length of 5.0 m and a mass of 30.0

kg is pivoted at its center. A 20.0 kg child sits on one end of the

seesaw.

a) Where should a person push with a force of 220 N in order to hold

the seesaw level?

b) Where should a 40.0 kg child sit to balance the seesaw?

3. Consider the diagram below :A load weighing 60 N is to be

supported by a force F applied at the end of a 5.0 kg, uniform, lever as

shown. What Force is necessary if the fulcrum is placed at position A?

A

1.2m

40cm

60 N

F


4. What force is needed to balance the 10.0 kg mass if:

A) the seesaw is massless. B) the seesaw has a mass of 42 kg

5. In order to hang a mass of M1=30.0kg from the horizontal flat roof

of a building, a plank of length 2.4 m is placed on the roof. A rock of

mass M2= 15.0 kg is placed on one end. How far can the end of the plank

reach over the building without tipping over?

2.0 m

1.0 m

10.0 kg

F


Cantilever Problems

1. A 1.5 x 10 3 kg car is crossing a 120 m long flat bridge which is

supported at both ends. When the car is 32 m from one end, what

force must each end support be able to provide?

2.A 4.0 m diving board is supported by two blocks, one at the end and

the second 1.0 m from the end. A 60.0 kg person stands at the end

of the board. Find the forces given to the board by the two

supports if:

A) The board is a Canadian Tire special - no mass.


B) The mass of the board is 40.0 kg.

3. A uniform rod of mass 13 kg and length 3.0m rests on two points,

one at its left end and one at the centre point. What are the contact

forces on the rod at these points? Comment on the stability of this

situation.


4. Two people of unequal strength must carry a uniform beam of

length L while holding it horizontal. The weaker of the two holds the

beam at one end.

A) How far from the other end must the stronger person hold the

beam in order to support three quarters of the weight?

B) Is there a way in which the stronger person can carry the

beam at one end and still support more than one half the weight of

the beam?

5. In the diagram below, a 10.0 m uniform horizontal beam, weighing

1.00 × 102 N is supported by a rope at each end. If a 4.00 × 102 N box is

positioned 2.0 m from the left end of the beam, what is the tension in

each of the support ropes (T1 andT2)? (June 2005 - Public)


Crane Problems

(or Suspended load from a strut and cable)

1. Determine the tension in the cable and the compression force in

the boom to support the 1.0 x 10 2 kg object. The angle between

the boom and the supporting cable is 37°.

2. A crane is used to lift a uniform 24 m long pipe with a mass of 730

kg as shown in the diagram below. What minimum tension is

required by the cable to lift the end of the pipe off the ground?


3. A traffic light hangs from a structure as shown. The uniform

aluminum pole AD is 4.0 m long and weighs 5.0kg. The weight of the

traffic light is 10.0 kg.

A) Determine the tension in the horizontal, massless cable CD.

B) Determine the vertical and horizontal components of the force

exerted by the pivot A on the aluminum pole


4. A uniform rod of length L and mass of 4.0 kg is hinged at the left

end. A 25.0 kg sign is suspended from the right end. A guy wire is

connected to the end of the rod and fastened to a wall.

A) Draw a free body diagram for the rod .

B) Determine the tension in the guy wire.

June 2004 Public

(i) Sketch the free body diagram for

the rod in the diagram. Label all

forces. (2 marks)


(ii) If the mass of the block is 5.0 kg and the rod is uniform with a

mass of 0.40 kg, what is the magnitude of the tension in the wire?

(3 marks)

Ladder Problems

For problems involving a ladder (or other object) leaning against a

wall, the _________ should be considered _______________.

These problems should be limited to ________ forces acting in

different directions

(i.e., three different sets of components).


1. A 8.2 kg ladder is resting against a wall such that the angle made

with the ground is 75o. Find the force friction required by the ground

to keep the ladder from moving.

2. A 4.0 m ladder is resting against a building such that the foot of

the ladder is 0.75 m away from the building. The ladder weighs 99 N.

Find the force of friction required at ground level to keep the ladder

from sliding if a 75 kg person stands at following locations along the

ladder:

A) 1.0 m from the bottom of the ladder.


B) at the middle of the ladder.

C) 3.0 m from the bottom.


D) 3.7 m from the bottom

3. A 5.0 m long ladder leans against a wall at a point 4.0 m above

the ground as shown. The ladder is uniform and has a mass of 12.0

kg. A 55 kg painter is standing 3.0 m up the ladder. Assuming the

wall is frictionless (but the ground is not) determine the forces

exerted on the ladder by the ground and the wall.

Unit 4 Statics - Centre for Distance Learning and … 4 Statics.pdf · Unit 4 Statics Physics...

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