1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vsevolod [243]
3 years ago
10

Rigid Body Statics in 3 Dimensions

Physics
1 answer:
slamgirl [31]3 years ago
7 0

Explanation:

Draw a free body diagram of the bar.

There are 3 reaction forces at O in the x, y, and z direction (Ox, Oy, and Oz).

There is a tension force Tac at A in the direction of the rope.  There are also tension forces Tbd and Tbe at B in the direction of the ropes.

Finally, there is a weight force mg pulling down halfway between A and B, where m = 400 kg.

There are 6 unknown variables, so we'll need 6 equations to solve.  Summing the forces in the x, y, and z direction will give us 3 equations.  Summing the torques about the x, y, and z axes will give us 3 more equations.

First, let's find the components of the tension forces.

Tbe is purely in the z direction.

Tbd has components in the y and z directions.  The length of Tbd is √8.

(Tbd)y = 2/√8 Tbd

(Tbd)z = 2/√8 Tbd

Tac has components in the x, y, and z directions.  The length of Tac is √6.

(Tac)x = 1/√6 Tac

(Tac)y = 1/√6 Tac

(Tac)z = 2/√6 Tac

Sum of the forces in the +x direction:

∑F = ma

Ox − (Tac)x = 0

Ox − 1/√6 Tac = 0

Sum of the forces in the +y direction:

∑F = ma

Oy + (Tac)y + (Tbd)y − mg = 0

Oy + 1/√6 Tac + 2/√8 Tbd − mg = 0

Sum of the forces in the +z direction:

∑F = ma

Oz − (Tac)z − (Tbd)z − Tbe = 0

Oz − 2/√6 Tac − 2/√8 Tbd − Tbe = 0

Sum of the torques counterclockwise about the x-axis:

∑τ = Iα

mg (2 m) − (Tac)y (2 m) − (Tbd)y (2 m) = 0

mg − (Tac)y − (Tbd)y = 0

mg − 1/√6 Tac − 2/√8 Tbd = 0

Sum of the torques counterclockwise about the y-axis:

∑τ = Iα

-(Tac)x (2 m) + (Tbd)z (1.5 m) + Tbe (1.5 m) = 0

-4 (Tac)x + 3 (Tbd)z + 3 Tbe = 0

-4/√6 Tac + 6/√8 Tbd + 3 Tbe = 0

Sum of the torques counterclockwise about the z-axis:

∑τ = Iα

-mg (0.75 m) + (Tbd)y (1.5 m) = 0

-mg + 2 (Tbd)y = 0

-mg + 4/√8 Tbd = 0

As you can see, by summing the torques about axes passing through O, we were able to write 3 equations independent of those reaction forces.  We can solve these equations for the tension forces, then go back and find the reaction forces.

-mg + 4/√8 Tbd = 0

4/√8 Tbd = mg

Tbd = √8 mg / 4

Tbd = √8 (400 kg) (9.8 m/s²) / 4

Tbd = 2772 N

mg − 1/√6 Tac − 2/√8 Tbd = 0

1/√6 Tac = mg − 2/√8 Tbd

Tac = √6 (mg − 2/√8 Tbd)

Tac = √6 ((400 kg) (9.8 m/s²) − 2/√8 (2772 N))

Tac = 4801 N

-4/√6 Tac + 6/√8 Tbd + 3 Tbe = 0

3 Tbe = 4/√6 Tac − 6/√8 Tbd

Tbe = (4/√6 Tac − 6/√8 Tbd) / 3

Tbe = (4/√6 (4801 N) − 6/√8 (2772 N)) / 3

Tbe = 653 N

Now, using our sum of forces equations to find the reactions:

Ox − 1/√6 Tac = 0

Ox = 1/√6 Tac

Ox = 1/√6 (4801 N)

Ox = 1960 N

Oy + 1/√6 Tac + 2/√8 Tbd − mg = 0

Oy = mg − 1/√6 Tac − 2/√8 Tbd

Oy = (400 kg) (9.8 m/s²) − 1/√6 (4801 N) − 2/√8 (2772 N)

Oy = 0 N

Oz − 2/√6 Tac − 2/√8 Tbd − Tbe = 0

Oz = 2/√6 Tac + 2/√8 Tbd + Tbe

Oz = 2/√6 (4801 N) + 2/√8 (2772 N) + 653 N

Oz = 6533 N

You might be interested in
What is happening if energy input remains constant and voltage remains the same in a circuit, but the current decreases?
atroni [7]
The resistance of the circuit will definitely increase. This can be proved by the Ohm's Law where it is said that the potential difference across a conductor is directly proportional to the current and the proportionality constant is known as the resistance. The law is expressed as V = IR. As we can see, when the voltage remains constant while the current decreases then the resistance will increase.<span />
3 0
2 years ago
Which quantity is a vector quantity A. Acceleration B. Mass C. Speed D. Volume
Marianna [84]

Answer:

Acceleration

Explanation:

A vector quantity has a magnitude and direction. Mass, Speed and Volume are all scalar quantities because they only have magnitude, and not direction.

5 0
3 years ago
Children are sled riding on a hill One little girl pulls her sled back up the hill and does 379.5 joules of work while pulling i
Serggg [28]

Answer:

2.2N

Explanation:

Given parameters:

Work done  = 379.5J

Height  = 173m

Unknown:

Amount of force exerted on the sled  = ?

Solution:

The amount of force she exerted on the sled is the same as her weight.

Work done is the force applied to move a body through a distance.

      Work done  = mgh

m is the mass

g is the acceleration due to gravity

h is the height

     mg  = weight;

        Work done  = weight x h

           379.5 = weight  x  173

           weight  = \frac{379.5}{173}   = 2.2N

4 0
2 years ago
You are holding the axle of a bicycle wheel with radius
erastova [34]

Answer:

The angular acceleration of the wheel is -6.54 rad/s²

Explanation:

We'll use the equations of motion for this.

w = 2πf

f = 75 rpm = 1.25 rps = 1.25 rev/s

w₀ = initial angular velocity = 2π × 1.25 = 7.85 rad/s

w = final angular velocity = 0 rad/s

t = 1.2 s

α = ?

w = w₀ + αt

0 = 7.85 + 1.2α

α = 7.85/1.2 = - 6.54 rad/s²

6 0
3 years ago
Describe how freezing could be used to remove sugar from a mixture of sugar and water?
VARVARA [1.3K]
When the mixture (the sugar and water) is frozen, it separates. The water molecules get closer together, separating and pushing the sugar crystals to the top.<span />
7 0
3 years ago
Read 2 more answers
Other questions:
  • You build a 2.0-kg mound of mashed potatoes on a kitchen scale (which is a spring scale). You then use a large spoon to press on
    15·2 answers
  • An air compressor compresses 15 L/s of air at 120 kPa and 20°C to 800 kPa and 300°C while consuming 6.2 kW of power. How much of
    7·1 answer
  • Describe the basis concept of the atwood’s machine
    11·1 answer
  • The step by step experiment to determine the cubic expansivity of a liquid
    15·1 answer
  • What are the similarities in the 3 types of waves
    6·1 answer
  • How long does it take to drive 500 miles at 70 mph?
    7·1 answer
  • Plz help...Thanks.
    6·1 answer
  • Earth's core is composed primarily of _____. -iron oxides and magnesium -silicon and iron -iron and nickel -magnesium and nickel
    11·1 answer
  • A 16 lb weight stretches a spring 6 inches in equilibrium. It is attached to a damping mechanism with constant c. Find all value
    9·1 answer
  • 1. Budding is a way that some very tiny organisms can reproduce.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!