A bucket crane consists of a uniform boom of mass
M = 201 kg and length L= 59.05 ft that pivots at a point on
the bed of a fixed truck. The truck supports an elevated bucket
with a worker inside at the other end of the boom, as shown in
the figure. The bucket and the worker together can be modeled
as a point mass of weight 201 lb located at the end point of
the boom.
Suppose that when the boom makes an angle of 68.7° with the
horizontal truck bed, the bucket crane suddenly loses power,
causing the bucket and boom to rotate freely toward the
ground. Find the magnitude of the angular acceleration la of
the system just after the crane loses power. Take the rotation
axis to be at the point where the boom pivots on the truck bed.
Use g = 9.81 m/s2 for the acceleration due to gravity. For unit
conversions, assume that 1 m = 3.28 ft and 1 lb = 4.45 N.
Express your answer to at least two decimal places.
Answers
Newton's second law for rotational motion allows finding the results for the angular acceleration of the system at the moment of losing power is:
α =0.616 rad / s²
Newton's second law for rotational motion relates the torque to the moment of inertia and the angular acceleration, in the special case where the angular acceleration is zero, it is called the rotational equilibrium condition.
[tex]\sum \tau = I \alpha[/tex]
[tex]\tau = F \ r \ sin \theta[/tex]
where τ is the torque, F is the force, r the distance to the pivot point and θ the angle between the force, the distance, I is the moment of inertia and α is the angular acceleration.
In this case they indicate the values in several different units, let's reduce to the international system of measurements (SI).
Beam mass M = 201 kg Beam length L= 59.05 ft (1m / 3.28 ft) = 18.0 m Worker and basket weight Wh = 201 lb (1N / 0.2248 lb) = 894.1 N Beam angle tea = 68.7º
We place our reference system at the base of the beam on the truck and counterclockwise turns as positive, and in the attached we see a free-body diagram of the system.
[tex]W_m \ L \ sin 68.7 + Mg \ \frac{L}{2} \ sin 68.7 = I \alpha[/tex]
The moment of inertia is an additive scalar quantity, the total moment of inertia is the moment of inertia of the pen plus the moment of inertia of the man.
Moment of inertia of the beam with respect to one end.
[tex]I_[/tex] = ⅓ ML²
moment of inertia of man
[tex]I_m = M_m L^2[/tex]
Let's substitute
[tex](W_m + \frac{Mg}{2} ) \ L \ sin 68.7 = (\frac{1}{3} M + m_m ) L^2 \alpha \\\alpha = \frac{(W_m + \frac{Mg}{2} ) sin 68.7 }{ (\frac{1}{3} M + m_m ) L }[/tex]
Let's calculate
The mass of man is
m = [tex]\frac{W_m}{g}[/tex]
m = 894.1 / 9.8
m = 91.2 kg
[tex]\alpha = \frac{(894.1 +2.1 \ 9.8 ) \ sin 68.7 }{ 18.0 ( \frac{201}{3} + 91 }[/tex]
α = 0.616 rad / s²
In conclusion using Newton's second law for rotational motion we can find the results for the angular acceleration of the system at the moment of losing power is 0.616 rad / s²
Learn more here: brainly.com/question/16428109
Related Questions
pleease help me please!!!
Answers
Answer:
4 filter funnel 7 round bottom flask sorry but that is all I know
A motorcycle travels 90.0 km/h. How many seconds will it take the motorcycle to cover 2.10 x 103 m?
Answers
Answer:
The time taken is 84 seconds, please give the brainliest award would be much appreciated.
What happens if hair has static electricity
Answers
Answer:
it goes up
Explanation:
A train travels meters in the first second of travel, 6 meters again during the second second of travel, and 6 meters again during the third second. Its
acceleration is
O 0 m/s
6 m/s
O 12 m/s/s
18 m/s
O None of the above
Answers
Answer:
0 m/sExplanation:
there is no acceleration, it's velocity is always 6m/s
so your answer is 0m/s
PLEASE HURRY!!
WILL GIVE BRAINLIEST!!!!!!!!
Which of the following types of stars had the smallest initial mass?
Blue main sequence
Neutron star
Red supergiant
White dwarf
Answers
Answer:
the answer is White dwarf
Explanation:
A grand prix racing car has an average lap speed of 180km/h.Each lap is 4.5 km. How many laps will it complete in 1.5 hours
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Lap speed = 180 km/h
Each lap is about 4.5 km
So, number of laps it will complete in 1.5 hour :
[tex] \dfrac{180}{4.5} \times 1.5[/tex][tex] \dfrac{180}{3} [/tex][tex]60 \: \: laps[/tex]Write the number below in scientific notation, 35,600 O A. 3.56 x 103 O B. 3.56 x 103 O C. 3.56 x 104 O D. 3.56 x 105
Answers
A plane moves 599 m northeast along a runway.
If the northern component of this displacement
is 89 m, how large is the eastern component?
Answers
The eastern component of the plane's displacement is 592.35 m.
The given parameters;
the resultant of the plane displacement = 599 mthe northern component of this displacement, Y = 89 mLet the eastern component of this displacement = XThe eastern component of the plane's displacement is calculated by applying Pythagoras theorem as follows;
X² + Y² = 599²
X² + 89² = 599²
X² = 599² - 89²
X² = 350880
X = √350880
X = 592.35 m
Thus, the eastern component of the plane's displacement is 592.35 m
Learn more here:https://brainly.com/question/17033407
An apple falls from a tree and 2.5 seconds later hits the ground. How fast is the apple falling when it hits the ground? Neglect air resistance.
O 2.5
05
O 20
0 25
Answers
Answer:
9.8 m/s²Explanation:
Since the ball rises for 2.5 s, the time to fall is 2.5 s. The acceleration is 9.8 m/s2 everywhere, even when the velocity is zero at the top of the path. Although the velocity is zero at the top, it is changing at the rate of 9.8 m/s² downward.The drawing shows a person looking at a building on top of which an antenna is mounted. The horizontal distance between the person’s eyes and the building is 85.5 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 38.9o with the horizontal. In part b the person is looking at the top of the antenna, and his line of sight makes an angle of 41.6o with the horizontal. How tall is the antenna?
Answers
tan(38.9°) = opposite / adjacent
tan(38.9°) = h1 / 85.5
85.5 tan(38.9°) = 68.990 (5sf)
height of building with antenna (h2):
tan(41.6°) = opposite / adjacent
tan(41.6°) = h2 / 85.5
85.5 tan(41.6°) = 75.910 (5sf)
height of antenna (h2 - h1)
75.910 - 68.990 = 6.92m
Which statement about magnetic force is FALSE?
Answers
Plzz help mee guys I need the ans
Answers
Answer:
the answer is c
Explanation:
copper and silver are the only 2 conductors listed.
Explaining How Temperature Affects the Speed of a Wave
Does sound travel faster in a warm room or a cold room?
Explain your answer
Answers
Answer:
Warm Room
Explanation:
Sound, like any wave, is a transfer of energy from one particle to another.
As temperature rises, each particle will have more energy; they will collide into other particles more often.
As the frequency of collisions increase, the speed of which the sound wave is transferred increases.
A car stops from a speed of 15 m/s in 3 s. How far did it go while stopping?
Answers
Answer:
5m/s
Explanation:
15m/s ÷ 3s = 5m/s
What are some of the strategies that you currently use to make consumer buying decisions
Answers
Answer: hope you find the explanation useful!
Explanation:
Consumer behavior considers numerous reasons why individual, situational, mental, and social individuals look for items, purchase, use, and afterward discard them.
Evaluative criteria are positive qualities that are imperative to you, for example, the cost of the knapsack, the size, the number of compartments, and shading. A portion of these attributes are valued highly as compared to others. For instance, the size of the rucksack and the cost may be more imperative to you than the shading except if, state, the shading is hot pink, and you despise pink.
please can anybody tell me what are these lab equipments
Answers
Answer:
5 is the tripoid stand
Thanks have a bangtastic day
Answer:
hii there
5 ) tripod
6 ) test tube holder
Explanation:
Hope it helps
Have a nice day : )
Since the bullets also have zero velocity, a more exact description of the bullet's state would be _____.
Answers
Answer:
Static equilibrium.
Explanation:
Which two limbic system structures are especially associated with forming new memories?
A. the thalamus and the hypothalamus
B. the thalamus and cerebellum
C. the hypothalamus and the substantia nigra
D. the hippocampus and amygdala
Answers
Answer:
c
Explanation:
because it was c no more explanation
Answer:
Which two limbic system structures are especially associated with forming new memories?
A. the thalamus and the hypothalamus
B. the thalamus and cerebellum
C. the hypothalamus and the substantia nigraD. the hippocampus and amygdala
two balls are dropped from rest and allowed to fall for 1 s and the other for 3 s, compare the distances they have fallen
Answers
distance traveled by 3 second ball ≈ 45m
distance traveled by 1 second ball ≈ 5m
Explanation:
Since the 2 balls started at rest, their v initial = 0, and since no other force is acting on them except for the gravitational force, they accelerate downwards at 10m/s2.
To calculate the distance traveled by both balls, we apply the second formula of UARM motion:
• Δx = 1/2(a)(t^2) + (v0)(t)
Applying both 1s and 3s in this formula will yield you 5m and 45m respectively.
Hope this helps, brainliest would be appreciated :)
Which of the following is an example of an acceptable time to ignore the rules and etiquette of a sport?
A.
when no one else notices
B.
when nobody really gets hurt
C.
when the outcome of the game isn't affected
D.
it's never acceptable to ignore rules and etiquette
Answers
Answer:
D-it's never acceptable to ignore rules and etiquette
Explanation:
We should know that it's never acceptable to ignore rules and etiquette.
What are the rules of etiquette in sports?The rules of etiquette in sports are the rules of the sports that have been document by the various sports federations.
We should know that it's never acceptable to ignore rules and etiquette. These will make the the sports a lawless act and full of chaos.
Learn more about etiquette in sports:https://brainly.com/question/979191
#SPJ2
please answer me!!! asappp
Answers
Answer:
omg this is hard
Explanation:
Yes it is lol
Please solve step by step
Answers
Answer:
F = 1 N
Explanation:
F = Gm₁m₂/r² + kq₁q₂/r²
F = (Gm₁m₂ + kq₁q₂) / r²
F = [6.674(10⁻¹¹)(0.50)(0.25) + 8.988(10⁹(5(10⁻⁶))(-2(10⁻⁶))] / 0.30²
F = 0.9986666667593611111...
F = 1 N
notice that the electrostatic force by itself results in an attraction of
0.99866666666666666666... N
The gravitational force is quite negligible in this example.
Which landform is the farthest north?
Answers
If an object is falling towards the ground with a force of 98 N and accelerates at a rate of 9.8 m/s², what is the mass of the object (mass will be in the unit of kilograms)?
Answers
Answer:
960.4
Explanation:
98x9.8=960.4
Question
What is the total distance traveled if you drive 5.0 miles to school, and then drive 5.0 miles back home?
10.0 miles
10.0 miles
25.0 miles
25.0 miles
0 miles
0 miles
not enough information
Answers
Answer:
10 miles
Explanation:
b/c distance all what we go 5+5=10
If a pool and a cup of water had the same temperature, which would have greater thermal energy?Why?
Answers
Despite being the same temperature, the swimming pool is a much larger thermal energy store than the beaker of water.
What is thermal energy?Thermal energy is the energy contained within a system that controls its temperature. The flow of thermal energy is defined as heat.
Thermodynamics is a branch of physics that deals with how heat is transferred between different systems and how work is done in the process.
Thermal energy sources include natural gas, coal, and oil, as well as solar, heat pump electric, and geothermal heat.
A swimming pool and a beaker of water can both be the same temperature.
Despite being the same temperature, the swimming pool contains significantly more thermal energy than the beaker of water. A heated swimming pool's thermal store contains a lot of energy.
Thus, If a pool and a cup of water had the same temperature, then swimming pool has a much larger thermal energy.
For more details regarding thermal energy, visit:
https://brainly.com/question/11278589
#SPJ6
Book A with a mass of 1.00 kg is placed on a horizontal table. Book B with a mass of 0.500 kg is placed on top of book A. What is the magnitude of the normal force exerted on book A by the table?
Answers
Answer:
Explanation:
N = mg = (1.00 + 0.500)(9.81) = 14.7 N
The magnitude of the normal force exerted on book A by the table is 14.7 N
ForcesFrom the question, we are to determine the magnitude of the normal force.
The normal force ca be calculated by using the formula
[tex]F_{n} = mg[/tex]
Where [tex]F_{n}[/tex] is the normal force
m is the mass
and g is the gravitational field strength ( g = 9.8 m/s²)
The mass will be addition of the masses since Book B is placed on top of the book.
Thus,
m = 1.00 kg + 0.500 kg = 1.50 kg
Then,
[tex]F_{n} = 1.5 \times 9.8[/tex]
[tex]F_{n} = 14.7 \ N[/tex]
Hence, the magnitude of the normal force exerted on book A by the table is 14.7 N
Learn more on Forces here: https://brainly.com/question/13707444
Helllppppp pleaseeeeee!!!
Answers
6. During an impact time casting 5 x 10-45 a gulf club exerts an average impar
force of 5000N on the ball. What linear impulse is delivered to the ball as a result?
Answers
Answer:
2.5 × 10-⁴¹ Ns
Explanation:
Impulse
I = F × t
I = 5000 N × 5 × 10-⁴⁵ s
I = 25 × 10-⁴² Ns
I = 2.5 × 10-⁴¹ Ns
#LearnWithEXO
Explain what would happen if an ebonite rod charged with fur is brought together with an acetate rod charged with silk
Answers
Answer:
The ebonite becomes negatively charged, and the fur becomes positively charged.
Explanation:
When an ebonite rod is rubbed against animal fur, some of the electrons from atoms of the fur are transferred to the rod.The ebonite becomes negatively charged, and the fur becomes positively charged.(a) A positive charge (+) and a negative charge (–) attract each other. (b) Two negative charges repel each other. (c) Two positive charges repel each other.
