A hollow sphere is attached to the end of a uniform rod. The sphere has a radius of 0.64 m and a mass of 0.48 kg. The rod has a length of 1.78 m and a mass of 0.50 kg. The rod is placed on a fulcrum (pivot) at X = 0.34 m from the left end of the rod.
(a) Calculate the moment of inertia (click for graphical table) of the contraption around the fulcrum. kg m2
(b) Calculate the torque about the fulcrum, using CCW as positive. N.m
(c) Calculate the angular acceleration of the contraption, using CCW as positive. rad/s2
(d) Calculate the linear acceleration of the right end of the rod, using up as positive. m/s2
Answers
The image of this hollow sphere and uniform rod is missing, so i have attached it.
Answer:
A) J = 0.7443 kg•m²
B) T = 1.9169 N•m CCW
C) α = 2.5754 rad/s²
D) a = 3.966 m/s²
Explanation:
A) The moment of inertia J of the contraption around the fulcrum is given by the formula;
J = Jℓ + Jr
Let's calculate Jℓ
Jℓ = [((0.34²/3) × 0.50 × 0.34)/1.78] + (0.48 × (0.34 + 0.64)²)
Jℓ = 0.4647 kg•m²
Now, let's Calculate Jr
Jr = ((1.78 - 0.34)²/3) × ((1.78 - 0.34)/1.78) × 0.50
Jr = 0.2796 kg•m²
Thus;
J = 0.4647 + 0.2796
J = 0.7443 kg•m²
(b) Using CCW as positive, Torque in Nm is calculated as;
T = Tℓ - Tr
Let's calculate Tℓ
Tℓ = [(0.48 × (0.64 + 0.34)) + (0.50 × 0.34/1.78) × 0.34/2)] × 9.81
Tℓ = 4.7739 N•m CCW
Now, let's Calculate Tr;
Tr = [(0.50 × (1.78 - 0.34)/1.78) × (1.78 - 0.34)/2)] × 9.81
Tr = 2.857 N•m CW
Thus;
T = 4.7739 - 2.857
T = 1.9169 N•m CCW
(c) The angular acceleration α of the contraption, using CCW is gotten from the formula;
α = T/J
α = 1.9169/0.7443
α = 2.5754 rad/s²
(d) The linear acceleration a of the right end of the rod, using up as positive is given by;
a = α*(1.78 - 0.34)
a = 2.5754 × 1.54
a = 3.966 m/s²
A) the moment of inertia of the contraption is 0.7443 kgm²
B) The torque about the fulcrum is 1.9169 Nm
C) Angular acceleration of the contraption is 2.5754 rad/s²
D) The linear acceleration of the contraption is 3.966 m/s²
Moment of inertia:(A) The moment of inertia I of the contraption around the fulcrum is given by :
[tex]I = [(0.34^2/3) \times 0.50 \times 0.34)/1.78 + (0.48 \times (0.34 + 0.64)^2)] + [(1.78 - 0.34)^2/3) \times (1.78 - 0.34)/1.78) \times 0.50][/tex]
I = 0.4647 + 0.2796
I = 0.7443 kgm²
(B) Using CCW as positive, Torque in Nm is given by;
T = [(0.48 × (0.64 + 0.34)) + (0.50 × 0.34/1.78) × 0.34/2)] × 9.81 - [(0.50 × (1.78 - 0.34)/1.78) × (1.78 - 0.34)/2)] × 9.81
T = 4.7739 - 2.857
T = 1.9169 Nm
(C) The angular acceleration (α) of the contraption is given by:
α = T/I
since, torque is defined as T = Iα
α = 1.9169/0.7443
α = 2.5754 rad/s²
(D) The linear acceleration (a) of the right end of the rod
a = αr
where r is the distance from the pivot
a = α × (1.78 - 0.34)
a = 2.5754 × 1.54
a = 3.966 m/s²
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Related Questions
1. A perspex box has a 10 cm square base and contains water to a height of 10 cm. A piece of rock of mass 600g is lowered into the water and the level rises to 12 cm.
(a) What is the volume of water displaced by the rock?
(b) What is the volume of the rock?
(c) Calculate the density of the rock
Answers
Answer:
(a) The volume of water is 100 cm³
(b) The volume of the rock is 20 cm³
(c) The density of the rock is 30 g/cm³
Explanation:
The given parameters of the perspex box are;
The area of the base of the box, A = 10 cm²
The initial level of water in the box, h₁ = 10 cm
The mass of the rock placed in the box, m = 600 g
The final level of water in the box, h₂ = 12 cm
(a) The volume of water in the box, 'V', is given as follows;
V = A × h₁
∴ The volume of water in the box, V = 10 cm² × 10 cm = 100 cm³
The volume of water in the box, V = 100 cm³
(b) When the rock is placed in the box the total volume, [tex]V_T[/tex], is given by the sum of the rock, [tex]V_r[/tex], and the water, V, is given as follows;
[tex]V_T[/tex] = [tex]V_r[/tex] + V
[tex]V_T[/tex] = A × h₂
∴ [tex]V_T[/tex] = 10 cm² × 12 cm = 120 cm³
The total volume, [tex]V_T[/tex] = 120 cm³
The volume of the rock, [tex]V_r[/tex] = [tex]V_T[/tex] - V
∴ [tex]V_r[/tex] = 120 cm³ - 100 cm³ = 20 cm³
The volume of the rock, [tex]V_r[/tex] = 20 cm³
(c) The density of the rock, ρ = (Mass of the rock, m)/(The volume of the rock)
∴ The density of the rock, ρ = 600 g/(20 cm³) = 30 g/cm³
Which of these statements best explains why the atmosphere of today was partly due to the interactions of spheres in the past?
Bacteria used nutrients in the soil for volcanic eruptions.
Chemicals released from water formed the atmosphere.
The molten Earth released hydrogen and helium into the atmosphere.
The increase in fertility of soil around the volcano helped produce rain.
Answers
Answer:
The answer is: Plants and animals exchange carbon dioxide and oxygen with the atmosphere.
Explanation:
Got the answer right.
Assume your computer has a power rating of 50.0 W, and you use your computer for 7.0 hours a day for a normal school day. If the electric company charges $0.10 per kWh, how much does it cost you to use your computer each school day?
35$
$0.035
$0.005
$0.35
Answers
HTTPS:/www.word doc.com
1. Alexandra and Rachel are on a train that sounds a whistle at a constant frequency as
it leaves the train station. Compared to the sound emitted by the whistle, the sound that
the passengers standing on the platform hear has a frequency that is
a. lower, because the sound-wave fronts reach the platform at a frequency
lower than the frequency at which they are produced
b. lower, because the sound waves travel more slowly in the still air above the
platform than in the rushing air near the train
c. higher, because the sound-wave fronts reach the platform at a frequency
higher than the frequency at which they are produced
d. higher, because the sound waves travel faster in the still air above the
platform than in the rushing air near the train
Answers
Answer: the answer would be C trust me i took the test if its not that its b
hope that helps
Explanation: i took the test
answer:
a) lower because the sound-wave fronts reach the platform at a frequency lower than the frequency at which they are produced
explanation :3
If the train is leaving the train station, then the people who are standing on the platform would hear a sound with a lower frequency since the train is moving further away. ^^
PLEASE HELP The United States spends over $20 billion a year on space exploration through NASA. Do you think that this has been worth the cost? In three to five sentences, provide two specific examples of things we have learned from space exploration, and explain how these examples influence your opinion.(4 points)
Answers
Answer: I think $20 billion a year it’s worth the cost. The reasoning behind that is because we can conduct research on various things that could help out humanity. Therefore we can conclude that’s spending billions of dollars every year is worth it.
Explanation:
How fast were both runners traveling after 4 seconds?
40
Distance (in yards)
30
20
10
1
2.
3
0
Time in seconds
Answers
Answer:
they were fast ⛷⛷
Rhodium is in period 5 of the periodic table. What does this tell you about this element
Answers
Answer:
. It is an extraordinarily rare, silvery-white, hard, corrosion-resistant, and chemically inert transition metal. It is a noble metal and a member of the platinum group.
Explanation:
[4] A tortoise and a hare cover the same distance in a race. The hare goes very fast but stops frequently while the tortoise has a steady pace and finish first
Answers
Answer:
I know that story where the hare sleeps
The average mean distance of Saturn from the sun is
Answers
Answer:
From an average distance of 886 million miles (1.4 billion kilometers), Saturn is 9.5 astronomical units away from the Sun. One astronomical unit (abbreviated as AU), is the distance from the Sun to Earth. From this distance, it takes sunlight 80 minutes to travel from the Sun to Saturn.
we have that from the Question"The average mean distance of Saturn from the sun is" it can be said that Tthe average mean distance of Saturn from the sun is
A distance of 1427 x 10^6 km or 886 696 691 milesFrom the Question we are told
The average mean distance of Saturn from the sun is
Generally
The Sun is the star of the milky way galaxy and its distance from every planet in the milky way determines in one way or another its properties and in-habitability
Saturn being a Planet of the milky way we see that Saturn is a significant distance away from sun
A distance of 1427 x 10^6 km or 886 696 691 miles
Therefore
The average mean distance of Saturn from the sun is
A distance of 1427 x 10^6 km or 886 696 691 miles
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an iron Tyre of diameter 50cm at 288k is to be shrank on to a wheel of diameter 50.35cm.To what temperature must the tyre be heated so that it will slip over the wheel with a radial gap of 0.5mm.Linear expansivity of iron is 0.000012k-1
Answers
Answer:
The answer should be D
Explanation:
Why are protists difficult classify?
Answers
Answer:
Protists are difficult to characterize because of the great diversity of the kingdom. These organisms vary in body form, nutrition, and reproduction. They may be unicellular, colonial, or multicellular.
Answer:
There are many varying characteristics and exceptions to each type of protist.
They have been previously categorized based on what they are not
Recent studies show that protists have not descended from one common ancestor.
Explanation:
its right i took test :)
A motorcycle traveling due east at a constant speed covers 75 kilometers in
1.5 hours. What is its velocity in km/h?
Answers
Answer:
The velocity of the motorcycle is 50km/hr due east.
Velocity=displacement /time
v=75/1.5
v=50km/hr East
A ball is sitting at the top of a ramp. As the ball rolls down the ramp, the potential energy of the ball decreases, what happens to the potential energy as the ball moves
Answers
Answer:
the potential energy decreases as it is converted to kinetic energy.
Explanation:
As things move, their potential energy converts to kinetic energy to power them along. When a ball rolls down the top of a ramp, all the potential energy it accumulated at the top of the ramp converts to kinetic energy to help it roll down. In other words, its potential energy decreases as its kinetic energy increases.
how can we minimise the use of plastic
Answers
Answer:
recyclable toothbrushes, cardboard or metal straws, cardboard gallons instead of plastic, use glass and reusable cups
Explanation:
Steel beams are used for load bearing supports in a building. Each beam is 4.0 m long with a cross-sectional area of 7.5 10-3 m2 and supports a load of 4.5 104 N. Young's modulus for steel is 210 ✕ 109 N/m2.
Answers
5.
2075 Set A Q.No. 20 2070 Supp. Set B Q.No. 2 B What
happens to the kinetic energy of photo electrons when
intensity of light is doubled?
[2]
Answers
Answer:
The energy of each photon can be transformed into kinetic energy and as this energy does not change, the energy of both photoelectrons remains constant,
Explanation:
The photoelectric effect was explained by Einstein, who assumed that the lz is made up of particles called photons each of a given energy, therefore the photoelectric effect can be explained as a collision of particles.
From this explanation we see that the intensity is proportional to the number of existing particles, when we double the intensity we double the number of particles, but the energy of each particle does not change, therefore if we use the conservation of energy.
The energy of each photon can be transformed into kinetic energy and as this energy does not change, the energy of both photoelectrons remains constant, only the number of electrons expelled changes.
____ is a chemical messenger released by virus infected cells
Answers
Answer:
Cytokines is the answer
Explanation:
it is another word for the chemical messanger
A foot spa machine is an electronic gadget used for soaking,bathing and massaging the feet.
Answers
Answer:
Just gonna take this at free points and yes you are right but I am confused on what you wanted us to do
Use the worked example above to help you solve this problem. An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the Eskimo exerts a force on the sled by pulling on the rope. Suppose the coefficient of kinetic friction between the loaded sled and snow is 0.200.
(a) The Eskimo pulls the sled 5.90 m, exerting a force of 1.10 102 N at an angle of θ = 0°. Find the work done on the sled by friction, and the net work. Wfric = Correct: Your answer is correct. . J Wnet = Correct: Your answer is correct. . J
(b) Repeat the calculation if the applied force is exerted at an angle of θ = 30.0° with the horizontal. Wfric = J Wnet = J
Answers
Answer:
(a)
W_friction = 98.1 J
W_net = 550.9 J
(b)
W_friction = 98.1 J
W_net = 463.95 J
Explanation:
(a)
First, we will calculate the work done by friction:
[tex]W_{friction} = \mu R = \mu W = \mu mg\\W_{friction} = (0.2)(50\ kg)(9.81\ m/s^2)\\[/tex]
W_friction = 98.1 J
Now, the work done by Eskimo will be:
[tex]W_{Eskimo} = FdCos\theta\\W_{Eskimo} = (110\ N)(5.9\ m)Cos\ 0^o\\[/tex]
W_Eskimo = 649 J
So, the net work will be:
W_net = W_{Eskimo} - W_{friction}
W_net = 649 J - 98.1 J
W_net = 550.9 J
(b)
First, we will calculate the work done by friction:
[tex]W_{friction} = \mu R = \mu W = \mu mg\\W_{friction} = (0.2)(50\ kg)(9.81\ m/s^2)\\[/tex]
W_friction = 98.1 J
Now, the work done by Eskimo will be:
[tex]W_{Eskimo} = FdCos\theta\\W_{Eskimo} = (110\ N)(5.9\ m)Cos\ 30^o\\[/tex]
W_Eskimo = 562.05 J
So, the net work will be:
W_net = W_{Eskimo} - W_{friction}
W_net = 562.05 J - 98.1 J
W_net = 463.95 J
In a test of an energy-absorbing bumper, a 2800-lb car is driven into a barrier at 5 mi/h. The duration of the impact is 0.4 seconds. When the car rebounds from the barrier [in the opposite direction], the magnitude of its velocity is 1.5 mi/h. Use the principle of impulse and momentum to determine the magnitude of the average horizontal force (lb) exerted on the car during the impact.
Answers
Answer:
F = 2074.13 lb
Explanation:
Given that,
Mass of car, m = 2800 lb = 1270.059 kg
Initial speed, u = 5 mi/h = 2.2352 m/s
Final speed, v = - 1.5 mi/h = -0.67056 m/s (in opposite direction)
Time, t = 0.4 s
We need to find the magnitude of the average horizontal force (lb) exerted on the car during the impact. It can be calculated as :
[tex]F=m\times \dfrac{v-u}{t}\\\\F=1270.059\times \dfrac{-0.67056 -2.2352 }{0.4}\\\\F=9226.21\ N[/tex]
or
F = -2074.13 lb
So, the required force is 2074.13 lb.
a boy standing by a lake sees a fish in the pond and tries to thrust a spear into it he will success or not explain with reason
Answers
He will not probably success to thrust a spear into the fish in the pond because when light travels from water to air , it bends due to refractive property of light.
What is refraction of light?Refraction is the bending of a wave as it travels through different media. The two materials' different densities are what lead to the bending.
Refraction is defined as "the change in a wave's direction as it passes through a medium."
Although light refraction is one of the most frequently seen phenomena, refraction can also occur with sound and water waves. We can use optical tools like lenses, prisms, and magnifying glasses thanks to refraction. We can focus light on our retina because of the refraction of light, which is another benefit.
When light travels from water to air , it bends due to refractive property of light. So, he e will not probably success to thrust a spear into the fish.
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A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping. 1)Which one makes it furthest up the ramp
Answers
Answer:
Both.
Explanation:
Given that a block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping. 1)Which one makes it furthest up the ramp ?
Since both of them have the same mass and the same initial velocity, then, they will both have the same kinetic energy.
That is,
K.E = 1/2mv^2
Friction is a force that opposes motion. And since the frictional force is zero,
Both of them will accelerate from Newton's law.
F = ma
We can therefore conclude that both of them will make it further up the ramp.
(will give brainliest to whoever is first and gives reason) A mass is spun in a circle with a frequency of 40Hz. What is the period of its rotation?
Answers
Answer:
[tex]\huge\boxed{T = 0.025\ seconds}[/tex]
Explanation:
Given:
Frequency = f = 40 Hz
Required:
Time period = T = ?
Formula:
[tex]\sf T = 1 / f[/tex]
Solution:
T = 1 / 40
T = 0.025 seconds
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807A projectile is fired with an initial velocity of 120.0 m/s at an angle, θ, above the horizontal. If the projectile’s initial horizontal speed is 55 meters per second, then angle θ measures approximately
Answers
Answer:
algm sabe tô precisando muito
TRUE OR FALSE
2 QUESTIONS
NEED HELP ASAP
THX :)
LOTS OF POINTS :>
Answers
Answer: Both False
Explanation:
Our Milky Way Galaxy is a spiral galaxy. Some spiral galaxies are what we call "barred spirals" because the central bulge looks elongated
Irregualuar glaxyices are all over the place
Sound travels at a speed of 330 meters/second. If Denise hears a police siren 150 meters away, approximately how long did it take for the siren sound to
travel from the police vehicle to her?
Answers
Answer:
It went about 2 meters away
Explanation:
Water enter the horizontal, circular cross-sectional, sudden-contraction nozzle sketched below at section (1) with a uniformly distributed velocity of 30 ft/s and a pressure of 80 psi. The water exits from the nozzle into the atmosphere at section (2) where the uniformly distributed velocity is 100 ft/s. Determinethe axial component of the anchoring force required to hold the contraction in place.
Answers
This question is incomplete, the missing image is uploaded along this answer.
Answer:
the axial component of the anchoring force required to hold the contraction in place is 365.6 lb
Explanation:
Given the data in the question and as illustrated in the image below;
first we calculate the area at section 1
A₁ = (πD²)/4
we substitute
A₁ = (π(3 in)²)/4
A₁ = 7.06858 in²
we know that; 1 ft = 12 in
A₁ = ( 7.06858 / (12²) ) ft²
A₁ = ( 7.06858 / 144 ) ft²
A₁ = 0.0491 ft²
now, we write the elation for area at section 2
A₂ = πd²/4
here, d is the diameter at section 2
next, we use the conservation of mass equation between the two section;
m" = pV₁A₁ = pV₂A₂
we calculate the mass flow rate;
m" = pV₁A₁
= (1.94[tex]\frac{slug}{ft^2}[/tex]) × 30[tex]\frac{ft}{s}[/tex] × 0.0491 ft²
= 2.8576 slug/s
Now, Apply the linear momentum along the horizontal direction for the control volume between 1 - 2
-pV₁A₁V₁ = pV₂A₂V₂ = P₁A₁ - F[tex]_A[/tex] - P₂A₂
m"( V₂ - V₁ ) = P₁A₁ - F[tex]_A[/tex] - P₂A₂
F[tex]_A[/tex] = P₁A₁ - P₂A₂ - m"( V₂ - V₁ )
we substitute
F[tex]_A[/tex] = ((80×[tex]\frac{144 in^2}{1 ft^2}[/tex])×0.0491 ft²) - (0×(πd²/4)) - 2.8576( 100 - 30 )ft/s
F[tex]_A[/tex] = 565.632 - 0 - 200.032
F[tex]_A[/tex] = 565.632 - 200.032
F[tex]_A[/tex] = 365.6 lb
Therefore, the axial component of the anchoring force required to hold the contraction in place is 365.6 lb
(5 Points)
a) At ground level, the pressure of the helium in a balloon is 1x105
Pa. The volume occupied by the helium is 9.6m The balloon is
released and it rises quickly through the atmosphere. Calculate
the pressure of the helium when it occupies a volume of 12m3.
(3 Marks)
b) A box is 15m below the surface of the sea. The density of sea-
water is 1020 kg/m.
Calculate the pressure on the box due to the sea-water.
(2 Marks)
Answers
Answer:
1. [tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa
2. P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]
Explanation:
1. From Boyles' law;
[tex]P_{1}[/tex][tex]V_{1}[/tex] = [tex]P_{2}[/tex][tex]V_{2}[/tex]
[tex]P_{1}[/tex] = 1 x [tex]10^{5}[/tex] Pa
[tex]V_{1}[/tex] = 9.6 [tex]m^{3}[/tex]
[tex]V_{2}[/tex] = 12 [tex]m^{3}[/tex]
Thus,
1 x [tex]10^{5}[/tex] x 9.6 = [tex]P_{2}[/tex] x 12
[tex]P_{2}[/tex] = [tex]\frac{100000 x 9.6}{12}[/tex]
= 80000
[tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa
2. Pressure, P = ρhg
where: ρ is the density of the fluid, h is the height/ depth and g is the acceleration due to gravity (9.8 m/[tex]s^{2}[/tex]).
Thus,
P = 1020 x 15 x 9.8
= 149940
P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]
A 41.0-kg crate, starting from rest, is pulled across level floor with a constant horizontal force of 135 N. For the first 15.0 m the floor is essentially frictionless, whereas for the next 12.0 m the coefficient of kinetic friction is 0.320. (a) Calculate the work done by all the forces acting on the crate, during the entire 27.0 m path. (b) Calculate the total work done by all the forces. (c) Calculate the final speed of the crate after being pulled these 27.0 m.
Answers
Answer:
Explanation:
From the information given;
mass of the crate m = 41 kg
constant horizontal force = 135 N
where;
[tex]s_1 = 15.0 \ m \\ \\ s_2 = 12.0 \ m[/tex]
coefficient of kinetic friction [tex]u_k[/tex] = 0.28
a)
To start with the work done by the applied force [tex](W_f)[/tex]
[tex]W_F = F\times (s_1 +s_2) \times cos(0) \ J[/tex]
[tex]W_F = 135 \times (12 +15) \times cos(0) \ J \\ \\ W_F = (135 \times 37 )J \\ \\ W_F =4995 \ J[/tex]
Work done by friction:
[tex]W_{ff} = -\mu\_k\times m \times g \times s_2 \\ \\ W_{ff} = -0.320 \times 41 \times 9.81 \times 12 \ J \\ \\ W_{ff} = -1544.49 \ J[/tex]
Work done by gravity:
[tex]W_g = mg \times (s_1+s_2) \times cos (90)} \ J \\ \\ W_g = 0 \ j[/tex]
Work done by normal force;
[tex]W_n = N \times (s_1 + s_2) \times cos (90) \ J[/tex]
[tex]W_n = 0 \ J[/tex]
b)
total work by all forces:
[tex]W = F \times (s_1 + s_2) + \mu_k \times m \times g \times s_2 \times 180 \\ \\ W = 135 \times (15+12) \ J - 0.320 \times 41 \times 9.81 \times 12[/tex]
W = 2100.5 J
c) By applying the work-energy theorem;
total work done = ΔK.E
[tex]W = \dfrac{1}{2}\times m \times (v^2 - u^2)[/tex]
[tex]2100.5 = 0.5 \times 41 \times v^2[/tex]
[tex]v^2 = \dfrac{2100.5}{ 0.5 \times 41 }[/tex]
[tex]v^2 = 102.46 \\ \\ v = \sqrt{102.46} \\ \\ \mathbf{v = 10.1 \ m/s}[/tex]
The current supplied to an air conditioner unit is 4.00 amps. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density is n=8.48×1028electronsm3n=8.48×1028electronsm3 . Find the magnitude of (a) current density and (b) the drift velocity.
Answers
Answer:
a. 7.6 * 10^5 A/m^2
b. 5.6 * 10-^5 m/s
Explanation:
lol