A solid sphere is released from the top of a ramp that is at a height
h1 = 2.20 m.
It rolls down the ramp without slipping. The bottom of the ramp is at a height of
h2 = 1.87 m
above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.14 m.
a.) Through what horizontal distance d, in meters, does the ball travel before landing?
b.) How many revolutions does the ball make during its fall?
Answers
Hi there!
We can use the work-energy theorem and apply it to this situation.
At the top of the ramp, the ball only has gravitational potential energy, and at the bottom of the ramp, the ball has BOTH translational and rotational kinetic energy.
We must use the following equations:
[tex]GPE = mgh \\KE_T = \frac{1}{2}mv^2\\\\KE_R = \frac{1}{2}I \omega^2[/tex]
m = mass of sphere (kg)
g = acceleration due to gravity (m/s²)
h = height of ramp (m)
v = final velocity (m/s)
I = Moment of Inertia (kgm²)
ω = angular velocity (rad/sec)
Since:
[tex]E_i = E_f\\\\mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega ^2[/tex]
In order to make things easier, since the ball is not slipping, we can relate angular velocity to translational velocity:
[tex]\omega = \frac{v}{r}[/tex]
Also, recall the equation for the moment of inertia for a solid sphere:
[tex]I = \frac{2}{5}mr^2[/tex]
We can use these to simply our equation:
[tex]KE_R = \frac{1}{2}(\frac{2}{5}mr^2)(\frac{v}{r})^2 = \frac{1}{5}mv^2[/tex]
Now, we can rewrite the equation and solve for 'v'.
[tex]mgh = \frac{1}{2}mv^2 + \frac{1}{5}mv^2\\\\mgh = \frac{7}{10}mv^2\\\\v = \sqrt{\frac{10gh}{7}} = \sqrt{\frac{10(9.8)(2.2 - 1.87)}{7}} = 2.149\frac{m}{s}[/tex]
a)
We can begin by solving for the time taken for the ball to land on the ground. The ball only has a horizontal velocity, so this is essentially a free-fall situation. Use the rearranged kinematic equation:
[tex]t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2(1.87)}{9.8}} = .6178 s[/tex]
Now, use the following equation to solve for horizontal distance given horizontal velocity and time:
[tex]d_x = v_x t\\\\d_x = 2.149 * .6178 = \boxed{1.328 m}[/tex]
b)
We can use the previously-stated relationship between translational and angular velocity to solve for the angular velocity.
[tex]\omega = \frac{v}{r}[/tex]
It is given that the diameter is 0.14 m, so the radius is 1/2th the diameter, or 0.07 m.
Solve for the angular velocity:
[tex]\omega = \frac{2.149}{0.07} = 30.706 \frac{rad}{sec}}[/tex]
Using the above fall time and dimensional analysis to convert from rad/sec to revolutions, we can solve for the # of revolutions made by the ball:
[tex]\frac{30.706rad}{sec} * .6178 sec * \frac{1 rev}{2\pi rad} = \boxed{3.019 rev}[/tex]
Related Questions
A flat coil of wire has an inductance of 40. 0 mh and a resistance of 6. 00 ω. It is connected to a 21. 2-v battery at the instant t = 0. Consider the moment when the current is 2. 50 a
Answers
For a flat coil of wire has an inductance of 40. 0 mh and a resistance of 6. 00 ω, the rate of energy being delivered is mathematically given as
P= 53 W
What rate is energy being delivered by the battery?Generally, the equation for the Battery power is mathematically given as
P = I (dt)V
Therefore
P= 2.50 A * 21.2V
P= 53 W
In conclusion, rate of energy being delivered
P= 53 W
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A flat coil of wire has an inductance of 40. 0 mh and a resistance of 6. 00 ω. It is connected to a 21. 2-v battery at the instant t = 0.The power developed will be 53 Watt.
What is electric power?Electric power is the product of the voltage and current. Its unit is the watt. It is the rate of the electric work done.
The given data in the problem is;
V is the voltage = 21.2 volt (V)
I is the electric current = 2.50 ampere (A)
The formula for the power is given as;
[tex]\rm P= V I \\\\\ P= 2.50 \times 21.2 \\\\ P=53 \ watt[/tex]
Hence electric power developed will be 53 Watts.
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Calculate the volume of 500 kilograms
to 2 decimal places
flead if the density of lead is 11400 kg/m². Give your answer
Enter your answer to 2 decimal places
Answers
Answer:
d (density) = M / V
V = M / d = 500 kg / (11400 kg / m^2 = .044 m^3
Explain why electromagnetic forces are essential to forming compounds.
Answers
Explanation:
formation of compounds because the electric forces compel the atoms to attract each other and formed bonds which leads to the formation of chemical compounds. The attractive or repulsive interaction between any two charged bodies is known as an electric force so the attraction between two opposite charged atoms causes the formation of compounds so we can conclude that electric forces are important for the formation of compounds.
1 point
8. A magnetic field of 30 T is directed perpendicular to the force of a coil
with an area of 0.36 m^2. Calculate the magnetic flux in the coil.
A)0.27 Wb
B)9.3 Wb
C)10.8 Wb
D)83.3 Wb
Answers
Answer:
the answer is. C.
Explanation:
[tex] 0.36 \times 30 = 10.8[/tex]
the solution
why is the freezing compartment kept at top in a refrigerator?
Answers
Answer:
Because Geography says the higher one goes the colder it gets
Answer:
The nature of convection.
Explanation:
Warm air rises; cold air falls, so the freezer at the top provides cold air for the other compartments at the bottom.
10. A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a location that is away from the Earth’s surface by twice the radius of the Earth. What is the acceleration due to gravity at that height and what is the period of the oscillations?
Please show all of your work.
Answers
Let's see
Radius of earth=6371mTwice of it=6371(2)=12742m[tex]\\ \rm\rightarrowtail T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
[tex]\\ \rm\rightarrowtail T=2\pi \sqrt{\dfrac{4}{g}}[/tex]
[tex]\\ \rm\rightarrowtail T=2\pi\dfrac{2}{\sqrt{g}}[/tex]
[tex]\\ \rm\rightarrowtail T=\dfrac{4\pi}{\sqrt{g}}[/tex]
So
[tex]\\ \rm\rightarrowtail g=\dfrac{16\pi ^2}{T^2}[/tex]
Answer:
g' = 1.09 m/s²
T = 12 s
Explanation:
Gravity due to acceleration
Distance from center of Earth = r + 2r = 3rgravity due to acceleration on surface, g = GM/r²Substitute 3r in the denominatorg' = GM/(3r)² = GM/9r²⇒ g' = g/9 = 9.8/9 = 1.09 m/s²
Time period
T = 2π√L/g'T = 2π√4/1.09T ≅ 12 sA student states, "The wave model is better than the particle model for electromagnetic radiation because it is easier to understand." Is the student's statement a scientific claim?(1 point)
Yes, it is because simpler scientific models are better.
No, it isn't because the particle model is better than the wave model.
No, it isn't because the statement is an opinion.
Yes, it is because there is ample proof that wave models are easier.
Answers
The student's claim did not follow the scientific method of discovery, hence, it is an opinion not a scientific claim.
What is the scientific method?The scientific method is a procedure employed by scientific towards understanding the world around them as well giving explanation for phenomena in the natural world.
The scientific method involves:
observations asking questions putting forward a hypothesis testing the hypothesis through experiments analyzing results of the experiments and drawing conclusions establishing a theory.Since the student in question just put forward an opinion without testing it out using the scientific method, the statement is not a scientific claim.
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amy bought 3 body lotions and 7 body spray for 80 jessica bought 6 body lotion and 3 body spray for 63.75 how much does one body spray cost
Answers
Answer:
Each body spray cost $ 21.25
Explanation:
Calculate the mass (in g) of 346 cm³ of polythene. The density of polythene is 0.95 g/cm³. Give your answer to 2 decimal places.
Answers
Answer:
M = 328.70g
Explanation:
From the given values:
V = 346 cm³
M of 1 cm³ of Polythene = 0.95g or 95/100g
Solve:
M = (95×346)
10
= 32870
100
M = 328.70g
A photon with wavelength 11. 0 nm is absorbed when an electron in a three-dimensional cubical box makes a transition from the ground state to the second excited state
Answers
For a photon with wavelength 11. 0 nm, the side length LL of the box is mathematically given as
L=1.414*10^{-27}m
What is the side length LL of the box?Generally, the equation for the change in energy is mathematically given as
[tex]dE=\frac{hc}{\lambda}[/tex]
Therefore
[tex]\frac{hc}{\lambda}=\frac{6h^2}{8ml}\\\\L=\sqrt{6h\lambda}{8mc}\\\\L=\sqrt{\frac{6(6.626*10^{-34})*11.0*10^{-9}}{8(9.11*10^31)(3*10^8)}}[/tex]
L=1.414*10^{-27}m
In conclusion, the side length LL of the box is
L=1.414*10^{-27}m
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The side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The change in the energy of the photon is found as;
[tex]\rm dE = \frac{hc}{\lambda} \\\\ \frac{hc}{\lambda} =\frac{6h^2}{8ml} \\\\ L= \sqrt{\frac{6h\lambda}{8mc} } \\\\ L = \sqrt{\frac{6 \times 6.626 \times 10^{-34}\times 11 \times 10^{-9}}{8 \times 9.11 \times 10^{31} \times 3 \times10^8} } \\\\ L= 1.414 \times 10^{-27} \ m[/tex]
Hence the side length of the box for a photon of wavelength 11. 0 nm will be [tex]\rm L = 1.414 \times 10^{-27}[/tex] m.
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Using the model above, which letter represents the position of the earth when the northern hemisphere is experiencing the shortest hours of daylight
A
B
C
D
Answers
Answer:
At position "B" the northern hemisphere is tilted the most from the earth-sun direction and will experience the shortest hours of daylight, (and also the most indirect sun rays).
What is the equation for finding the amount of inertia in forces and motion? Explain how you solve that equation.
Answers
Answer:
Inertia = angular momentum / angular velocity
A 23. 6 g ball of clay is thrown horizontally to the right at 40. 4 m/s toward a 1. 70 kg block sitting at rest on a frictionless surface. The clay hits and sticks to the block.
What is the speed of the block and clay right after the collision?
Answer in m/s to three significant figures
Answers
Answer:
0.142 m/s
Explanation:
You solve it by conservation of momentum.
Before the impact the total momentum is, considering right the positive direction,
[tex]m_1v_1+m_2v_2 =6\cdot10^-^3\times 40.4\ kg\cdot m/s + 1.7\times 0 \ kg\cdot m/s =242.4\cdot 10^-^3\ kg\cdot m/s[/tex]
After the impact, we have a single body of mass [tex]m_1+m_2[/tex] and thus a single value of speed, V.
[tex](m_1+m_2)V =1.703 kg \cdot V[/tex]
Since no external forces are applied, the two quantities are equal after the impact. That allows us to solve for V
[tex]V= (242.4\cdot10^-^3 \ kg\cdot m/s )\div (1.703\ kg)=142.337\cdot10^-^3 m/s = 0.142 m/s[/tex]
define one meter lendth
Answers
Explanation:
The metre is currently defined as the length of the path travelled by light in a vacuum in 1299 792 458 of a second.
Hope it helps
Have a great day
TC
:DD
To predict whether a star will ultimately become a black hole, what is the key property of the star we should look at?.
Answers
A star will ultimately become a black hole when it collapses due to end of fuel.
Which star becomes a black hole?When a star burns through the last of its fuel, the object may collapse, or fall into itself. For smaller stars which are about three times the sun's mass, the new core will become a white dwarf but when a larger star collapses, it turns into a black hole.
So we can can conclude that a star will ultimately become a black hole when it collapses due to end of fuel.
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At what constant velocity must a spacecraft travel from earth if it is to reach the star in 3. 7 years, as measured by travelers on the spacecraft?
Answers
The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s
Given data :
Distance of star from earth = 4.3 light years
Observers time = 3.7 years
Determine the constant velocity the spacecraft must travelObservers time = 3.7 * 365 * 24 * 60 * 60
Distance of star from earth = 4.3 * 9.46 * 10¹⁵
The velocity the spacecraft must travel will be calculated using the equation
V = distance / time
= ( 4.3 * 9.46 * 10¹⁵ ) / ( 3.7 * 365 * 24 * 60 * 60 )
= 3.49 * 10⁸ m/s
Hence we can conclude that The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s
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Attached below is the missing detail related to the question
The constant velocity must the spacecraft travels from the earth will be 3.49×10⁸ m/sec.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is
Distance of earth from stars = 4.3 light year
The given time = 3.7 year
One year converted into the second as;
[tex]\rm 1 \ year = 3.7 \times 365 \ days \ \times 24 \ hour \times 60 \ minute \times 60 \ sec \\\\ 1 year = 116 \times 10^6 \ sec[/tex]
1 light-year into a kilometer as;
[tex]\rm 4.3 \ light year = 4.3 \times 9.46 \times 10^{15 metre} \\\\[/tex]
At what constant velocity must a spacecraft travel from the earth if it is to reach the star in 3. 7 years,
The velocity of the spacecraft's travel from the earth will be;
[tex]\rm V = \frac{d}{t} \\\\ V= \frac{4.3 \times 9.46 \times 10^{15}}{3.7 \times 365 \times 24 \times 60 \times 60 } \\\\\ V= 3.49 \times 10^8 \ m/sec[/tex]
Hence the constant velocity must the spacecraft travels from the earth will be 3.49×10⁸ m/sec.
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A wave oscillates 4.0 times a second and has a wavelength of 3.0 m.
What are the (a) frequency, (b) period, and (c) speed of this wave?
Answers
a) The frequency of the wave is 4.0 Hz
b) The period T of the wave is 0.25s
c) The speed of the wave is 12m/s
Given the data in the question;
Number of oscillation per seconds = 4.0Wavelength; [tex]\lambda = 3.0m[/tex]Frequency; [tex]f = \ ?[/tex]Period; [tex]T = \ ?[/tex]Speed of the wave; [tex]v = \ ?[/tex]Frequency, Period and speed.Frequency is simply the number of occurrences of a repeating phenomenon per unit time.
Period is the time needed for a complete cycle of vibration to pass a given point.
It is expressed as;
[tex]T = \frac{1}{f}[/tex]
Where f is the frequency
Speed is simply the distance traveled in a given interval of time or time ratio.
It is expressed as;
[tex]v = \lambda * f[/tex]
Where [tex]\lambda[/tex] is wavelength and f is frequency
a) Frequency
We said frequency is the number of occurrences of a repeating phenomenon per unit time.
Since the wave oscillates 4.0 times a second
Hence, the frequency of the wave is 4.0 Hz
b) Period
[tex]Period\ T = \frac{1}{f} \\\\Period\ T = \frac{1}{4.0Hz}\\\\Period\ T = \frac{1}{4.0s^{-1}}\\\\Period\ T = 0.25s[/tex]
Therefore, the period T of the wave is 0.25s
c) Speed
[tex]v = \lambda * f\\\\v = 3.0m * 4.0Hz\\\\v = 3.0m * 4.0s^{-1}\\\\v = 12ms^{-1}\\\\v = 12m/s[/tex]
Therefore the speed of the wave is 12m/s.
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A particular lightbulb is designed to consume 40 W when operating on a car's 12-V DC electric power. If you supply that bulb with 12-V AC power from a transformer, how much power will it consume
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The main environmental effects of ozone depletion could include all of the following except
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The main environmental effects of ozone depletion could include the following:
higher risk of skin cancersunburnsquick ageingweakend immune systemWhat is ozone depletion?Ozone depletion is the gradual thinning of the ozone layer in the upper atmosphere as a result of the relelase of chemical compounds or gases.
Ozone layer helps prevent the Earth surface against incoming ultraviolet radiations that could cause damage to our environment.
Therefore, the main environmental effects of ozone depletion could include the following:
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The following are some of the primary environmental implications of ozone depletion and increased risk of skin cancer, sunburns, rapid aging, and the immune system being weakened.
What is ozone depletion, and how does it happen?The progressive weakening of the ozone layer in the upper atmosphere as a result of the release of chemical compounds or gases is known as ozone depletion.
The ozone layer protects the Earth's surface from harmful UV rays that may harm our environment. As a result, the primary environmental effects of ozone depletion could include:
1. An increased risk of skin cancer
2. Sunburns
3. Rapid aging
4. The immune system is weakened.
Hence increased risk of skin cancer is the main environmental effect of ozone depletion.
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Cars enter a car wash at a mean rate of 33 cars per half an hour. What is the probability that, in any hour, exactly 22 cars will enter the car wash? round your answer to four decimal places
Answers
Answer:Cars enter a car wash at a mean rate of 4 cars per half an hour.
Explanation:
The probability that, in any hour, exactly 22 cars will enter the car wash will be 0.0920.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The mean rate of car is,[tex]\rm \lambda = 66 \ car/hour[/tex]
[tex]P(x=K) = \frac{8^k e^{-8}}{k\!}\\\\P(x=22) = \frac{66^{22} e^{-22}}{22\!}\\\\ P(x=22)=\frac{0.000000000000691\times 1.07\times 10^{40}}{22} \\\\\ P(x=22)=0[/tex]
Hence the probability that, in any hour, exactly 22 cars will enter the car wash will be 0
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write comparison between Electrical Circuit and Magnetic Circuit.
[tex] \\ \\ \\ \\ \\ \\ \\ [/tex]
Thanks¡!¡:)
Answers
Magnetic circuit, closed path to which a magnetic field, represented as lines of magnetic flux, is confined.
In contrast to an electric circuit through which electric charge flows, nothing actually flows in a magnetic circuit.
Explanation:
Hope it helps you (`▿▿▿▿´ƪ)
Question 1(Multiple Choice Worth 2 points)
(04.05 LC)
The number of protons plus the number of neutrons in an atom is equal to its
O atomic number
O mass number
O nuclear model
O energy level
Question 2 Multiple Choice Worth 2 points)
Answers
Answer: Mass Number
Explanation:
Atomic number is the number of just protons;
Nuclear Model is a theoretical description of what an atom looks like;
Energy levels are the energy states that electrons are in;
However, mass number is by definition the number of protons + number of neutrons. :)
Photoelectrons are emitted from the surface of a metal when light shines on it. If the wavelength of the light is decreased
Answers
Answer:
what are your answer choices if you have any?
Explanation:
(my ask question thingy isnt working)
Which Tesla would win in a drag race?
(A) 2009 Tesla Roadster
(B) 2016 Tesla Model X
Answers
Answer:B
Explanation:
A has about 248 hp but B has about 683 hp. 2016 is younger too. good day
A skateboarder initially has 5 kJ of kinetic energy. As she freewheels along a flat section of path, she does 400 J of work against friction and air resistance. Calculate her final kinetic energy.
Answers
The final kinetic energy of the skateboarder after she freewheels and did work against friction on the flat section of the path is 4,600 J.
Conservation of energyThe final kinetic energy of the stakeboarder is determined by applying the principle of conservation of energy as shown below;
ΔK.E = -W
K.Ef - K.Ei = -W
where;
K.Ef is the final kinetic energyK.Ei is the initial kinetic energyW is work doneK.Ef = K.Ei - W
K.Ef = 5,000 J - 400 J
K.Ef = 4,600 J
Thus, the final kinetic energy of the skateboarder is 4,600 J.
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How to know if two vectors are linearly independent
Answers
Answer:
Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0.
Explanation:
You may verify if a group of vectors is linearly independent by expressing the vectors as columns of the matrix A and solving Ax = 0.
What is a vector?A vector is a quantity or phenomena with magnitude and direction that are independent of one another. The phrase also refers to a quantity's mathematical or geometrical representation.
If no vector can be written as a linear combination of the others, a set of vectors is said to be linearly independent.
If no vector in a collection of vectors can be written as a linear combination of the ones mentioned before it, the set is said to be linearly independent.
A nontrivial linear combination yields the zero vector, the vectors are said to be dependent.
You may verify if a group of vectors is linearly independent by expressing the vectors as columns of the matrix A and solving Ax = 0.
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The presence of which magnetic feature best explains why a magnet can act at a distance on other magnets or on objects containing certain metals? fields dipoles domains forces
Answers
The orientation with the largest magnetic torque on the dipole is Orientation B (See attached image).
What is Magnetic Torque?The torque on the dipole is defined as:
τ = µ×B,
where B is the external magnetic field.
The magnitude of this torque is µB sinθ, where θ is the angle between B and µ
Magnetic Torque is highest when;
→ →
µ ⊥ β
That is when θ = 90°. Hence B is the correct answer. Please see attached image.
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Answer:
b
Explanation:
I have an answer but I'm not it sure about it. I just need someone to help confirm it. Thanks
Answers
Answer:
0.40s. He's dead, Jim.
Explanation:
The block accelerates at a rate of [tex]9.81 ms^-^2[/tex]. The moment it's 14 meters from the ground, it has traveled 39 meters, in about [tex]39=\frac12(9.81)t^2 \rightarrow 2.82 s[/tex].
For the man to dodge, the time left is the distance the block takes to go down to 2 meters from ground, or 51 meters from its starting point. Which translates in [tex]51=\frac12(9.81)t^2\rightarrow 3.22s[/tex]
He has thus less than half a second ([tex]0.40s[/tex] to be exact) to dodge.
15. A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?
The answer is 0.389 kg but please show your work.
Answers
Let's look at relationship
[tex]\\ \rm\rightarrowtail T=2\pi\sqrt{\dfrac{m}{k}}[/tex]
[tex]\\ \rm\rightarrowtail T\propto \sqrt{m}[/tex]
Hence
[tex]\\ \rm\rightarrowtail \dfrac{T_1}{T_2}=\sqrt{\dfrac{m1}{m2}}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{1.5}{2}=\sqrt{\dfrac{0.5}{m2}}[/tex]
[tex]\\ \rm\rightarrowtail 0.75^2=\dfrac{0.5}{m2}[/tex]
[tex]\\ \rm\rightarrowtail m_2=\dfrac{0.5}{0.75^2}[/tex]
[tex]\\ \rm\rightarrowtail m_2=0.889[/tex]
Hence
Mass needs to added =0.889-0.500=0.389kgAnswer
Mass needs to added =0.889-0.500=0.389kg
Explanation:
A 120 N accelerates an object 1. 2 m/s? What is the mass of the object?
Answers
Answer:
m = 100 kg
Explanation:
F = ma
120 = m × 1.2
m = 120 ÷ 1.2
m = 100 kg