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
One billiard ball strikes another billiard ball, and they move away from each other
at a 90° angle. The momentums involved include (blank) of the velocity before and after the collision.
(A) only the direction
(C) the magnitude and direction
(B) only the magnitude
(D) the square of the magnitude
Answers
Answer:
C) The magnitude and direction
Explanation:
Velocity is a vector quantity, meaning that it has both magnitude and direction.
For the momentum, we look at both the direction of the ball (negative, positive) and the magnitude of the velocity (5 m/s, 10 m/s) when figuring out what to use for "v" in p = mv.
28. (a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is 9.79m/s2 is moved to a location where it the acceleration due to gravity is 9.82m/s2. What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.
The answer is "(a) 2.99541 s(b) Since the period is related to the square root of the acceleration of gravity, when the acceleration changes by 1% the period changes by (0.01)2=0.01% so it is necessary to have at least 4 digits after the decimal to see the changes." But please include the steps to each solution.
Answers
Answer:
See below ↓
Explanation:
Assuming the motion of a simple pendulum, the time period is given by
⇒ T = 2π√(L/g)⇒ T₁/T₂ = √(g₂/g₁)The values we have
T₁ = 3 sg₁ = 9.79 m/s²g₂ = 9.82 m/s²Solving
T₂ = T₁/√(g₂/g₁)T₂ = 3/√(9.82/9.79)T₂ = 3.004593 secondsThis many digits are needed because the acceleration is changed by a very small percentage (roughly 2 decimal places)So on taking the square root of the ratio of the gravity due to acceleration (2 values), 4 decimal places will be present at the very least
What type of charge is acquired when a rubber is rubbed with a fur
Answers
Answer:
The triboelectic charging process (a.k.a., charging by friction) results in a transfer of electrons between the two objects that are rubbed together. Rubber has a much greater attraction for electrons than animal fur.
Explanation:
HOPE IT HELP^_^
THANKS^_^
If a satelite with a mass of 9 x 10^2 kg is placed in an orbit around a planet with a mass of 6 x 10^20 kg, at a speed of 17000 m/s, find the distance from the center of the planet to the satelite.
Answers
Hi there!
We can begin by deriving an equation for the orbital radius.
For an object orbiting the earth, it is experiencing a centripetal force due to the force of gravitation.
Recall Newton's Law of Universal Gravitation:
[tex]F_g = \frac{Gm_1m_2}{r^2}[/tex]
G = Gravitational Constant (6.67 × 10⁻¹¹ Nm²/kg²)
m = masses (kg)
r = radius (m)
This is equivalent to the satellite's centripetal force experienced:
[tex]F_c = \frac{m_sv^2}{r}[/tex]
[tex]m_s[/tex] = mass of satellite (kg)
v = velocity (m/s)
r = radius (m)
Set the two equal, and rearrange for the orbital radius of the satellite.
[tex]\frac{Gm_sm_p}{r^2} = \frac{m_sv^2}{r}\\\\\frac{Gm_p}{r} = v^2\\\\r = \frac{Gm_p}{v^2}[/tex]
Notice that the orbital radius of the satellite does NOT depend on the satellite's mass. (we canceled it out).
Now, plug in the given values.
[tex]r = \frac{(6.67\times 10^{-11})(6\times 10^{20})}{17000^2} = \boxed{138.478 m}[/tex]
11. Which of the following is a type of energy
that is not involved in the human body's
everyday processes?
A. mechanical energy
B. nuclear energy
C. thermal energy
D. chemical energy
Answers
Answer:
nuclear
Explanation:
A: a type of mechanical energy is kinetic, which comes from velocity/movement
C: people produce heat
D: converting food energy into usable energy within the body
A 10. 0 cm object is 5. 0 cm from a concave mirror that has a focal length of 12 cm. What is the distance between the image and the mirror? 3. 5 cm –3. 5 cm 8. 6 cm –8. 6 cm.
Answers
The distance between the image and the mirror is -8.6 cm
What is concave mirror?A concave mirror has a reflective surface that is curved inward and away from the light source. Concave mirrors reflect light inward to one focal point.
Unlike convex mirrors, the image formed by a concave mirror shows different image types depending on the distance between the object and the mirror.
Let's use the mirror equation to solve the problem:
[tex]\dfrac{1}{f}=\dfrac{1}{d_o}+\dfrac{1}{d_i}[/tex]
where f is the focal length of the mirror, the distance of the object from the mirror, and the distance of the image from the mirror.
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for by using the numbers given in the text of the problem:
[tex]\dfrac{1}{12}=\dfrac{1}{5}+\dfrac{1}{d_i}[/tex]
[tex]\dfrac{1}{d_i}=-\dfrac{7}{60}[/tex]
[tex]d_i=-8.6\ cm[/tex]
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.
Hence the distance between the image and the mirror is -8.6 cm
To know more about concave mirror follow
https://brainly.com/question/1147247
On the electromagnetic spectrum, what type of light is higher energy: X-rays or radio waves?
Answers
Answer:
Radio
Explanation:
X-rays is 10 x 10^-10
radio is 10⁴
WILL GIVE BRAINLEST!!! What is the magnification of a virtual image if the image is 10.0 cm from a mirror and the object is 20.0 cm from the mirror?
a. -2.0
b. 0.50
c. 2.0
d. -0.50
Answers
option D
hope it helps...!!!
Answer:
B.
Explanation:
You have to divide.
10.0/20.0 = 0.50
I apologize if it is incorrect-
I hope it helps! Have a great day!
Anygays-
a car starts from the rest and accelerates at 9.54m/s for 6.5 seconds. what is the distance covered by the car
Answers
Answer:
= 201.53 meters
Explanation:
A car started from rest and accelerated at 9.54 m/s^2 for 6.5 seconds. How much distance was covered by the car?
Use the formula d = [tex]\frac{at^{2} }{2} ,[/tex]
where d is the distance, t is the time and "a" is the acceleration.
[tex]d=\frac{9*54*6*5^{2} }{2} = 201.53 m[/tex]
Select the correct answer.
Which of the following social events are often centered around sporting events?
A. Tailgate Parties
B. Parades
C. Pep Rallies
D. All of the above
Answers
Control rods are used to slow down the reaction in the reactor core when the core becomes too hot. Please select the best answer from the choices provided T F.
Answers
The best answer is true. Yes, control rods are used to slow down the reaction in the reactor core when the core becomes too hot.
What is a nuclear reactor?A nuclear reactor, often known as an atomic pile, is a device that initiates and controls nuclear chain reactions or nuclear fusion processes.
Nuclear reactors are used in nuclear power plants to generate energy as well as in nuclear marine propulsion.
Control rods are employed in nuclear reactors because the processes that occur in a nuclear reactor are very exothermic.
As a result, when these control rods are infused into a nuclear reactor, they absorb neutrons and aid in the management of the chain reaction. As a result, the rate of the chain reaction is brought under control.
As a result, we may infer that the statement control rods are employed to slow down the reaction in the reactor core when it gets too hot is correct.
Hence the best answer is true. Yes, control rods are used to slow down the reaction in the reactor core when the core becomes too hot.
To learn more about the nuclear reactor refer to the link;
https://brainly.com/question/896706
What do we call objects that form like a star (from a contracting gas cloud), but do not have enough mass to ignite hydrogen fusion in their centers
Answers
A brown dwarf is a starlike body that do do not have enough mass to ignite hydrogen fusion in their centers.
What is a brown dwarf?Brown dwarf refer to a body of substellar that is not huge or big enough to undergo nuclear fusion of o hydrogen into helium in their cores. This formed when there is contraction of gases in the intercellar spaces. The have a mass between 13 to 80 times that of Jupiter.
Therefore, brown dwarf is a starlike body that do don't not have enough mass to ignite hydrogen fusion in their centers.
Learn more about brown dwarf below.
https://brainly.com/question/15722167
Explain the terms boiling and boiling point.
How is the volume of water affected when it boils at 100°C.?
Don't spam..
Answers
The particular temperature at which vaporisation occurs is known as the boiling point of liquid. Volume of water increases when it boils at 100° C. 1 cm3 of water at 100 ° C becomes 1760 cm3 of steam at 100 ° C.
Hope it helps!!!!!!!!!!!!!!!!!!!!! ~~~~~~~~~~~~~~~~~~~
ಥ‿ಥ
The particles in a balloon push out on the sides of the balloon. What is the reaction force?
A. The balloon wall pushes the enclosed air particles inwards.
B. The string of the balloon on the particles in the environment.
C. There are no forces involved in a balloon filled with air.
Answers
Jessie hits a foul ball
straight up in the air
during a softball game.
Assuming all energy is
conserved, at what height
did the 3 kg ball travel if it
had a velocity of 11 m/s?
Answers
Answer:
GPE=(3*11^2)/2
(3*121)/2
363/2
GPE=181.5J
Explanation:
(WILL MARK BRAINLIST) Pure substances can be made of atoms that are attracted to each other or atoms that are not attracted to each other. Which type of pure substance can create elaborate structures? (1 point)
Atoms that are attracted to each other because the bonds that form between them can support the creation of the structure.
Atoms that are attracted to each other because they will mix together to form a mixture with a different structure.
Atoms that are not attracted to each other because they will form bonds with each other and create a larger structure.
Atoms that are not attracted to each other because they will stay still and end up laying on top of each other.
Answers
→ Pure substances can be made of atoms that are attracted to each other or atoms that are not attracted to each other. Which type of pure substance can create elaborate structures?
SOLUTION;Option c) Atoms that are not attracted to each other because they will form bonds with each other and create a larger structure.
Based on the figure, a decrease in _________ could cause the economy to move from point a to point b
Answers
A decrease in production of goods could cause the economy to move from point a to point b.
What cause shifts in economy?Shifts in the production are due to many factors that change the output of an economy such as advances in technology, changes in resources, more education or training and changes in the labor force.
So we can conclude that a decrease in production of goods could cause the economy to move from good to poor.
Learn more about economy here: https://brainly.com/question/17996535
If you travel for three hours at a speed of 30 km/h, how far will you go?
Answers
Distance = (speed) x (time) <== This is important. You should memorize it.
Distance = (30 km/hr) x (3 hr)
Distance = (30 x 3) (km/hr x hr)
Distance = 90 km
A distant star gives off a visible range of light whose color depends on its temperature. Which model of light does this example support? O A. The interference model B. The particle model O C. The diffraction model OD. The wave model
Answers
The statement 'a distant star gives off a visible range of light whose color depends on its temperature' is supported by the wave model.
What is wavelength?The wavelength can be defined as the periodic distance of a given wave that repeats in a constant way.
The emissivity of particles is a function of both wavelength and temperature of a given material/object. Visible wavelengths range from 700 nm to 400 nm (violet color).
Star temperature largely determines its color, blue stars are warmer than yellow and red stars, and red stars are cooler than yellow stars.
Learn more about visible wavelengths here:
https://brainly.com/question/10728818
Two wave pulses move toward each other along a rope. two small triangular crests moving toward each other. which diagram shows the resulting wave when they cross at point x? a straight line. a triangular crest. a rectangular crest. a triangular trough.
Answers
The triangular crest. shows the resulting wave when they cross at a point x. The meeting point of two waves is known as wave interference ia x.
What is wave pulse?A wave pulse is a short, non-periodic wave that is formed by a single energy input rather than a continuous or repeated energy input.
Wave interference is the result of multiple waves interacting. There are two types of interference: constructive and destructive.
The relative displacement of the waves is the difference between the two. Wave beats are frequently caused by wave interference.
Hence the triangular crest. shows the resulting wave when they cross at a point x.
To learn more about the wave pulse refer to the link;
https://brainly.com/question/1291549
Answer:
B
Explanation:
Got it right on edge
4. Which best explains the function of the alveoli in the respiratory system?
Page 135
A. The alveoli help to keep the lungs healthy by providing a way for all the cells
in the lungs to obtain nutrients from the bloodstream
B. The alveoli help to keep the lungs inflated when you breathe out and make it
possible to absorb oxygen
C. The alveoli provide a large surface area for absorbing oxygen from the air and
releasing carbon dioxide wastes from the bloodstream
D. The alveoli provide a large surface area for absorbing oxygen from the air
when you breathe in and look like a bunch of grapes
a
Answers
Answer:
C
Explanation:
Alveoli are tiny functioning structures that compose your lungs. They help with respiration. They have a large total surface area, which is very useful for respiration. The more surface area there is, the more transactions can happen. Which means that breathing will be easier/faster when you have more alveoli. (Please rate this answer if you have time!)
A small car with mass of 0.800 kg travels at a constant speed
on the inside of a track that is a vertical circle with radius 5.00
m. If the normal force exerted by the track on the car when it
is at the bottom of the track is 25 N,
a) What is the normal force on the car when it is at the (i)
top, (ii) rightmost and (iii) leftmost point of the track?
b) What is the speed of the car as it travels around the
vertical circle?
Answers
Answer:
The equation of equilibrium at the top of the vertical circle is:
\Sigma F = - N - m\cdot g = - m \cdot \frac{v^{2}}{R}
The speed experimented by the car is:
\frac{N}{m}+g=\frac{v^{2}}{R}
v = \sqrt{R\cdot (\frac{N}{m}+g) }
v = \sqrt{(5\,m)\cdot (\frac{6\,N}{0.8\,kg} +9.807\,\frac{kg}{m^{2}} )}
v\approx 9.302\,\frac{m}{s}
The equation of equilibrium at the bottom of the vertical circle is:
\Sigma F = N - m\cdot g = m \cdot \frac{v^{2}}{R}
The normal force on the car when it is at the bottom of the track is:
N=m\cdot (\frac{v^{2}}{R}+g )
N = (0.8\,kg)\cdot \left(\frac{(9.302\,\frac{m}{s} )^{2}}{5\,m}+ 9.807\,\frac{m}{s^{2}} \right)
N=21.690\,N
(please answer) It is better to jump on a smooth, flat surface than on thick carpeting.
Question 5 options:
True
False
Answers
I believe the answer to your question would be True
Why does the spectroscopic parallax method only work for main sequence stars?.
Answers
Answer:
Only main sequence stars have a well-defined relationship between spectral type and luminosity.
Explanation:
Low-mass stars have much longer lifetimes than high-mass stars.
A 0. 5 kg mass on a 1-m-long string swings in a circle on a horizontal, frictionless table at a steady speed of 2 m/s. How much work does the tension in the string do on the mass during one revolution?
Answers
The tension does no (zero) work
F· S = W
Since the tension is perpendicular to the direction of motion, and there is no change in S the work done is zero.
A car of 15 kg is traveling on a circular track. If the radius of the track is
7. 8 m and the period is 8. 5 seconds, what's the centripetal force on
the car? (Round to the nearest hundredth)
Answers
The magnitude of the centripetal force on the car is 69.6 N.
What is centripetal force?This is a force acting on a body in circular path and it is directed to the center around which the body is moving.
To calculate the centripetal force on the car, we use the formula below.
Formula:
F = m(4π²/t²)........ equation 1Where:
F = Magnitude of the centripetal force on the car, m = mass of the cart = timeFrom the question,
Given:
m = 15 kgt = 8.5π = 3.14Substitute these values into equation 1
F = 15(4×3.14²/8.5²)F = 69.6 NHence, the magnitude of the centripetal force on the car is 69.6 N.
Learn more about centripetal force here: https://brainly.com/question/20905151
A mass m on a frictionless plane, inclined at an angle θ with respect to the horizontal, is connected by a cord that runs parallel to the inclined plane and is wrapped around a flywheel of radius r and moment of inertia
[tex]i=\frac{3mr^{2}}{4}[/tex]
what is the acceleration of the mass down
the plane?
Answers
The acceleration of the mass down the plane is determined as (4mg sinθ)/(3mr²).
Conservation of angular momentumThe acceleration of the mass down the plane is determined by applying the principle of conservation of angular momentum.
Fr = Iα
where;
F is weight of the object parallel to the planer is the radius of the flywheelI is moment of inertiaα is angular acceleration(mg sinθ)r = Iα
(mg sinθ)r = I(ar)
(mg sinθ) = I(a)
[tex]a = \frac{mg \times sin(\theta)}{I} \\\\a = \frac{mg \times sin(\theta)}{3mr^2/4} \\\\a = \frac{4mg \times sin(\theta)}{3mr^2}[/tex]
Thus, the acceleration of the mass down the plane is determined as (4mg sinθ)/(3mr²).
Learn more about acceleration here: https://brainly.com/question/14344386
The kinetic energy of a javelin is 81 J, and its speed is 9.0 m/s. What is its mass?
A. 0.5 kg
В. 1.0 kg
C. 2.0 kg
D 9.0 kg
help asap
Answers
Explanation:
[tex]kinetic \: energy = \frac{1}{2} m {v}^{2} [/tex]
[tex]81 = \frac{1}{2}m {(9)}^{2} [/tex]
[tex] \frac{81 \times 2}{81} = m[/tex]
[tex]m = 2kg[/tex]
A direct current of 3.0 A flows through a circuit consisting of a battery and a 6.0 A resistor. Calculate the potential difference across the resistor. a
Answers
Question :-
A Direct Current of 3.0 A flows through a Circuit consisting of a Battery and a 6.0 Ohm's Resistor. Calculate the Potential Difference across the Resistor .Answer :-
Potential Difference is 18 Volt's .Explanation :-
As per the provided information in the given question, we have been given that the Current of the Device is 3.0 Ampere . The Resistance is given as 6.0 Ohm's . And, we have been asked to calculate the Potential Difference .
As we know ,
V = I RWhere ,
V denotes to Potential DifferenceI denotes to CurrentR denotes to ResistanceTherefore , by Substituting the given values in the above Formula :-
[tex] \sf {\dag \: \: \: Potential \: Difference \: = \: Current \: \times \: Resistance} [/tex]
[tex] \sf {\Longrightarrow \: \: \: \sf Potential \: Difference \: = \: 3.0 \: \times \: 6.0} [/tex]
[tex] \sf {\Longrightarrow \: \: \: \sf Potential \: Difference \: = \: 3 \: \times \: 6} [/tex]
[tex] \bf {\Longrightarrow \: \: \: \bf {Potential \: Difference \: = \: 18 \: }} [/tex]
Hence :-
Potential Difference = 18 Volt's .[tex] \underline {\rule {210pt}{4pt}} [/tex]
Additional Information :-
[tex] \Longrightarrow \: \: \: \sf {Voltage \: = \: Current \: \times \: Resistance} [/tex]
[tex]\Longrightarrow \: \: \: \sf {Current \: = \: \dfrac {Voltage}{Resistance} } [/tex]
[tex]\Longrightarrow \: \: \: \sf {Resistance \: = \: \dfrac {Voltage}{Current} } [/tex]
[tex] \underline {\rule {210pt}{4pt}} [/tex]
Note :-
Kindly Scroll the Screen from Right to Left for Better View .Calculate the temperature for which the minimum escape energy is 15 times the average kinetic energy of an oxygen molecule. Answer in units of K.
Answers
The temperature for which the minimum escape energy is 15 times the average kinetic energy of an oxygen molecule is 10,684.4 K.
Conservation of energyThe temperature for which the minimum escape energy is 15 times the average kinetic energy of an oxygen molecule is determined by applying principle of conservation of energy as shown below;
E = K + U
E = K - GmM/R
0 = K - GmM/R
K = mgR
When the minimum escape energy is 15 times average kinetic energy;
15K = mgR
[tex]15 \times \frac{3}{2} kT = mgR[/tex]
where;
m is mass of oxygen per atom = (0.032 kg)/(6.02 x 10²³) = 5.316 x 10⁻²⁶ kg/atomg is acceleration due gravity = 9.8 m/s²R is radius of Earth = 6.371 x 10⁶ m.k is Boltzmanns’ constant = 1.38066 x 10⁻²³ J/K.[tex]T = \frac{2mgR}{15 \times 3k} \\\\T = \frac{(2)(5.316 \times 10^{-26})(9.8)(6.371 \times 10^6)}{45(1.38066 \times 10^{-23})} \\\\T = 10,684.4 \ K[/tex]
Thus, the temperature for which the minimum escape energy is 15 times the average kinetic energy of an oxygen molecule is 10,684.4 K.
Learn more about minimum escape energy here: https://brainly.com/question/16008094