a uniform wheel in the shape of a solid disk is mounted on a frictionless axle at its center. the wheel has mass 5.00 kg and radius 0.800 m. a thin rope is wrapped around the wheel, and a block is suspended from the free end of the rope. the system is released from rest and the block moves downward. what is the mass of the block if the wheel turns through 8.00 revolutions in the first 5.00 s after the block is released?]
Answers
The mass of the block is approximately 3.98 kg.
Let's start by analyzing the forces acting on the block. There are two forces: the force of gravity (downward) and the tension in the rope (upward). Since the block is accelerating downward, we know that the force of gravity is greater than the tension.
Next, let's analyze the motion of the wheel. Since there is no friction, the wheel will rotate without any torque, and its angular momentum will be conserved. The total angular momentum of the system (wheel + block) will therefore be constant.
Initially, the system is at rest, so the total angular momentum is zero. After the block starts moving, it will acquire some angular momentum due to its downward motion. This means that the wheel must also acquire some angular momentum in the opposite direction in order to keep the total angular momentum of the system equal to zero.
We can use the formula for the angular momentum of a rotating object, L = Iω, where I is the moment of inertia and ω is the angular velocity, to relate the angular momentum of the block to the angular momentum of the wheel.
Let's first find the moment of inertia of the wheel. Since it is a solid disk, we can use the formula\(I = (1/2)mr^2\), where m is the mass and r is the radius. Plugging in the given values, we get:
\(I = (1/2)(5.00 kg)(0.800 m)^2 = 1.60 kg m^2\)
Let's also define the mass of the block as m_b.
Now we can set up an equation for the conservation of angular momentum:
\(L_block + L_wheel = 0\)
where L_block is the angular momentum of the block and L_wheel is the angular momentum of the wheel. We can express these quantities in terms of the masses, velocities, and moment of inertia:
\(L_block = r m_b v_bL_wheel = I ω\)
where r is the radius of the wheel, v_b is the velocity of the block, and ω is the angular velocity of the wheel.
We can also relate the linear velocity of the block to the angular velocity of the wheel using the fact that the rope is wrapped around the wheel. The distance traveled by the block is equal to the circumference of the wheel, which is 2πr. Therefore:
\(v_b = r ω\)
Substituting this into the equation for L_block, we get:
\(L_block = r^2 m_b ω\)
Substituting all these equations into the conservation of angular momentum equation, we get:
\(r^2 m_b ω + I ω = 0\)
Solving for the angular velocity ω, we get:
\(ω = - I / (r^2 m_b)\)
Now we can use the fact that the wheel completes 8.00 revolutions in 5.00 s to find the angular velocity:
\(ω = (8.00 rev / 5.00 s) * (2π rad / rev) = 10.05 rad/s\)
Substituting this into the equation for ω, we get:
\(10.05 rad/s = - (1.60 kg m^2) / (0.800 m)^2 m_b\)
Solving for the mass of the block m_b, we get:
\(m_b = - (1.60 kg m^2) / (0.800 m)^2 / 10.05 rad/s = 3.98 kg\)
Therefore, the mass of the block is approximately 3.98 kg.
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Related Questions
When you drop a 0.43 kg apple, Earth ex erts a force on it that accelerates it at 9.8m / (s ^ 2) toward the earth's surface. According to New ton's third law, the apple must exert an equal but opposite force on Earth. If the mass of the earth 5.98 * 10 ^ 24 * kg what is the magnitude of the earth's acceleration toward the apple?
Answer in units of m / (s ^ 2)
Answers
Answer:
The answer to the question is highlighted in the box
0
What is 33 C in absolute temperature? hs
Answers
Answer:
33 Celsius is 306.15 in absolute temperature
How is capacitance related to the distance between the plates of a capacitor?
It is directly proportional, so the capacitance increases as the distance increases.
It is inversely proportional, so the capacitance increases as the distance increases.
It is directly proportional, so the capacitance decreases as the distance increases.
It is inversely proportional, so the capacitance decreases as the distance increases.
Answers
Answer:C
Explanation: I studied, and C is correct
Answer:
D
Explanation:
An object is placed 10 cm in front of a diverging mirror. What is the focal length of the mirror if the image appears 2 cm behind the mirror?
Answers
Answer:
the focal length of the mirror is : \(f=-2.5\,\,cm\)
Explanation:
Use the formula for the formation of image using a divergent mirror and recalling that the image (s') that this mirror formed is virtual, so it is entered as a negative number in the formula. Use the object position (s) as 10, the image position (s') as -2, and derive the value of the focal length:
\(\frac{1}{s} +\frac{1}{s'}=\frac{1}{f}\\\frac{1}{10} +\frac{1}{-2}=\frac{1}{f}\\\frac{1}{10} -\frac{1}{2}=\frac{1}{f}\\\frac{10\,f}{10} -\frac{10\,f}{2}=\frac{10\,f}{f}\\f-5\,f=10\\-4\,f=10\\f=-2.5\,\,cm\)
If the centripetal force acting on an object in uniform circular motion is removed the object will.
a. continue moving in a spiral until it reaches the center of the circular path.
b. stop moving.
c. continue moving in a straight line with constant speed.
d. move depending on the type of force providing the centripetal force.
Answers
Answer:
If the centripetal force acting on an object in uniform circular motion is removed, the object will continue moving in a straight line with constant speed.
In uniform circular motion, the centripetal force is responsible for keeping the object moving in a circular path. If this force is removed, there is no longer a force acting towards the center of the circle to change the object's direction, and the object will move in a straight line with a constant speed tangent to its previous circular path.
Option c. "continue moving in a straight line with constant speed" is therefore the correct answer.
By moving her arms outward, an ice skater speeds up a spin, while moving her arms inward slows down a spin. Question options: True False
false
Answers
ITS TURE.When there is no torque acting on a body, its angular momentum is constant. Net force changes momentum, while net torque changes angular momentum.
Answer: false
Explanation:
A free-falling golf ball strikes the ground and exerts a force on it. Which sentences are true about this situation?
A golf ball striking the ground is a collision.
The ground exerts an equal force on the golf ball.
The ground doesn’t exert a force on the golf ball.
The force is zero because the golf ball has little mass.
Answers
A golf ball striking the ground is a collision. The ground exerts an equal force on the golf ball. Both these sentences are right.
What is Newton's third law of motion?Newton's third law of motion tells us that "for every action, there is an equal and opposite reaction". This means that when two objects interact, they exert equal and opposite forces on each other.
In the case of the golf ball striking the ground, the action is the force of the golf ball hitting the ground. According to Newton's third law, the reaction to this action is an equal and opposite force exerted by the ground on the golf ball. This is why the golf ball bounces back up after hitting the ground.
The force of the golf ball on the ground and the force of the ground on the golf ball are equal and opposite in magnitude and direction.
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what is the formula to calculate Acceleration?
Answers
Answer:
too much :(
Explanation:
\overline{a} = \frac{v - v_0}{t} = \frac{\Delta v}{\Delta t}
\overline{a} = average acceleration
v = final velocity
v_0 = starting velocity
t = elapsed time
Answer:
a = Δv⁄t.
Explanation:
A train leaves a station traveling north at 45 km/h. 2 hours
later, an express train leaves the same station on a parallel track
traveling north at 75 km/h. How far from the station will the
trains me
Answers
Explanation:
First train has 2 hr * 45 km/hr = 90 km head start
Closing speed between the two trains 745 - 45 = 30 km
to cover the 90 km between them will take 3 hours
and the second train will be at 75 km/hr * 3 hr = 225 km from the station
Han Solo is moving from left to right along the curvey y= x^2 while orbiting the planet of
Tatooine. He wants to shut off the engines of the Millenium Falcon at a certain point, so
that he will go off along the tangent line and land. At what point should he shut off the
engines in order to reach the landing point (4, 15)? Show all of your work.
Answers
At position (3, 9), where the tangent line passes through, Han Solo should turn off the engines (4, 15).
What should you do if an engine fails while you're in flight?The first three things need to be completed, or at least started, right away: Fly the aircraft as you instantly apply full carb heat and check the gasoline in both or one of the tanks, hit the fuel boost or pump, and mix the fuel to full richness.
Finding the tangent line to the curve y = x2 at that location will help us determine when Han Solo should turn off the engines.
The derivative of the function determines the slope of the tangent line at any point on the curve y = x2.: dy/dx = 2x
Han Solo should turn off the engines at position (x1, y1). Next, we have
y1 = x1^2 (since the point is on the curve y = x^2)
dy/dx = 2x1 (since this is the slope of the tangent line at (x1, y1))
The equation of the tangent line via (4, 15) can be expressed using the point-slope form of a line as follows:
y - y1 = m(x - x1)
Substituting y1 = x1^2 and m = 2x1, we get:
y - x1^2 = 2x1(x - x1)
Now, we can substitute the coordinates of the point (4, 15) to solve for x1:
15 - x1^2 = 2x1(4 - x1)
15 - x1^2 = 8x1 - 2x1^2
x1^2 - 8x1 + 15 = 0
This quadratic equation can be factored as:
(x1 - 3)(x1 - 5) = 0
Therefore, the possible values of x1 are 3 and 5.
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When you know both the speed and direction of an object’s motion, you know the
Answers
Answer:
When you know both the speed and direction of an object's motion, you know the velocity of the object.
When you know both the speed and direction of an object’s motion, you know the magnitude of the speed and direction in which it is moving.
What is Speed ?Speed is a rate of change of distance with respect to time. i.e. v =dx÷dt.
Speed can also be defined as distance over time
i.e. speed= distance ÷ time
it is denoted by v and its SI unit is m/s. it is a scalar quantity. i.e. it has only magnitude not direction. ( velocity is a vector quantity, it has both magnitude and direction. when we define velocity, we should know about its direction)
Speed shows how much distance can be traveled in unit time.
As speed is scalar quantity it has nothing to do with the direction. but when magnitude of speed is given and the direction as well, then we can say that a car or body is moving with this much speed at this direction(east, north, west, south).
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Which property of the water molecule causes two water molecules to be attracted to each other? (2 points)
Polar bonds between H and O atoms
Ionic bonding between water molecules
Hydrogen bonds between H atoms
Ionic bonding between O atoms
Answers
Answer:
hydrogen bonding between H atoms.
Explanation:
Which of the following is the best example of motion?
A. Waving your arms
B. Tossing and turning in your bed
C. Walking from home to school
D. Your dog wagging his tail
Answers
Answer:
Maybe A. waving your arms?
Colloid osmotic pressure (COP) is an osmotic pressure gradient equal to a. interstitial OP – capillary OP b. interstitial OP + capillary OP c. capillary OP – interstitial OP d. hydrostatic pressure + net filtration pressure
Answers
Colloid osmotic pressure (COP) is an osmotic pressure gradient equal to c. capillary OP – interstitial OP.
Colloid osmotic pressure, also known as oncotic pressure, is the osmotic pressure exerted by proteins and other colloidal particles present in the blood plasma. It plays a vital role in maintaining the balance of fluids between the capillaries and the surrounding interstitial fluid.
The capillary osmotic pressure refers to the osmotic pressure exerted by the proteins and colloids within the capillaries, which tends to draw fluid back into the capillaries. On the other hand, the interstitial osmotic pressure represents the osmotic pressure in the interstitial fluid, which is typically lower than the capillary osmotic pressure.
The colloid osmotic pressure gradient is the difference between these two pressures: capillary osmotic pressure minus interstitial osmotic pressure. This gradient helps to counterbalance the hydrostatic pressure and maintain fluid balance by preventing excessive filtration of fluid from the capillaries into the interstitial space.
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What would happen if you didn't have chemical energy in your body? Choose the best answer.
A You wouldn't be able to think.
B You wouldn't be able to move.
C You wouldn't be able to sleep.
D You wouldn't be able to sit.
ill give a thanks
Answers
Answer:B
Explanation:
Because chemical energy fuels your body with energy so without it u wont have enough energy to move.
What is the magnitude of the electric field at a position that is 1.2 m from a 4.2 x 10-6 C point charge?
a
2.91x10^-6 N/C
b
26.25 N/C
c
29,100 N/C
d
26,250 N/C
Answers
The magnitude of the electric field at a position 1.2 m from the point charge is approximately 2.91 x 10^-6 N/C. The correct option is a.
To find the magnitude of the electric field at a distance of 1.2 m from a point charge, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric field (E) created by a point charge (Q) at a distance (r) is given by the equation:
E = k * (Q / r^2)
where k is the electrostatic constant (k ≈ 9 x 10^9 N m^2/C^2).
Substituting the given values into the equation, we have:
E = (9 x 10^9 N m^2/C^2) * (4.2 x 10^-6 C) / (1.2 m)^2
Calculating this expression, we get:
E ≈ 2.91 x 10^-6 N/C
Therefore, the magnitude of the electric field at a position 1.2 m from the point charge is approximately 2.91 x 10^-6 N/C. Thus, option (a) is the correct answer.
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What temperature has the Big Bang cooled to by now? A) about 3,000 K B) about 300 K C) 5,800 K D) just over 2.7 K E) 1.4 K
Answers
The temperature the Big Bang has cooled to by now is just over 2.7 K. T
The correct answer is option D.
The universe has cooled significantly since its beginning, and the current temperature is approximately 2.7 Kelvin, which is a result of the cosmic microwave background radiation.
The universe came into being around 13.8 billion years ago with the Big Bang. At that time, a hot, dense fog of radiation and elementary particles wafted in space, which was rapidly expanding. The density and temperature decreased just as quickly, and the light particles (photons) lost increasingly more energy. After about 380,000 years, this plasma had cooled down to 3000 Kelvin. It was then possible for stable atoms to be created. And the photons had a free path and spread out into space. The cosmos became transparent so to speak.
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Carbon dioxide undergoes a phase change called sublimation, how does a single molecule of carbon dioxide change as a result of this process in terms of its energy and physical characteristics? a. There is a physical change from a gas to a liquid; energy is released into the environment reducing the molecular movement. b. There is a physical change from the solid state to a gas state where energy between the molecules increases. c. There is a chemical change between the carbona nd oxygen resulting int he formation of oxygen gas which has more energy d. There is a chemical change as the carbon dioxide is transferred from a liquid to a solid reducing the amount of energy
Answers
The correct answer is(b). There is a physical change from the solid state to a gas state where energy between the molecules increases.
What is the process of sublimation in carbon dioxide?During sublimation, carbon dioxide transitions directly from the solid state (dry ice) to the gas state without passing through the liquid phase. In this process, individual molecules of carbon dioxide gain energy from the surroundings, leading to an increase in their kinetic energy and molecular movement.
As a result, the carbon dioxide molecules separate from each other and form a gas. This phase change is considered a physical change rather than a chemical change since the chemical composition of carbon dioxide remains the same throughout the process.
Therefore, the sublimation of carbon dioxide results in a physical change where the molecules transition from the solid state to the gas state, gaining energy and increasing their molecular movement.
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what is the acceleration (in m/s2) of gravity on the surface of the moon? m/s2 (b) what is the acceleration (in m/s2) of gravity on the surface (or outer limit) of venus? the mass of venus is 4.88 ✕ 1024 kg and its radius is 6.06 ✕ 106 m.
Answers
The acceleration due to gravity on the surface of the Moon is 1.635 m/s² and on the surface of Venus is 8.8634 m/s².
What is the acceleration due to gravity?There is acceleration, gravitational force, and acceleration due to gravity, all three are completely different from each other.
Acceleration due to gravity denoted by 'g' is the combined force of centrifugal force and gravitation force.Here g= 9.8 m/s² this force is caused by the force acting on the body due to the gravitational field.We know that the acceleration of gravity on the moon = 1/6 acceleration of gravity on the Earth
Therefore, the acceleration of gravity on the surface of the moon is given as
= 9.81 / 6
= 1.635 m/s²
b) For any planet (Venus) the acceleration of gravity is given as
g = GM/ R²
G = 6.67 × 10⁻¹¹
M = 4.88 × 10²⁴
R = 6.06 × 10⁶
g = ( 6.67 × 10⁻¹¹)(4.88 × 10²⁴) / (6.06 × 10⁶)²
g = 8.634 m/s²
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The magnetic field around current carrying wire is blank proportional to the currant and blank proportional in the distance tot he wire
Answers
The magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
The magnetic field strength generated by a current-carrying wire follows the right-hand rule. As the current increases, the magnetic field strength also increases. This relationship is described by Ampere's law.
Additionally, the magnetic field strength decreases as the distance from the wire increases, following an inverse square law. This means that doubling the current will double the magnetic field strength, while doubling the distance from the wire will reduce the field strength to one-fourth of its original value. Therefore, the magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
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the force applied to the cart in the above question by spring scale fa is still 10.5n. the cart now moves toward the right with an acceleration also toward the right of 1.75m/s2. what is the magnitude of friction force (in n)? 1.0
Answers
Since the cart is moving towards the right, the direction of frictional force will be towards the left (opposite to the direction of motion). The magnitude of the frictional force can be found using the following equation:
fa - ff = ma
where fa is the applied force (10.5 N), ff is the frictional force, m is the mass of the cart, and a is the acceleration of the cart.
We know that the mass of the cart is 1.0 kg and the acceleration is 1.75 m/s^2, so we can substitute these values into the above equation:
10.5 N - ff = (1.0 kg)(1.75 m/s^2)
Solving for ff, we get:
ff = 10.5 N - (1.0 kg)(1.75 m/s^2) = 8.75 N
Therefore, the magnitude of the frictional force acting on the cart is 8.75 N.
What is a magnitude ?Magnitude is a term used in physics and mathematics to describe the size or quantity of a physical property or mathematical entity. It can refer to the absolute value of a number or vector, the intensity of a physical quantity like force, energy, or voltage, or the amplitude of a wave or vibration. Magnitude is often measured in units, such as meters for distance, newtons for force, and volts for electric potential. In some cases, magnitude may also refer to the degree or intensity of a quality or characteristic, such as the magnitude of an earthquake or the magnitude of a person's emotional response.
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describe relative motion with an examples
Answers
Answer:
The measurement of an object's motion with respect to any other object that is moving or stationary is called Relative Motion.
Gordon is making a list of forces for his science class. Which of the following should Gordon not list as a force? a mass b gravity c friction d a push or pull
Answers
Answer: mass
Explanation:
Its not a force its mass. We have mass but we arent having mass done to us.
A river flows north at 4 miles per second and a boy swims straight across it at 2 miles per second is the river is 8 miles wide how far will the boy be from his starting point after crossing the river
Answers
Answer:
16 miles (with the crazy number units given)
Explanation:
Find out how long it takes to swim across....use this time times the flow rate to see how far downstream he travels.....before he goes over the dam!
2 miles per second ??? VERY fast ( that is 7200 mph)
8 miles / 2 miles/sec = 4 seconds to swim across
river flow is 4 miles per second <=======extremely fast!!
4 mi/sec * 4 s = 16 miles
To overcome an object's inertia, it must be acted upon by __________. A. Gravity B. Energy C. Force D. Acceleration Please select the best answer from the choices provided. A B C D.
Answers
Taking into account the Newton's first Law, the correct answer is option C. To overcome an object's inertia, it must be acted upon by a force.
Newton's First Law, also called the Law of inertia, indicates that "Every body perseveres in its state of rest or of uniform rectilinear motion unless it is forced to change its state by forces impressed on it." This means that for a body to come out of its state of rest or of uniform rectilinear motion, it is necessary for a force to act on it.
In other words, it is not possible for a body to change its initial state (be it rest or motion) unless one or more forces intervene.
Finally, the correct answer is option C. To overcome an object's inertia, it must be acted upon by a force.
Learn more:
https://brainly.com/question/1083492https://brainly.com/question/14113252?referrer=searchResultsAnswer:
C) Force
Explanation:
If Bulb B burns
out, what happens?
A Bulb A and C will stay lit.
Answers
Answer: C
Explanation:
Since bulb B is burnt out, the wires can't transfer to bulb A, so that's why bulb A will burn out.
If I get it wrong, sorry. Im still learning.
130 An object, initially at rest, is dropped from a height of 12.0m. The change in gravitational potential
energy when it falls to the ground is 565J.
The frictional forces are negligible
mgh
What is its speed when it hits the ground?
A
4.71 m/s
B
15.5m/s
C 47.1 m/s
D 240 m/s
Answers
The speed when it hits the ground is option (B) 15.5 m/s.
To determine the speed of the object when it hits the ground, we can use the principle of conservation of energy. The initial potential energy of the object is converted into kinetic energy as it falls.
The change in gravitational potential energy is given as ΔPE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
We know that ΔPE = 565 J, and the height h = 12.0 m.
Since the object is initially at rest, its initial kinetic energy is zero.
The total mechanical energy (sum of potential and kinetic energy) is conserved, so:
ΔPE = ΔKE
mgh = (1/2)mv^2
Here, m cancels out, giving:
gh = (1/2)v^2
Substituting the known values:
(9.8 m/s^2)(12.0 m) = (1/2)v^2
117.6 = (1/2)v^2
Dividing both sides by (1/2):
235.2 = v^2
Taking the square root of both sides:
v ≈ 15.33 m/s
Therefore, the speed of the object when it hits the ground is approximately 15.33 m/s.
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Look at the chemical equation. There is a number in the chemical equation that is not a subscript. What do you think the number 2 on the right side of the chemical equation represents?
H2 + Cl2 → 2HCl
Answers
Answer:
Number of moles or volume
Explanation:
The number 2 on the right hand side signifies the number of moles of the product being formed.
It is necessary to include this number so as not to flout the law of conservation of mass when writing a chemical equation. The law of conservation of mass states that "matter is neither created nor destroyed during the course of a chemical reaction".
Since we must have equal number of matter on both sides of the expression, the coefficient number like the 2 seen in the expression is used to create a balance.
Here, 2 moles of HCl is formed which consists of 1 hydrogen atom and 1 chlorine atom.
A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110.0 m.
Determine the acceleration of the car.
Answers
Answer: a = 8.10 m/s^2
Explanation:
The car starts at rest, so:
V0= 0m/s
t= 5.21m/s
S = 110.0 m
Using one of the five uniformly accelerated motion formulas
S= V0t + 1/2 at^2
but V0 = 0 m/s
S = 1/2 at^2
a= 2S/ t^2
a = 2(110m)/ (5.21 s)^2
a = 8.10 m/s^2
In a parallel circuit with a single power source, The current that leaves and reenters the power source is called _____?
Answers
Answer:
total current
Explanation:
In a parallel circuit, the current leaves the power source and then splits into multiple branches that have individual components. Each branch operates independently of the other branches, and the current flows through each component and then recombines and enters back into the power source.
Because each branch is independent, the current flowing in each branch can be different, depending on the resistance of the components in that branch. However, the total current entering the circuit is equal to the sum of the currents in each branch, as long as the circuit is properly wired.
So the total current that leaves and reenters the power source in a parallel circuit is equal to the sum of the currents in each branch, and this is known as the total or overall current of the circuit.