To cause the 10 g particle that moves to the left at 28 m/s to move to the right at 48 m/s, the net work that must be done is 7.6 J.
The unit of the net work is Joule (J).
We know that the formula for kinetic energy is given by:
KE=1/2mv^2
where KE is Kinetic energy,
m is the mass of the particle,
v is the velocity of the particle
When a particle changes its direction, its velocity changes from positive to negative.
In this case, the velocity of the 10 g particle changes from -28 m/s to 48 m/s.
We want to find the net work done on the particle. Since no external force acts on the particle, we know that the net work done on the particle is equal to the change in the kinetic energy of the particle.
The initial velocity of the particle is -28 m/s and its mass is 10 g = 0.01 kg.
Therefore, the initial kinetic energy of the particle is
KEi=1/2 * 0.01 * 28^2
=3.92 J
The final velocity of the particle is 48 m/s.
Therefore, the final kinetic energy of the particle is
KEf =1/2 * 0.01 * 48^2
=11.52 J
The change in the kinetic energy of the particle is therefore,
ΔKE = KEf - KEi
=11.52 - 3.92
=7.6 J
This is the net work done on the particle to cause it to move to the right at 48 m/s.
Therefore, the net work that must be done on the particle is 7.6 J. This is the final answer.
However, we need to express the answer in the appropriate unit which is Joule.
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a hoop with a moment of inertia of 0.1 kg m2 spins about a frictionless axle with an angular velocity of 5 rad/s. at what radius from the center of the hoop should a force of 2 n be applied for 3 seconds in order to accelerate the hoop to angular speed of 10 rad/s?
Tthe radius from the center of the hoop at which a force of 2 N should be applied for 3 seconds in order to accelerate the hoop to angular speed of 10 rad/s is 0.25 m.
Given data:
Initial angular velocity ω1 = 5 rad/s
Final angular velocity ω2 = 10 rad/s
Force applied F = 2 N
Time taken t = 3 seconds
Moment of inertia I = 0.1 kg m²
Formula used: τ = Iα Where,τ = torque
I = moment of inertiaα = angular acceleration
Let's calculate the torque required to change the angular speed: Initial torque τ1 = Iω1
Final torque τ2 = Iω2
Change in torque Δτ = τ2 - τ1 = I(ω2 - ω1)
We know that τ = F × r where,
F is the force applied
r is the distance from the center of mass where the force is applied
Let's calculate the distance r: Δτ = τ = F × rr = Δτ / F = I(ω2 - ω1) / F
Substitute the values, r = 0.1 × (10 - 5) / 2 = 0.25 m
Therefore, the radius from the center of the hoop at which a force of 2 N should be applied for 3 seconds in order to accelerate the hoop to angular speed of 10 rad/s is 0.25 m.
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A small squishy ball is thrown against the side of a large cube of concrete. While the objects are in contact with each other, which experiences the larger force?
the correct option is b. The large cube of concrete exerts a larger force on the small squishy ball.
It tends to be described as a connection that influences an article's movement on the off chance that there is no resistance. The straightforward meaning of force, then again, is the push or pull that any article gets. Force is a vector amount, consequently, it has a magnitude and a bearing.
Nonetheless, gravity is a force in a more broad sense since it represents the connection that happens when two masses are near each other. Gravitational effects are on a very basic level brought about by the extension of spacetime and the movement of things through the extended spacetime. The impact, by and by, is by all accounts the consequence of utilizing force.
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the complete question is:
1) A small squishy ball is thrown against the side of a large cube of concrete. While the objects are in contact with each other, which experiences the larger force? a. The small squishy ball exerts a larger force on the large cube of concrete b. The large cube of concrete exerts a larger force on the small squishy ball C. Neither object exerts a force on the other while they are in contact. d. The small squishy ball and the large cube of concrete exert equal force on each other.
A battery of EMF 1. 5V has terminal pd of 1. 25V when a resistor of 25 ohm is joined to it. Calculate the current flowing, internal resistance and terminal pd when resistance of 25 ohm is replaced by 10 ohm
Using Ohm's law, we can find the current flowing in the circuit: I = V / R where I is the current, V is the voltage, and R is the resistance.
When a resistor of 25 ohms is connected to the battery, the terminal pd is 1.25 V. This means that the voltage drop across the internal resistance of the battery is: 1.5 V - 1.25 V = 0.25 V. Using Ohm's law, we can find the internal resistance of the battery: 0.25 V / I = R_internal. Substituting the given values, we get: R_internal = 0.25 V / (1.5 V / 25 ohm) = 4.17 ohm. The current flowing in the circuit is: I = 1.25 V / 25 ohm = 0.05 A. When the resistance is replaced by 10 ohms, the current flowing in the circuit is: I = 1.5 V / 35 ohm = 0.043 A. Using the same approach as before, the terminal pd can be calculated as: 1.5 V - 0.043 A * (R_internal + 10 ohm) = V_terminal. Substituting the value of R_internal, we get: V_terminal = 1.5 V - 0.043 A * (4.17 ohm + 10 ohm) = 1.34 V. Therefore, when the resistance is replaced by 10 ohms, the current flowing in the circuit is 0.043 A, the internal resistance of the battery is 4.17 ohm, and the terminal pd is 1.34 V.
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1. The speed of a bobsled is increasing because it has an acceleration of 2. 4 m/3. At a given instant in time, the forces resisting the motion, including kinetic friction and air resistance, total 450 N. The combined mass of the bobsled and its riders is 270 kg. (a) What is the magnitude of the force propelling the bobsled forward? (b) What is the magnitude of the net force that acts on the bobsled?
(a) The magnitude of the force propelling the bobsled forward is 648 N. (b) The magnitude of the net force acting on the bobsled is 198 N.
Use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). Rearranging the formula, we get F = ma, where F is the force, m is the mass, and a is the acceleration.
So, the force propelling the bobsled forward is,
F = ma = (270 kg)(2.4 m/s^2) = 648 N
The net force acting on the bobsled can be calculated by subtracting the forces resisting the motion from the force propelling the bobsled forward. So, the net force acting is,
Net force = Force propelling forward - Forces resisting motion
Net force = 648 N - 450 N
Net force = 198 N
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o dramatize the loss of energy in an automobile, consider a car having a weight of 5000 lb that is traveling at 35 mi>h. if the car is brought to a stop, determine how long a 100-w light bulb must burn to expend the same amount of energy. (1 mi
The light bulb must burn for approximately 46.2 minutes to use the same amount of energy as the car lost during its deceleration.
Consider a 5,000-pound vehicle at 35 mph to illustrate energy loss in an automobile. When the automobile stops, its kinetic energy is transformed into heat and sound, resulting in a large energy loss. We use a 100-Watt light bulb to understand this loss.
The car's initial kinetic energy is [tex]KE = 0.5 * mass * velocity^2[/tex]. Next, we calculate 100-Watt light bulb energy usage per second. Finally, we divide the automobile's kinetic energy by the light bulb's energy consumption per second to determine the time needed for the light bulb to use the same amount of energy as the car.
The light bulb must burn for 46.2 minutes to utilise as much energy as the automobile lost during deceleration. This striking depiction illustrates the significant energy waste required in halting a moving automobile and emphasises energy conservation and efficient transportation systems.
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A 15-cm-long aluminum tank is filled with ethyl alcohol. A high-frequency ultrasound wave travels horizontally through one wall of the tank and then through the alcohol. There are 275 times more cycles of the wave in the alcohol than in the aluminum wall. How thick is the wall of the tank?
The aluminium wall measures about 0.273 centimetres in thickness.
Let's assume that the frequency of the ultrasound wave is denoted by f and the thickness of the aluminum wall is denoted by x. We know that the speed of the ultrasound wave in aluminum is greater than that in ethyl alcohol. Since the wavelength of the wave is constant, we can use the formula:
f1 x1 = f2 x2,
where f1 and f2 are the frequencies of the ultrasound wave in aluminum and ethyl alcohol, respectively, and x2 is the thickness of the alcohol.
We are given that the ratio of the number of cycles in the alcohol to that in the aluminum wall is 275. Therefore:
f2 = 275 f1.
We also know that the speed of the ultrasound wave in aluminum is approximately 5 times that in ethyl alcohol. Therefore:
x1 = 5 x2.
Substituting these values into the equation gives:
275 f1 x2 = f1 (5 x2),
which simplifies to:
x2 = (1/55) x1.
Finally, we substitute the length of the aluminum tank (15 cm) for x1 to get:
x2 = (15 cm) / 55 = 0.273 cm.
Therefore, the thickness of the aluminum wall is approximately 0.273 cm.
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The moment magnitude scale is a scale that rates earthquakes by estimating the total energy released by an earthquake . Estimating the total amount of energy released, enables comparison of earthquakes more accurately. It measures only small earthquakes.
It uses data collected by a seismograph.
It shows only the strength of seismic waves that were produced.
It determines the amount of damage caused by an earthquake.
The total amount of energy released, enables comparison of earthquakes more accurately. Thus, b. It makes use of seismograph data.
How the moment magnitude scale rates earthquakes?
The moment magnitude scale rates earthquakes by estimating the total energy released by an earthquake, based on data collected by a seismograph. It takes into account several factors, including the size of the fault that ruptured, the amount of movement that occurred, and the strength of the rocks involved.
The resulting magnitude value indicates the relative size or strength of the earthquake, and allows for more accurate comparison of earthquakes of different sizes. It does not directly determine the amount of damage caused by an earthquake, but a larger magnitude earthquake is generally capable of causing more damage than a smaller magnitude earthquake.
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A car traveling at 28. 5 m/s E skids to a stop in 2. 58 s. Determine the skidding displacement of the car (assume uniform acceleration). 27
The car's displacement when sliding is 73.66 metres.
We can use the kinematic equation for displacement with constant acceleration to solve for the skidding displacement of the car:
d = vi * t + 0.5 * a * t^2
where d is the displacement, vi is the initial velocity, t is the time, and a is the acceleration.
First, we need to find the acceleration of the car. We can use the equation for average acceleration:
a = (vf - vi) / t
where vf is the final velocity (which is 0 since the car comes to a stop), vi is the initial velocity (28.5 m/s to the east), and t is the time (2.58 s).
a = (0 - 28.5 m/s) / 2.58 s
a = -11.05 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
Now we can substitute the values into the first equation:
d = vi * t + 0.5 * a * t^2
d = (28.5 m/s) * (2.58 s) + 0.5 * (-11.05 m/s^2) * (2.58 s)^2
d = 73.66 m
Therefore, the skidding displacement of the car is 73.66 meters.
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algol is a binary system consist of a 3.7 msun main-sequence star and a 0.8 msun subgiant (a sub giant is just a small red giant). why is this surprising? 1 the two stars in a binary system should both be at the same stage of their lives. 2 a star with a mass of 3.7 msun is too big to be a main-sequence star. 3. it doesn't make sense to find a subgiant in a binary star system. 4 in a binary system, the more massive star should be more evolved than its companion.
The correct answer is 4. In a binary system, the more massive star should be more evolved than its companion.
In the case of Algol, the 0.8 m sun subgiant is more evolved than the 3.7 m sun main-sequence star, which is surprising and not what we would expect based on our understanding of stellar evolution. This discrepancy is believed to be due to the fact that the two stars did not form together as a binary system, but rather the less massive star was captured by the more massive star after it had already evolved off the main sequence. The more massive star evolves more quickly and will reach later stages of evolution (such as a red giant phase) before the less massive star
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Work is done only when..... _ causes an object to _
Work is characterized as the resultant action when a force moves an object in the force's direction.
What does force mean in science?It is clear what the word "force" means. The terms "push" and "pull" are perfectly acceptable at this level to describe forces. An object does not have a force inside of it or within it. Another object applies a force to the first.
In what ways do forces differ?When two items come into contact with one another physically and interact, these kinds of forces are involved. Frictional, tensional, normal, air resistance, applied, and spring forces are examples of the several types of contact forces.
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1. Find FG between the earth and a football player 100 kg in mass. Fgrav =980 N
2. What is the radius of the moon when an astronaut of madd 70kg is having a gravitational force
117 N when standing in the surface of the moon
3. Determine the mass of Jupiter if a gravitational force on a scientist whose weight when in earth is 686 N, is Fgrav = 1823 N
You have a concave mirror. A candle is located 22 cm from the mirror. The image of the candle appears at a distance 7.0 cm from the mirror. What is the focal length of the mirror?
I will give you an example to know how to do it, watch and learn.
Question:
The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of mirror at a distance of 60 cm from its pole. What is the nature of the mirror. Find its focal length. If the height of flame is 2.4 cm , find the height of image.
Given :-
u = - 30 cm
v = 60 cm
h = 2.4 cm
Solution :-
Using mirror formula,
1/f = 1/v - 1/u
⇒ 1/f = 1/60 - (1/- 30)
⇒ 1/f = 1/60 + 1/30
⇒ 1/f = 3/60
⇒ 1/f = 1/20
⇒ f = 20 cm
Magnification, M = v/u = Height of image/height of object
⇒ v/u = 60/-30
⇒ v/u = h'/2.4
⇒ h' = - 60/30 × 2.4
⇒ h' = - 4.8 cm
Hence, The required height of the image is - 4.8 cm
The image formed by the mirror is inverted.
Now thats how you do it. get the idea?
Hope it helps :)
If you have a concave mirror. A candle is located 22 cm from the mirror. The image of the candle appears at a distance of 7.0 cm from the mirror. Then the focal length of the mirror is 5.31 cm.
To find the focal length of the concave mirror, we can use the mirror formula:
1/f = 1/u + 1/v
where:
f = focal length of the mirror
u = object distance (distance of the candle from the mirror)
v = image distance (distance of the candle's image from the mirror)
We are given that:
u = -22 cm (negative sign indicates that the object is in front of the mirror)
v = -7.0 cm (negative sign indicates that the image is formed behind the mirror)
Plugging in the values, we get:
1/f = 1/-22 + 1/-7.0
Simplifying, we get:
1/f = (-7.0 + (-22)) / (-22 × -7.0)
1/f = 29 / 154
f = 5.31 cm (rounded to two decimal places)
Therefore, the focal length of the concave mirror is 5.31 cm.
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Determine the total resistance for the current
The total flow of electricity from the source is equivalent to the sum of the currents through each path. To calculate the total impedance in a parallel circuit, use the method below : 1/Rt Equals 1/R1 + 1/R2 + 1/R3 +...
How do you find total resistance of a current?IT = VT/RT or I total = V total / R total or the total current = the total voltage / the total resistance.
Current still flows along the other routes even if one of the parallel ones is blocked.
R_total = R1 + R2 +... + Rn The sum of all individual resistances makes up the system's overall resistance. Take the example issue below as an
example. A resistor with a 100 ohm electrical resistance value is linked to a resistor with a 200 ohm electrical resistance value.
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Princess Leia once fell out of the spaceship. She came back with the Force. From the farthest spot (zero speed) back to the spaceship was 10 meters, and it took 5 second. She weighed 50 kg. Assume constant force during this trip. Find the force needed. (It is not much, but to get a force while floating in space is magic.)
The force needed to propel Princess Leia from a stationary position 10 meters back to the spaceship in 5 seconds would be 100 Newtons. This force can be determined by using the formula F = m x a, where m is the mass of the object and a is the acceleration.
The force required to propel Princess Leia from a stationary position 10 meters back to the spaceship in 5 seconds would be equal to the work done divided by the time taken, or 50 kg x 10 m/5 s = 100 Newtons. This is the force that is needed to move her 10 meters in 5 seconds, taking into account her 50 kg mass.
To explain this in a little more detail, the force required is determined by the formula F = ma, where F is force, m is mass and a is acceleration. Since the acceleration is constant in this scenario, the force applied is equal to the mass multiplied by the acceleration, or F = m x a. This means that to move the 50 kg mass of Princess Leia from zero speed to 10 meters in 5 seconds, a force of 100 Newtons is required.
To illustrate this with an example, if you were to pick up a 50 kg weight and move it 10 meters in 5 seconds, you would need to exert 100 Newtons of force. This is the same force required to move Princess Leia in the same way in space, taking into account her 50 kg mass.
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During a tug of war game, both teams apply a force of 75 N. What is the net force?
The net force is 0 N. This is because the forces from each team are equal but opposite in direction, so the net force is the difference between the two forces, which is 0 N.
What is force ?Force is an interaction between two or more objects that results in a change in the motion of one or more of the objects. It is a vector quantity, meaning it has both magnitude and direction. Force can be divided into two categories: contact forces, which occur when two objects physically touch one another, and non-contact forces, which occur when objects interact without direct physical contact. Examples of contact forces include friction, tension, normal force, and air resistance. Examples of non-contact forces include gravitational force, electric force, and magnetic force.
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vegetables donot burn if we use oil while frying it why?
Explanation:
This is because the oil is an unsaturated fat (liquid at room temperature) and when heated to such high temperature becomes saturated.
What is the condition of the atmosphere at a certain place and time?
The condition of the atmosphere at any given place and time depends on a variety of factors, such as air temperature, air pressure, wind speed and direction, humidity, precipitation, and cloud cover.
Air temperature can influence wind speed and direction, humidity, and cloud cover. Air pressure can impact wind speed and direction, and can create large-scale weather patterns. Wind speed and direction can determine the location of rain or snow, and also affect the temperature. Humidity influences air temperature, as well as precipitation and cloud cover. Precipitation can determine the amount of moisture in the atmosphere, and can be affected by the temperature and humidity of the air. Cloud cover affects the amount of solar radiation that reaches the surface, and can be determined by the temperature and humidity of the atmosphere.
In conclusion, the condition of the atmosphere at any given place and time depends on the interaction of several different factors. Air temperature, air pressure, wind speed and direction, humidity, precipitation, and cloud cover all interact to form the atmospheric conditions in any particular place and time.
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A cup of hot chocolate with a temperature of 40°c is placed inside a
refrigater at 5°c .An identical cup of hot chocolate at 90°c is placed on a table in a
room at 25°c. A third identical cup of hot chocolate at 80°c is placed on an
outdoor table, where the surrounding air has a temperature at 0°c, for which
of the three cups has the most energy been transferred as heat when
equilibrium has been reached?
Al The first cup has the largest energy transfer
B/ The second cup has the largest energy transfer
c/ The third cup has the largest energy transfer
O The same amount of energy is transferred as heat for all three cups
Answer:
The answer is c
Explanation:
The third cup has the largest energy transfer
A one-piece cylinder has a core section protruding from the larger drum and is free to rotate around its central axis. A rope wrapped around the drum of radius 1. 39 m exerts a force of 3. 34 N to the right on the cylinder. A rope wrapped around the core of radius 0. 48 m exerts a force of 8. 52 N downward on the cylinder. What is the magnitude of the net torque acting on the cylinder about the rotation axis? Answer in units of N ∗ m
The magnitude of the net torque acting on the cylinder about the rotation axis is 8.73 Nm.
τ1 = F1 * r1
where F1 is the force on the drum, and r1 is the radius of the drum. Substituting the given values:
τ1 = 3.34 N * 1.39 m = 4.64 Nm
The torque due to the force on the core is given by:
τ2 = F2 * r2
where F2 is the force on the core, and r2 is the radius of the core. Substituting the given values:
τ2 = 8.52 N * 0.48 m = 4.09 Nm
The net torque is the sum of the two torques:
τnet = τ1 + τ2
τnet = 4.64 Nm + 4.09 Nm = 8.73 Nm
Magnitude is a term used in physics to describe the size or amount of a physical quantity, such as length, mass, force, or energy. It is often represented by a numerical value and a unit of measurement. In physics, the magnitude of a vector is the length of the vector, and it is a scalar quantity. For example, the magnitude of the force acting on an object is the amount of force, irrespective of its direction.
Magnitude is also used to describe the intensity of phenomena such as earthquakes, sound waves, and light waves. The Richter scale, for example, is a measure of the magnitude of an earthquake, while the decibel scale is used to measure the magnitude of sound waves. In summary, magnitude is an important concept in physics that allows us to quantify the size or amount of physical quantities and phenomena.
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A spacecraft is orbiting a planet at a distance of 10,000 km from the planet's center. The spacecraft's speed is constant at 20,000 km/hr. Suddenly, the spacecraft's engines fail and it begins to free fall towards the planet's surface. Assuming that the planet has a uniform density and a radius of 5,000 km:
1. What is the gravitational acceleration experienced by the spacecraft as it falls towards the planet's surface?
2. What is the maximum velocity that the spacecraft can reach just before impacting the planet's surface?
3. What is the kinetic energy of the spacecraft just before impacting the planet's surface?
The gravitational acceleration experienced by the spacecraft would be 13.33 m/s^2.
The maximum velocity the spacecraft can reach would be 1633.5 m/s.
The kinetic energy of the spacecraft would be KE = 1/2mv^2
Gravitational acceleration problemThe gravitational acceleration experienced by the spacecraft as it falls toward the planet's surface can be calculated using the formula
g = G*M/r^2Thus:
g = (6.67 x 10^-11 N m^2/kg^2) * (4/3 * pi * (5000 km)^3 * 5500 kg/m^3) / (10000 km)^2 = 13.33 m/s^2.
The maximum velocity that the spacecraft can reach just before impacting the planet's surface can be calculated using the formula
v = sqrt(2gh)The height from which the spacecraft falls is equal to the distance from the planet's surface to the spacecraft's initial position, which is 10,000 km - 5000 km = 5000 km.
Thus, v = sqrt(2 * 13.33 m/s^2 * 5,000,000 m) = 1633.5 m/s.
The kinetic energy of the spacecraft just before impacting the planet's surface can be calculated using the formula
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how much work dose billy perform if he pushes the 800N stalled car a distence of 25m?
Answer:
20,000 J
Explanation:
Work = Force multiplied by Displacement
The work done on a object can only be calculated when the applied force is causing an object to move in the direction the force is being applied towards.
The given information:
Billy applies a form of 800N on a staller car and the total distance it was pushed was 25 meters.
To calculate the work done, substitute the given information into the formula for work.
Work = (800 N) × (25 m)
Work = 20,000 J
Note: Remember the SI unit for Work is Joules (J).
Suppose you are driving through a valley whose bottom has a circular shape. If your mass is M, what is the magnitude of the normal force Fn exerted on you by the car seat as you drive past the bottom of the hill A) Fn < Mg B) Fn = Mg C) Fn > Mg
The right response is (c) Fn > Mg
When you are driving through a circular valley, the direction of the net force acting on you is constantly changing. At the bottom of the valley, your velocity vector is horizontal and your acceleration vector is pointing upwards.
According to Newton's second law, F = ma, where F is the net force, m is your mass, and a is your acceleration. Therefore, the net force acting on you is greater than your weight (Mg) and is equal to the sum of the normal force and the force of gravity.
Thus, the correct answer is (c) Fn > Mg. The normal force is greater than your weight to provide the additional force required to maintain the circular motion.
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What is physical significance of dimension of physical quantity
The dimension of a physical quantity is the power to which the fundamental units must be raised to, to represent it. Mass, length, time, temperature, electric current, luminous intensity and amount of substance are the fundamental quantities
Temperature is a measure of the degree of hotness or coldness of an object or substance. It is a fundamental concept in physics, chemistry, and engineering and is one of the most commonly measured physical parameters in scientific and industrial applications. The temperature of an object or substance is related to the average kinetic energy of its particles. In other words, the faster the particles are moving, the higher the temperature.
Temperature is measured using a variety of devices, including thermometers, thermocouples, and pyrometers. The most common unit of temperature is the Celsius (°C) scale, which is based on the freezing and boiling points of water. Another commonly used scale is the Fahrenheit (°F) scale, which is used primarily in the United States.
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halfway through her swing, when the golf club is parallel to the ground, does the acceleration vector of the club head point (a) straight down, (b) parallel to the ground, approximately toward the golfer's shoulders, (c) approximately toward the golfer's feet, or (d) toward a point above the golfer's head? explain.
The acceleration vector of the club head point straight down(a)
Acceleration is a vector, and it may have a direction other than the acceleration of gravity.
The club head accelerates due to the forces exerted by the golfer, which include a torque applied by the golfer's hands, which generates angular acceleration that causes the club to rotate.
The acceleration vector points down because the club head is still at the beginning of the downswing.
As the club head approaches the ball, it begins to move away from its initial position and pick up velocity, resulting in a more complicated acceleration profile.
To summarise, during the downswing, halfway through the swing, the acceleration vector of the golf club head points straight down.
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2. A disc speeds up from rest at a constant rate of 2. 5 rad/s^2.
a. What is the final angular speed of the disc after 18 secs. ? (45 rad/s)
b. How many revolutions will the disc go through during this time period?
(64. 5 revs)
C. WHat is the linear speed of a point at the end of the disc after 18 secs. (The radius
of the disc is 50 cm. (22. 5 m/s)
I
a. The final angular speed of the disc after 18 seconds is 45 rad/s.
b. The disc goes through approximately 64.5 revolutions during this time period.
c. The linear speed of a point at the end of the disc after 18 seconds is 22.5 m/s.
a. The angular acceleration of the disc is constant at 2.5 [tex]rad/s^2[/tex].
Using the formula for angular velocity with constant angular acceleration, we have:
ωf = ωi + αt
Where:
ωi = initial angular velocity (0, since the disc starts from rest)
α = angular acceleration (2.5 [tex]rad/s^2[/tex])
t = time (18 s)
ωf = 0 + 2.5 × 18
ωf = 45 rad/s
Therefore, the final angular speed of the disc after 18 seconds is 45 rad/s.
b. To find the number of revolutions the disc goes through during this time period, we need to first find the total angle rotated by the disc. Using the formula for angular displacement with constant angular acceleration, we have:
θ = ωit + 1/2 α[tex]t^2[/tex]
Where:
ωi = initial angular velocity (0, since the disc starts from rest)
α = angular acceleration (2.5 [tex]rad/s^2[/tex])
t = time (18 s)
θ = 0 + 1/2 × 2.5 × [tex]18^2[/tex]
θ = 405 rad
One revolution is equal to 2π radians,
so the number of revolutions is given by:
N = θ / 2π
N = 405 / 2π
N ≈ 64.5 revolutions
Therefore, the disc goes through approximately 64.5 revolutions during this time period.
c. The linear speed of a point at the end of the disc is given by:
v = rω
Where:
r = radius of the disc (50 cm = 0.5 m)
ω = angular velocity (45 rad/s)
v = 0.5 × 45
v = 22.5 m/s
Therefore, the linear speed of a point at the end of the disc after 18 seconds is 22.5 m/s.
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Drag each tile to the correct box.
Arrange the images in order to show how lake-effect snow occurs.
The images below demonstrate how lake effect snow occurs:
Cold Arctic air is passing over warm lake waters.
The surface of the lake adds heat and water vapour to the cold air mass.
Water vapour condenses in rising air to form clouds.
Snow blankets the lake and the downwind shore.
Where does lake effect snow most commonly occur?Lake effect snow most commonly occurs in the Great Lakes region of North America, which includes parts of the United States and Canada. The Great Lakes generate significant amounts of moisture, and when cold air passes over the relatively warm water, it picks up moisture and heat, leading to the formation of clouds and precipitation. As the air moves over land, it can release large amounts of snowfall in areas downwind of the lakes. This phenomenon is most common during the winter months and can produce heavy snowfalls that can impact transportation, infrastructure, and daily life in affected areas.
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4. You throw a m = 128 g ball up into the air at an initial velocity v₁ = 4.8 m/s. How high, h, does the ball reach before slowing down to vi = 2.4 m/s?
The ball will reach a height of 1.17 meters before slowing down to Vi = 2.4 m/s
Kinematic motion problemFirst, we can use the equation for the final velocity of an object under constant acceleration:
v_f^2 = v_i^2 + 2ah
where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, h is the height reached by the ball, and we assume that the acceleration due to gravity is -9.8 m/s^2 (negative because it acts downwards).When the ball is thrown upwards, it experiences a constant downward acceleration due to gravity, so we can take a = -9.8 m/s^2.
At the maximum height, the final velocity of the ball will be zero, so we can set v_f = 0 and solve for h:
0 = (4.8 m/s)^2 + 2(-9.8 m/s^2)h
h = [(4.8 m/s)^2]/[2(9.8 m/s^2)] = 1.17 m
So the ball reaches a maximum height of 1.17 meters.
Next, we can use the same equation with v_i = 2.4 m/s and v_f = 0 to find the height where the ball reaches a velocity of 2.4 m/s on its way down:
0 = (2.4 m/s)^2 + 2(-9.8 m/s^2)h
h = [(2.4 m/s)^2]/[2(9.8 m/s^2)] = 0.29 m
Therefore, the ball reaches a maximum height of 1.17 meters and then falls to a height of 0.29 meters before reaching a velocity of 2.4 m/s.
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a transformer on a pole near a factory steps the voltage down from 3600 v to 120 v. the transformer is to deliver 1000 kw to the factory at 90% efficiency. find (a) the power delivered to the primary, (b) the current in the primary, and (c) the current in the secondary.
A) The power delivered to the primary is 1111.1 kWB) The current in the primary is 308.6 A.C) The current in the secondary is 9258 A.
We can use the formula for power to solve this problem: Power = Voltage x Current x Efficiency, where efficiency is a decimal between 0 and 1.
(a) The power delivered to the primary can be found by dividing the power delivered to the secondary by the efficiency of the transformer:
Power_primary = Power_secondary / Efficiency
Power_secondary is the power delivered to the factory, which is 1000 kW.
Efficiency is given as 90%, or 0.9.
Power_primary = 1000 kW / 0.9 = 1111.1 kW
Therefore, the power delivered to the primary is 1111.1 kW.
(b) To find the current in the primary, we can use the formula for power again:
Power_primary = Voltage_primary x Current_primary
We know that the voltage on the primary side is 3600 V. Rearranging the formula, we get:
Current_primary = Power_primary / Voltage_primary
Current_primary = 1111.1 kW / 3600 V = 308.6 A
Therefore, the current in the primary is 308.6 A.
(c) To find the current in the secondary, we can use the turns ratio of the transformer:
Turns_ratio = Voltage_primary / Voltage_secondary
We know that the voltage on the secondary side is 120 V, and the turns ratio is:
Turns_ratio = 3600 V / 120 V = 30
The turns ratio tells us that the secondary voltage is 1/30th of the primary voltage, and the current on the secondary side is 30 times greater than the current on the primary side.
Therefore, the current in the secondary is:
Current_secondary = Current_primary x Turns_ratio
Current_secondary = 308.6 A x 30 = 9258 A
Therefore, the current in the secondary is 9258 A.
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What would be the weight of a 60-kg astronaut on a newly discovered planet that is found to have density 2/3 ρᴇ and radius 2Rᴇ , where ρᴇ and Rᴇ are the density and radius of Earth, respectively?
A) 200N
B) 600N
C) 800N
D)1800N
The weight of the astronaut on the newly discovered planet is approximately 1800N, which is option D.
How is acceleration due to gravity calculated?The weight of an object is given by the formula W=mg, where g is the gravitational acceleration and m is the mass of the object. The gravitational acceleration on the surface of a planet can be calculated using the formula [tex]g = GM/R^2[/tex], where M is the mass of the planet, R is its radius, and G is the gravitational constant.
In this case, we are given that the planet has density 2/3 ρᴇ and radius 2Rᴇ. The mass of the planet can be calculated using the formula M = (4/3)π[tex]R^3[/tex]ρ, where ρ is the density of the planet. Substituting the given values, we get:
M = (4/3)π(2Rᴇ[tex])^3[/tex](2/3ρᴇ) = (32/27)πρᴇRᴇ[tex])^3[/tex]
The gravitational acceleration on the surface of the planet can be calculated as:
g = GM/R^2 = G[(32/27)πρᴇRᴇ^3]/(2Rᴇ[tex])^2[/tex] = (4/3)Gπρᴇ
The weight of the astronaut on the planet can be calculated as:
W = mg = 60[(4/3)Gπρᴇ] = (80/3)Gπρᴇ
Substituting the value of G and ρᴇ, we get:
W = (80/3)([tex]6.67 * 10^-^1^1[/tex])([tex]5.5 * 10^3[/tex])π ≈ 1818.9 N
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Which of the following is an example of acceleration?
O A. 15 m/s
OB. 25 m/s east
O C. 60 km/hr
OD. -2 m/s² west
Option D: -2 m/s² west is an example of acceleration.
What is the definition of acceleration?Acceleration is the rate of change of velocity with respect to time. It is a vector quantity and can be positive or negative depending on the direction of the change in velocity.
Why is option D an example of acceleration?Option D is an example of acceleration because it includes both the magnitude (-2 m/s²) and direction (west) of the change in velocity. The negative sign indicates that the velocity is decreasing, and the direction (west) indicates the direction of the change in velocity.
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