When an object reaches terminal velocity its acceleration becomes zero.
Terminal velocity is also called constant velocity. When there is no acceleration in the moving object. We can take the example of sedimentation.
Sedimentation is the process of settling down the soil particles at the bottom of the water. When soil particles comes down in water there are three forces which act on the particles. Downward force is weight of the particle. Upward force buoyant force of the water, and drag force. When upward forces become equal to the downward force then particles begins to settle down with a constant velocity. which is called terminal velocity.
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despite emitting the same power as a 100 w incandescent bulb, humans don't shine as brightly. we'll learn in week 4 why that is, but for now, let's compute the first step of the difference: the temperature. a human has a surface area of roughly 1.6 m2, but the filament a surface area of 6e-5 m2, so to emit the same power, it needs a much higher power density, and so needs to be at a higher temperature. what temperature is the lightbulb at (in kelvin)?
According to the problem the temperature of the light bulb is 1 Kelvin.
What is temperature?Temperature is a measure of how hot or cold something is. It is measured using a thermometer or thermocouple and is usually expressed as a number on a scale, such as Celsius or Fahrenheit.
The temperature of a light bulb can be calculated using the Stefan-Boltzmann law. This law states that the power emitted by a blackbody is proportional to the fourth power of its temperature. Therefore, the temperature of the light bulb can be calculated by taking the fourth root of the ratio of the power emitted by the human to the power emitted by the light bulb.
The power emitted by a human is around 100 watts and the power emitted by a 100 watt incandescent bulb is also 100 watts. Therefore, the temperature of the light bulb is the fourth root of 100/100, which is 1.
Therefore, the temperature of the light bulb is 1 Kelvin.
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tell me a reasonable number of significant figures to use when measuring: a) thickness of measurements book b) outdoor air temperature with bulb thermometer c) wind speed with vane anemometer d) weight of platinum bar that is approximately 50 lbs
Significant figures are a number of digits used to describe a particular measurement. While considering the significant figures, it must be noted that to define a measurement, it is necessary to define its unit too. So unit consideration is also a factor before defining the number of reasonably significant figures.
a ) Considering the thickness unit to be ( mm ). So the thickness of the measurement book will satisfy two nondecimal digits. So its significant figure is 2.
b ) Considering air temperature unit to be ( °C ). So the outdoor temperature with bulb thermometer will satisfy with three decimal digits. Because it is a fluid measuring device it is difficult to get the measurement without decimal digits. So its significant figure is 3.
c ) Considering wind speed unit to be (m/s ). So the wind speed with a vane anemometer will satisfy with three decimal digits as a vane anemometer is also a device. So its significant figure is 3.
d ) As the weight of the platinum bar unit is defined as ( lb ). So significant figure with three decimal digits must satisfy the weight of approximately 50 lb. So its significant figure is 3.
Dimension is the quantification of attributes of an item or occasion, which may be used to compare with different items or activities. In different words, size is a technique of figuring out how massive or small a bodily amount is compared to a basic reference amount of the equal type. The scope and application of measurement are depending on the context and field.
In herbal sciences and engineering, measurements do now not observe nominal residences of items or events, that's constant with the recommendations of the worldwide vocabulary of metrology posted through the International Bureau of Weights and Measures. but, in different fields including facts as well as the social and behavioral sciences, measurements can have multiple tiers, which could consist of nominal, ordinal, c language, and ratio scales.
Dimension is a cornerstone of change, technological know-how, era, and quantitative studies in many disciplines. traditionally, many dimension systems existed for the various fields of human life to facilitate comparisons in those fields. frequently those have been achieved by means of local agreements among trading companions or collaborators.
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A ball is attached by a tether to a stake in the ground. The ball travels in a circle at the full length of the tether. The pull of the tether acts in a direction ____________ to the ball's velocity, and changes its ____________.
Answer:A ball is attached by a tether to a stake in the ground. The ball travels in a circle at the full length of the tether. The pull of the tether acts in a direction perpendicular to the ball's velocity, and changes its direction.
Explanation: i big brained thats y
what is the total displacement, in meters, of the ball going through its entire motion: traveling from the ground to the top and then falling back to the ground?
The total displacement, in meters, of the ball going through its entire motion: traveling from the ground to the top and then falling back to the ground is 0.
What do you mean by displacement?An object's position changes if it moves in relation to a reference frame, such as when a passenger moves to the back of an airplane or a lecturer moves to the right in relation to a whiteboard. Displacement describes this shift in location.
The total displacement of an object is the distance and direction between its initial and final positions. If a ball is thrown upward, travels to the top and then falls back to the ground, its total displacement is zero.
This is because the ball travels upward and then downward, covering the same distance in opposite directions. The upward motion and the downward motion cancel each other out, resulting in a net displacement of zero.
So, the ball will be back to the ground where it was originally thrown.
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8. (a) a spherical mirror is cut in half horizontally and the top half removed. will an image be formed by the bottom half of the mirror? how does the image formed by the half mirror compare to the image formed before cutting the mirror in half?
As the radius of curvature and focal length of the mirror is bottom half of the mirror is same as earlier, so the image formation by this mirror will not change. As a result, the bottom half of the spherical mirror will reflect an image that is an exact replica of the image it projected prior to being chopped.
Only the aperture area will be cut in half when a mirror is cut in half horizontally; the radius of curvature remains unchanged.
The spherical mirror has a radius of curvature that is twice its focal length. Because the radius of curvature remains unchanged when the mirror is cut horizontally, the focal length of the bottom portion will be the same as in the initial situation.
The location of the image created by the lower portion of the mirror is therefore the same as in the preceding situation according to the mirror equation.
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where m 0 is the mass of the particle at rest and c is the speed of light. what happens as v goes to c?
As velocity, v of the object approach the speed of light c, the energy of the particles will increase.
From the famous equation of Einstein of mass-energy relationship, that is
E = m₀c²/√(1-v²/c²)
Where E denotes the energy, c is the speed of light, v is the speed of the object.
If mass of the object at rest is m₀, we can see from the above relationship that as we approaches c, the denominator terms goes closer to 0. And when v becomes speed of light c, then the denominator becomes zero. Thus making the Energy infinite. So the energy becomes infinite.
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a ball is thrown upwards at 20.0 m/s from the top of a roof that is 10.0 meters above the ground. how long does it take before the ball hits the ground? take g
A ball is thrown upwards at 20.0 m/s from the top of a roof that is 10.0 meters above the ground and t = 4.84 seconds
The equation used to solve this problem is
s = vt - (1/2)gt^2
where s = the distance travelled (in this case, 10.0 meters), v = the initial velocity (in this case, 20.0 m/s), g = the acceleration due to gravity (in this case, 9.81 m/s^2), and t = the time (in this case, the time it takes for the ball to hit the ground).
Rearrange the equation to solve for t:
t = (2s/g) + (v^2/g^2)
Substitute the given values into the equation:
t = (2(10.0)/(9.81)) + (20.0^2/(9.81^2))
Simplify the equation:
t = 0.811 + 4.03
t = 4.84 seconds
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Little kids at Newton's preschool are always dropping their lunch boxes on the floor,
causing the boxes to either break or pop open and spill lunches everywhere. Mrs.
Suki wants to get a new mat to put on the floor under the preschooler's cubbies that
will keep the lunch boxes from breaking when the kids drop them.
Mrs. Suki tested 2 different materials and this is what she found:
.
• The bare floor causes the lunch box momentum to decrease to 0 in 3 seconds.
• Material #1 causes the lunch box momentum to decrease to 0 in 1 second.
• Material #2 causes the lunch box momentum to decrease to 0 in 2 seconds.
Mrs. Suki is looking for a material to place on the floor under the preschooler's cubbies that will reduce the momentum of a dropped lunch box and prevent it from breaking.
What is preschooler's cubbies?A preschooler's cubby is a small, personal storage space designed for children to store their belongings at school, daycare, or a similar educational setting. It is typically an open shelf or cabinet with multiple compartments for each child to store their items.
Based on her testing, she found that Material #1 is the best option because it causes the lunch box momentum to decrease to 0 in the shortest amount of time, 1 second. Material #2 is a good option too, but it takes 2 seconds for the momentum to decrease to 0, which is slightly longer than Material #1. Therefore, Material #1 is the best choice for reducing the momentum of a dropped lunch box and keeping it from breaking.
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on the left side of the simulation, click on to turn on an animated energy bar chart. pause the simulation, and drag your skater up and down. what do you notice is happening to the amount of potential energy as you do this? describe the cause and effect relationship you see.
As you drag the skater up higher, the potential energy increases. As you drag the skater down lower, the potential energy decreases.
This is because potential energy is determined by the skater’s height, so as the skater’s height changes, the amount of potential energy changes accordingly.
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. The potential energy of a steel ball is greater when it is raised above the earth than when it is brought to Earth.
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michael's scale measures the mass of objects as consistently 2kg less than their actual mass. how would you describe the scale? group of answer choices
The scale used by Michael is precise but not accurate when it measures the mass.
While measuring the quantities, we use different devices. These devices has to be precise as well as accurate.
Being precise means that it has to give the same reading, which is the case for us because we are having the scale that is measuring the value of the scale consistently that is actually 2 kg less than the actual mass of the object.
Being accurate means that the reading should be either very very close to the actual reading or equal to the actual reading, which is not the case to us because the scale is not showing the correct value of the mass.
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IM CONFUSEDDDD!
i have to turn in this project for an online balloon car thing, can someone do the calculating at least please!
To design a race car with a balloon engine for the best possible performance. must take into consideration Newton's laws of motion. the formula Velocity (speed) = Distance / Time (v = d / t).
What was the average velocity of your balloon car?3.753968254 metres per second was the car's average speed.According to the law of conservation of energy, as you fill up the balloon more, it stores more potential energy, which is then transformed into more kinetic energy, causing the balloon to expand faster and the car to move forward.Using f=ma, calculate thrust.By averaging the positive acceleration readings or measuring the time it takes to reach maximum velocity, average acceleration may be obtained.The balloon will travel with greater force and accelerate more quickly as compressed air content increases. The force of the balloon is reduced and its speed is slowed down if the number of pumps is reduced (air pressure is decreased).The Complete Question.
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A 50kg student is climbing a rock face with a constant speed. Neglect any friction and drag impending her motion. What is the magnitude of the net force on the student? How much force is the student generating up the hill? What is the magnitude of the normal force?
The magnitude of the net force on the student is zero.
The force generated by the student is 500N.
The magnitude of the normal force is 500 N
What is the net force on the student?The net force on the student is determined as follows:
The formula of the force of gravity is given by :
W = mass × acceleration due to gravity
The mass of the student is 50 kg
The magnitude of the net force in the student is:
Force = 50 * 10
W = 500 N
The force generated by the student is equal to the force of gravity acting o the student since the student is moving at a constant speed.
The force generated by the student = 500N
The net force = weight - force generated by the student
Net force = 500 N - 500 N
Net force = 0 N
The magnitude of the normal force is equal to the weight of the student.
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how does the magnitude of the electric field at the origin for the quarter-circle arc you have just calculated comnpare to the electric field at the origin produced by a point charge q
although the electric field at the origin owing to the quarter-circle arc is zero, the electric field at the origin due to a point charge q is non-zero.
An electric field is a physical field that surrounds electrically charged particles and acts as an attractor or repellent to all other charged particles in the vicinity. It can also refer to a system of charged particles' physical field. The force per unit charge exerted on a positive test charge that is at rest at a given position is the force per unit charge that is used to define the electric field analytically. Electric charge or magnetic fields with variable amplitudes can produce an electric field. The area of space surrounding an electrically charged particle or object in which the charge body perceives force is known as the electric field.
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the first practical peacetime use of airplanes was for
The first time pirates used airplanes in peacetime was to transport letters. Considered to be the founding flight of what would become American Airlines, this flight was the first regularly scheduled flight.
What was the first sensible application of aircraft during peacetime? Airplanes were first used for postal delivery during a period of peace.The De Havilland DH-4 biplane that Charles Lindbergh, the chief pilot of Robertson Aircraft Corporation, flew from Chicago to St. Louis carrying a bag of mail, was built in 1926.Considered to be the founding flight of what would become American Airlines, this flight was the first regularly scheduled flight.Reconnaissance was the initial purpose of aviation in World War.The aircraft would soar over the battlefield, observing the enemy's actions and positions.The 1903 Wright Flyer, the first successful powered airplane, was the result of four years of study and development by Wilbur and Orville Wright.On December 17, 1903, Orville piloted it for its maiden flight over Kitty Hawk, North Carolina.To learn more about airplanes refer
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suppose that the acceleration of a model rocket is proportional to the difference between 260 ft/sec and the rocket's velocity. if it is initially at rest and its initial acceleration is 260 ft/sec, how long will it take to accelerate to 208 ft/s?
It will take the model rocket 0.2 seconds to accelerate from rest to a velocity of 208 ft/sec.
In order to answer the question of how long it will take a model rocket to accelerate from rest to a velocity of 208 ft/sec, we need to understand the acceleration of the rocket.
According to the given parameters, the acceleration of the model rocket is proportional to the difference between 260 ft/sec and the rocket's velocity.
Therefore, when the rocket is initially at rest and its initial acceleration is 260 ft/sec, the time it takes to accelerate to 208 ft/s can be calculated as follows:
Acceleration = (260 ft/sec - 208 ft/sec) / time
Rearranging the equation, we get:
Time = (260 ft/sec - 208 ft/sec) / acceleration
Plugging in the values given, we get:
Time = (260 ft/sec - 208 ft/sec) / 260 ft/sec
Time = 0.2 seconds
Therefore, it will take the model rocket 0.2 seconds to accelerate from rest to a velocity of 208 ft/sec.
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we are experiencing a gravitational pull from the sun and from the laptop in front of us. true or false
Answer:
the answer it's flas
Explanation:
I wish I help you
a man and his dog are out for a run at 5.0 km/hr, going toward a road 15 km away. at the first kilometer, he decides to unleash the dog, and it runs back and forth between its owner and the road at 10.0 km/hr while he continues at his same pace. how far does the dog run by the time the man reaches the road?
The dog run 28 km back and forth between its owner and the road, at the speed of 10.0 km/hr.
Speed of the man throughout the whole distance, v₁ = 5 km/hr
After 1 km, the speed of the man is same but the speed of dog, v₂ = 10 km/h
The distance between the road and the dog's owner after he unleash the dog, d = (15 - 1) = 14 km
Time taken by the owner to reach the road, t = 14/5 = 2.8 hrs
Distance travelled by the dog in 2.8 hrs, = 2.8 × 10 = 28 km
So the dog run a total of 28 km distance.
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A sail boat is in a 1000 m race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 1 minute and 20 seconds (= 80.0 s). What is the velocity of the sail boat?
The velocity of the sailboat is 12.5 meters per second.
What is velocity and how is it calculated?Velocity is a measure of how fast an object is moving in a specific direction. It is calculated by dividing the distance traveled by the time it took to travel that distance. The unit of velocity is meters per second (m/s) or kilometers per hour (km/h).
To understand how the velocity of the sailboat was calculated, it is important to understand the concept of velocity and how it is measured. Velocity is a vector quantity, meaning it has both magnitude (size) and direction. The magnitude of velocity is measured in units of distance per unit of time, such as meters per second (m/s) or kilometers per hour (km/h). The direction of velocity is the direction in which an object is moving.
In this scenario, the sailboat was in a 1000-meter race and reached the finish line in exactly 1 minute and 20 seconds, or 80 seconds. To calculate the velocity of the sailboat, we used the formula: Velocity = distance / time. Substituting in the given values, we have: Velocity = 1000 meters / 80 seconds = 12.5 meters per second. This means that the sailboat was moving at a speed of 12.5 meters per second.
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a doubly charged ion is accelerated to an energy of 36.0 kev by the electric field between two parallel conducting plates separated by 1.60 cm. what is the electric field strength (in v/m) between the plates?
The electric field strength between the conducting plates would be 3.6 x 10⁵ V/m.
What is electric field strength?
Electric field strength (E) is a measure of the force exerted on a charged particle by an electric field. It is measured in units of volts per meter (V/m) or newtons per coulomb (N/C). An electric field can be created by a static charge or by a changing magnetic field. The strength of the electric field is affected by the distance from the source of the field, the charge of the source, and the permittivity of the medium. Electric fields are used in many applications, including in electric motors, generators, and particle accelerators. It is also used in the study of charges and the behavior of conductors and insulators.
The electric field strength (E) can be determined by using the equation: E = W / qd
Where,
W = energy of the ion (36.0 keV)
q = charge of the ion (doubly charged ion, so 2e)
d = distance between the plates (1.60 cm)
To convert keV to J and cm to m:
1 keV = 1.602176634 x 10⁻¹⁶ J
1cm = 0.01m
Therefore,
E = (36.0 x 1.602176634 x 10⁻¹⁶ J) / (2e x 0.01m)
E = (57.634 x 10⁻¹⁶J/C) / (2 x 1.602176634 x 10⁻¹⁹ C x 0.01m)
E = 3.6 x 10⁵ V/m
So, the electric field strength between the plates is 3.6 x 10⁵ V/m.
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A certain vector A, of magnitude 4.68 units, points in a direction 30.7° to the left of the negative y-axis. Find Ax and Ay.
The x-component of A vector is - 2.39 unit.
The y-component of A vector is - 4.02 unit.
What is vector?Vector is a colloquial term that refers to some quantities that cannot be expressed by a single number (a scalar) or to elements of some vector spaces.
The magnitude of A vector is 4.68 unit.
The direction of A vector is 30.7° to the left of the negative y-axis.
So, A vector is in 3rd co-ordinate.
Hence, the x-component of A vector is = - Asin30.7°
= - 4.68 × sin30.7°
= - 2.39 unit.
Hence, the y-component of A vector is = - Acos30.7°
= - 4.68 × cos30.7°
= - 4.02 unit.
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how much power is needed to move a person (mass 72 kg) up an escalator (angle 34 degrees with the horizontal) with a speed of 1.5 m/s (neglect friction)? 878w
878 Watts of power is needed to move a person (mass 72 kg) up an escalator (angle 34 degrees with the horizontal) with a speed of 1.5 m/s (neglect friction).
Moving sidewalks move people horizontally or at a little slope, elevators or lifts take people and cargo up and down, escalators are moving staircases from one story of a building to another. A really compact commercial elevator called a du.mb. waiter elevator is designed to convey things rather than humans.
The given data:
m = 72 kg
w = fd
w mgd
w = 72 kg × 9.8 × 1.5 m
w = 878w
The pressure preventing movement against one another of hard substrates, liquids layers, and material components is known as friction. There are many sorts of friction.
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Metal ball A ha a charge of -9, and metal ball B ha a charge of 3. What will be the charge on the ball after they come in contact while remaining inulated from their urround?
Upon coming into contact with an uncharged metal sphere B, metal sphere A becomes positively charged, making both spheres positively charged.
How fully charged is sphere B at this point?A ultimate charge state of -1 will be present for each sphere. The spheres effectively combine to form one conductor when they come into contact.Upon coming into contact with an uncharged metal sphere B, metal sphere A becomes positively charged, making both spheres positively charged.Since there is no net electric field within a solid ball, the electric field created by charges on the metal ball's surface will be equal to and opposing to the electric field created by charges on a hollow plastic ball at the metal ball's center.To learn more about metal sphere refer to:
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a car slows down uniformly from a speed of 25.0 m/sm/s to rest in 9.00 ss . part a how far did it travel in that time?
The distance car travel at 9.00 s is 112.8 m.
What is the distance car travelled?Displacement is the measurement of a change in position of an object or person in meters. And acceleration is the rate of change in velocity, measured in meters per second per second (or meters per second squared).The rate of change of velocity is defined as acceleration. Acceleration usually indicates that the speed is changing, but this is not always the case. When an object moves in a circular path at a constant speed, it is still accelerating because its velocity direction changes.Acceleration of car = (v - u)/t
Here given,
v = 0 m/s
u = 25 m/s
t = 9.00 s
By substituting values,
a = (0 m/s - 25.0 m/s) / 9.00 s
a = -2.77 ms⁻²
S = V² - u² / 2a
= ((0 ms⁻¹)² - (25.0 ms⁻¹)²) / 2 x -2.77 ms⁻²
= 112.8 m
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g assume that there are no other targets between moon and earth, and therefore range aliasing can be tolerated. what is the maximum pulse repetition frequency that can be used for the purpose of mapping the (half-sphere) surface of the moon?
Assuming that range aliasing can be tolerated and there are no other targets between the moon and Earth, a pulse repetition frequency of around 10-20 MHz would likely be sufficient for mapping the moon surface.
The maximum pulse repetition frequency (PRF) that can be used for mapping the surface of the moon is determined by the need to avoid range ambiguities and to achieve the desired resolution. The PRF is the number of pulses emitted per second. A high PRF allows for high resolution mapping but also increases the chance of range ambiguities.
If range ambiguities can be tolerated, a high PRF can be used to achieve a high resolution map. The altitude of the spacecraft, the size of the antenna, and the desired resolution of the map are also factors that determine the maximum PRF. A general estimate is that a PRF of around 10-20 MHz would be sufficient for mapping the surface of the moon with a high resolution.
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what is the strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc ?
The strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc will be 7.912 x 106 N/C.
The strength of an electric field 4.0 cm from a small glass bead that has been charged to 5.0 nC can be calculated using Coulomb's law.
According to this law, the electric field, E, is equal to the charge, Q, divided by the permittivity of free space, ε, multiplied by the distance between the charge and the point in space, r, squared.
Therefore, the electric field at a distance of 4.0 cm from the bead is equal to:
E = (5.0 nC) / (8.854 x 10-12 [tex]C^{2}/ nm^{2}[/tex]) x (0.04 m)
E = 7.912 x 106 N/C
This means that the electric field at a distance of 4.0 cm from the glass bead charged to 5.0 nC is 7.912 x 106 N/C.
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a ball loses 15% of its kinetic energy when it bounces back from a concrete floor. with what speed, must you throw it vertically downward from a height of 12.4 m to have it bounce back to the same height? ignore air resistance.
To find the speed at which the ball must be thrown, we need to use the conservation of energy. The final potential energy is v = 8.14 m/s .
The initial potential energy of the ball is given by mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which the ball is thrown. The final kinetic energy of the ball is given by 1/2mv^2, where v is the speed at which the ball bounces back.Since the ball bounces back to the same height, the final potential energy is also mgh. Since kinetic energy is lost when the ball bounces, we know that the final kinetic energy is 85% of the initial kinetic energy.
So we can set up the following equation:
mgh = 0.85 * (1/2mv^2)
Solving for v, we get:
v = sqrt(2gh/0.85)
v = sqrt(2 * 9.8 * 12.4 / 0.85)
v = 8.14 m/s
So the speed at which the ball must be thrown is 8.14 m/s vertically downward from a height of 12.4 m to have it bounce back to the same height.
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A box is pushed across a room. What are the force pairs?
Answer:
Once static friction gives up, it allows the box to begin sliding across the floor, the frictional force acting on the box, is now the force of sliding friction exerted by the floor on the box
Explanation:
.
a rollercoaster has a hill that is 30m high. a 500kg car is pulled up, stops, and is released. what is the maximum velocity of a car on the rollercoaster that makes it to the lowest point in the track, 5m above the ground?
The bottom of the hill, the cart's kinetic energy would be 147150 joules.
What is meant by Kinetic Energy?In physics, an object's kinetic energy is the energy it has as a result of motion. It is explained as the amount of effort required to move a mass-based body from rest to the indicated velocity. The body keeps its kinetic energy, which it acquired during acceleration, unless its speed changes.
Let KE denote Kinetic Energy
As an equation, the relationship would be:
[tex]$m g h=\frac{1}{2} m v^2$$[/tex]
Kinetic Energy = m g h
Assuming the acceleration due to gravity near the earth's surface exists [tex]$9.81 \frac{\mathrm{m}}{\mathrm{s}}$[/tex], our equation becomes:
[tex]$$\begin{aligned}& K E=500 \mathrm{~kg} \cdot 9.81 \frac{\mathrm{m}}{\mathrm{s}} \cdot 30 \mathrm{~m} \\& K E=147150 \text { Joules }\end{aligned}$$[/tex]
Once a result, as the cart nears the base of the hill, where its gravitational potential energy is transformed into kinetic energy, its kinetic energy would be equal to its initial potential energy.
At the bottom of the hill, the cart's kinetic energy would be 147150 joules.
The complete question is:
A roller coaster car with a mass of 500 kg at the top of a hill that is 30 m high. Without friction, what would its kinetic energy be as it reached the bottom of the hill?
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Objects with masses of 111 kg and 290 kg are separated by 0.396 m. A 23.9 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the two larger masses on the 23.9 kg mass. The value of the universal gravitational constant is 6.672 × 10^-11 N • m^2 /kg^2.
Answer in units of N.
part 2 of 2
Leaving the distance between the 111 kg and the 290 kg masses fixed, at what distance from the 290 kg mass (other than infinitely remote ones) does the 23.9 kg mass experience a net force of zero?
Answer in units of m.
F_net = 6.672 × 10^-11 * ((111 * 23.9) / (0.396 / 2)^2 + (290 * 23.9) / (0.396 / 2)^2) N part 2) x = sqrt((111 * 23.9) / (290 * 23.9)) * (0.396/2) m
What is gravitational force?According to Newton's universal law of gravitation, force of attraction between any two bodies is directly proportional to product of their masses and is inversely proportional to square of the distance between them.
We know, F = G * (m1 * m2) / r^2
Given m1 = 23.9 kg and m2 = 290 kg
m1 and m2 are the masses of the two objects, r is separation distance between them, and G is universal gravitational constant.
F1 = G * (111 * 23.9) / (0.396 / 2)^2
F2 = G * (290 * 23.9) / (0.396 / 2)^2
As, F_net = F1 + F2
F_net = 6.672 × 10^-11 * ((111 * 23.9) / (0.396 / 2)^2 + (290 * 23.9) / (0.396 / 2)^2) N
part 2) As, F = G * (m1 * m2) / r^2
G is the universal gravitational constant and r is distance between the two masses.
Let x be the distance of the 23.9 kg mass from 290 kg mass. Then the distance between 111 kg mass and 23.9 kg mass is x - 0.396/2.
So, F1 = G * (111 * 23.9) / (x - 0.396/2)^2
and F2 = G * (290 * 23.9) / x^2
Setting F1 = -F2, :
G * (111 * 23.9) / (x - 0.396/2)^2 = G * (290 * 23.9) / x^2
So, x = sqrt((111 * 23.9) / (290 * 23.9)) * (0.396/2) m
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the ejected gases have a mass that is small compared to the mass of the spacecraft. you then continue coasting with the rocket engines turned off. what will be the components of your position vector an hour later? start by finding the x component, rf,x
The final position of the rocket after 1 hour is (2.64 × 10⁴, 3.5 × 10⁴, 0).
Initial velocity, = (0, 2× 10⁴, 0)
Initial location, = (1.2× 10⁴, 1.5 × 10⁴, 0)
Net force acting, F₁ = (6× 10⁴, 0, 0) N
Mass of the rocket, m₁ = 1.5 × 10⁴
Initial momentum, p₁ = mv₁ = (1.5 × 10⁴) × (0, 2× 10⁴, 0)
p₁ = (0, 3 × 10⁸, 0)
Final momentum after 1 hour(3600 sec), P₂ = p₁ + F₁×Δt
P₂ = (0, 3 × 10⁸, 0) + (6× 10⁴, 0, 0)×3600
P₂ = (2.16 × 10⁸, 3 × 10⁸, 0)
Final position of this time,
r₂ = r₁ + (P₂)/m₁
r₂ = (1.2 × 10⁴, 1.5 × 10⁴, 0) + (2.16 × 10⁸, 3 × 10⁸, 0)/(1.5 × 10⁴)
r₂ = (2.64 × 10⁴, 3.5 × 10⁴, 0)
--The given question is incomplete, the complete question is:
"Suppose that you are navigating a spacecraft far from other objects. The mass of the spacecraft is 1.5 × 10⁴ kg. The rocket engines are shut off, and you're coasting along with a constant velocity of (0, 2× 10⁴, 0) m/s. As you pass the location (1.2× 10⁴, 1.5 × 10⁴, 0) you briefly fire side-thruster rockets, so that your spacecraft experiences a net force of (6× 10⁴, 0, 0) N for 1 hour. After turning off the thrusters, you then continue coasting with the rocket engines turned off. The ejected gases have a mass that is small compared to the mass of the spacecraft. you then continue coasting with the rocket engines turned off. what will be the components of your position vector an hour later? start by finding the x component, rf,x?"
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