Answers
ANSWER
10 m
EXPLANATION
Given:
• The mass of the cart, m = 500 kg
,• The velocity of the cart at the bottom of the hill, v = 14.0 m/s
,• The velocity of the cart at the top of the hill, v₀ = 0 m/s (we know that it is at rest)
Unknown:
• The height of the hill, h.
By the law of conservation of energy, the initial energy of the cart at the top of the hill must be equal to the final energy at the bottom of the hill. Knowing that the cart starts from rest, we can conclude that when it is at the top it has gravitational potential energy and no kinetic energy - since it is not moving. Also, when it reaches the bottom of the hill, its potential energy drops to 0, while its kinetic energy is at its maximum - which is the same as the potential energy the cart had at the top of the hill,
\(\begin{gathered} PE_i=KE_f \\ m\cdot g\cdot h=\frac{1}{2}\cdot m\cdot v^2 \end{gathered}\)Solving for h,
\(h=\frac{v^2}{2\cdot g}\)As we can see, it does not depend on the mass of the cart. Replace with the values - remember that g = 9.8 m/s²,
\(h=\frac{14^2m^2/s^2}{2\cdot9.8m/s^2}=\frac{196m^2/s^2}{19.6m/s^2}=10m\)Hence, the height of the hill is 10 meters.
Related Questions
A 6.35 kg bowling ball moving 8.49 m/s strikes
a 1.59 kg bowling pin at rest. After, the pin moves 20.1 m/s at a -77.0° angle. What is
the x and y component of the ball's final velocity?
Answers
The x and y component of the ball's final velocity are respectively 7.35 m/s and 4.90 m/s.
What is velocity?
The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Given that:
Mass of the ball: M = 6.35 kg.
Initial velocity of ball: U = 8.49 m/s.
Mass of the pin at rest: m = 1.59 kg.
Final velocity of pin: v = 20.1 m/s at a -77.0° angle.
Let the x and y component of the ball's final velocity are respectively V₁ m/s and V₂ m/s.
Appling conservation of momentum along x axis:
MU + m.0 = MV₁ + mvcos(-77.0°)
⇒ V₁ = u - (m/M) v cos(-77.0°)
After putting the values we get:
V₁ = 7.35 m/s.
Appling conservation of momentum along y-axis:
M.0 + m.0 = MV₂ + mvsin(-77.0°)
⇒ V₂ = - (m/M) vsin(-77.0°)
After putting the values we get:
V₂ = 4.90 m/s.
Hence, the x and y component of the ball's final velocity are respectively 7.35 m/s and 4.90 m/s.
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Explain the difference between the speed of an Electromagnetic wave and its frequency?
Answers
Answer:
Electromagnetic waves differ in their wavelengths and frequencies. The higher the frequency of an electromagnetic wave, the greater its energy. The speed of an electromagnetic wave is the product of its wavelength and frequency, so a wave with a shorter wavelength has a higher frequency, and vice versa.
Explanation:
It takes less energy to cool a hot car than it does to cool a medium-sized home in Atlanta, Georgia during the summer!
false
true
Answers
The given statement is false.
Atlanta which is in Georgia have high temperatures during summer.
Although Georgia is near ocean but Atlanta is landlocked.
This place is also located a bit towards the tropic of cancer and this altitude is near to the equator.
With such a location, it is justified for the summers to be hot.
But in comparison to car, medium sized homes tend to cool down faster.
This is because of the good ventilation in the houses.
While in car, already the body is heat absorbing and traps heat in summer which then leads to the switching on of ACs in the car.
While in such hot summer when the AC is turned on then the ventilation becomes null. Which makes the hot air rise above and the cool air settle down.
But since there's no way for hot air to move, it remains inside the car and make it hotter in the summer and this in turn make people turn on their AC at cooler temperature and for longer time, thus consuming in more energy.
While in house, due to proper ventilation, there's a movement maintained in the atmosphere.
Therefore, it takes more energy to cool a hot car than it does to cool a medium-sized house in Atlanta during summer.
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how to find potential energy
Answers
Answer:
The formula for potential energy depends on the force acting on the two objects.
two vectors undergo vector addition. vector a has a magnitude of 217 units and points to the north. vector b has a magnitude of 156 units and points to the west. what is the direction of the resultant vector? (the angle)
Answers
Explanation:
Given that,
The magnitude of vector A = 217 units to north
The magnitude of vector B = 156 units to west
Let R is the resultant. So,
\(R=\sqrt{217^2+156^2} \\\\R=267.25\ \text{units}\)
Let \(\theta\) is the direction of the resultant vector. So,
\(\tan\theta=\dfrac{y}{x}\\\\\tan\theta=\dfrac{217}{156}\\\\\theta=\tan^{-1}\left(\dfrac{217}{156}\right)\\\\\theta=54.28^{\circ}\)
Hence, this is the required solution.
explain the statement that what is matters in an experiment is asking the right questions and not finishing the right answer
Answers
The statement that what matters in an experiment is asking the right questions and not necessarily finding the right answer potryas the importance of the scientific process and inquiry-based approach.
How do we explain ?The aim of scientific study is to learn about and comprehend the natural world. This is accomplished through developing hypotheses, posing questions, carrying out experiments, and evaluating the outcomes. While getting the right response is critical, it's just as important to ask the right questions in the first place.
Asking the right questions helps to define the scope and objectives of the experiment and also guides the researcher to focus on specific variables, design appropriate experiments, and gather relevant data.
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What is the advantage in solving motion problems using energy conservation principles instead of free body diagrams
Answers
Answer:
However, the disadvantages are:
1. Many atimes for some motion prolems, free-body diagrams has to be drawn many times so to have enough equations to solve for the unknowns. This is not the same with energy conservation principles.
2. In situations where we need to find the internal forces acting on an object, we can't truly solve such problems using free-body diagram as it captures external forces. This is not the same with energy conservation principles.
Explanation:
Often times the ideal method to use in solving motion problem related questions are mostly debated.
Energy conservation principles applies to isolated systems are useful when object changes their positions in moving upward or downward converts its potential energy due to gravity for kinetic energy, or the other way round. When energy in a system or motion remains constant that is energy is neither created nor destroyed, it can therefore be easier to calculate other unknown paramters like in the motion problem velocity, distance bearing it in mind that energy can only change from one type to another.
On the other hand, free body diagram which is a visual representation of all the forces acting on an object including their directions has so many advantages in solving motion related problems which include finding relationship between force and motion in identifying the force acting on a body.
A catapult of pole length 4r throws a pumpkin from one
end of a pole which rotates about an axis at the other
end with angular speed w.
A smaller catapult of pole length r throws another
pumpkin from one end of a pole which rotates about an
axis at the other end with the same angular speed was
the first catapult.
How does the linear speed of the larger catapult's
pumpkin Vlarge compare with the smaller catapult's
pumpkin Vsmall?
Answers
Answer:
vlarge = 4vsmall
Explanation:
Khan Academy
20 POINTS
In order to maximize the acceleration of an object, one should
maximize the mass
maximize the force
minimize the velocity
maximize the inertia
Answers
What happens to the temperature of a substance while it is changing state?
A. It decreases first and then remains constant.
B. It increases first and then decreases.
C. It remains constant.
D. It varies randomly.
Answers
The temperature remains constant while the substance is changing state.The correct answer is option C.
When a substance undergoes a change of state, such as melting, boiling, or condensing, the temperature of the substance remains constant during the phase transition. The process of changing state requires the absorption or release of heat energy without a change in temperature.
For example, when a solid is heated, its temperature increases until it reaches the melting point. At this point, the substance starts to change from a solid to a liquid, but the temperature remains constant until all the solid has melted.
The absorbed heat energy is used to break the intermolecular forces holding the particles together, rather than increasing the kinetic energy of the particles.
Similarly, during the process of condensation or freezing, a substance releases heat energy as it changes state. This released energy is used to form intermolecular forces and convert the substance from a gas to a liquid or a liquid to a solid. The temperature remains constant until the phase transition is complete.
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Helppppppppppppppppppppppppppppp
Answers
Answer:
Option #3 is your answer.
Explanation:
Part B
Describe how well you think your modeled position matches the observed position for the man.
Answers
To show an object's direction and location, motion maps are employed. The motion map provides the following information about the object's position and speed: With a high velocity, the object begins to travel away from the origin.
Justify the motion map?The object moves away from the origin at a fast initial speed before slowing down and returning. It moves away from the origin with a larger velocity after stopping for a little period of time, before turning around and moving back in the opposite direction.Refer to the motion map in the attachment for more information. The position of the object is indicated by the number next to each arrow on the motion map.Keep in mind that the short arrow indicates a low velocity, whereas the long arrow indicates a high velocity.Our next step is to use the arrows to determine the direction and position.According to the first arrow, the object accelerates rapidly as it leaves the origin.The third arrow indicates a greater velocity of motion for the object from the origin.The fourth and fifth arrows' orientation and placement show that the object next goes more slowly and back toward the origin.
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You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 tall, is walking along side the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg? Assume that the egg is in free fall.Take the free fall acceleration to be 9.80 m/s^2
Answers
The physics professor should be 3.60m far from the physics building for the egg to successfully fall on professor's head, assuming freefall motion of the egg and acceleration to be 9.80 m/s^2.
The height of the building = 46 m
The height of the professor = 1.80 m
The effective height for freefall of the egg = 46.00 - 1.80 = 44.2 m
As S = ug + 1/2a\(t^{2}\)
44.2 = 0 + 1/2 × \(t^{2}\) × 9.8
\(t^{2}\) = (2 × 44.2) / 9.8
\(t^{2}\) = \(\sqrt{9.02}\)
\(t\) = 3.003 s
Let the distance travelled by the professor be x
The time taken by the egg to fall is equal to the time taken by the professor to reach the building through distance x
Speed with which the professor is walking = 1.20 m/s
Now as Distance = Speed × Time,
x = 1.20 × 3.003
x = 3.6036 meters.
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What makes an electric motor spin?
A. The permanent magnet and the electromagnet continuously attract each other.
B.The permanent magnet and the electromagnet continuously repel each other.
C.The permanent magnet and the electromagnet alternately attract and repel each other. O The permanent magnet and the electromagnet alternately attract and repel the power source.
Answers
The thing that makes an electric motor spin is that;
A: The permanent magnet and the electromagnet continuously attract and repel each other.
Electric MotorAn electric motor is simply defined as an electrical machine that is used to convert electrical energy into mechanical energy.
The outer part of the electric motor has stator which is simply a permanent magnet that does not move while the inner part of the electric motor has a rotor and this does move.
Now, when Direct current (DC) power is sent through the rotor, this tends to create a temporary electromagnetic field which interacts with the permanent magnetic field of the stator.
Thus, a torque is created that makes the motor spin.
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The data points you have taken on your lab graphs roughly form a straight line. How do you interpret the slope of this line?
Steeper slopes mean higher speeds.
Steeper slopes mean lower speeds.
Steeper slopes mean higher error.
Steeper slopes mean lower error.
The slope has no relation to speed or error
Answers
Answer: Steeper slopes mean lower speeds.
Explanation:
But if it’s a wavy slope then it’s a
Approximately how many times louder is a 150-dB sound than a 80-dB sound?
Answers
a 150-dB sound is approximately 10 million times louder than an 80-dB sound.
What is the range of sound?Provide instances of the differences between the audible, ultrasonic, and infrasonic frequency ranges. Three sorts of sound waves, each covering a distinct frequency range, are used. These are what they are:
Waves that fall inside the ear's sensitivity range are referred to be audible waves.Infrasonic waves are those whose frequencies fall below the range of human hearing. Ultrasonic waves are those with frequencies higher than those of sound.The difference in decibels between two sounds is related to the ratio of their intensities (or power) by the following formula:
dB₂ - dB₁ = 10 log10(I₂ / I₁)
where dB₁ and dB₂ are the decibel levels of the two sounds, and I₁ and I₂ are their intensities (or power).
Using this formula, we can find the ratio of the intensity of a 150-dB sound to that of an 80-dB sound:
150 dB - 80 dB = 10 log10(I₁₅₀ / I₈₀)
70 = 10 log10(I₁₅₀ / I₈₀)
7 = log10(I₁₅₀ / I₈₀)
10^7 = I₁₅₀ / I₈₀
I₁₅₀ = 10^7 * I₈₀
This shows that the intensity of a 150-dB sound is 10 million times greater than that of an 80-dB sound.
Therefore, a 150-dB sound is approximately 10 million times louder than an 80-dB sound.
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Identify the stage in cellular respiration that produces carbon dioxide as a waste product
Answers
Which of the following describes the relationship between the velocity and
pressure of a fluid?
A. Pascal's principle
B. Archimedes' principle
C. Bernoulli's principle
D. Flow rate equation
Answer is c
Answers
Explanation:
I think its a option pascal's principal
Answer:
c
Explanation:
Just took the quiz
A 2.8 F capacitor and a 3,440
Ω
resistor are connected to a battery of voltage 5 V as shown in the circuit. After
closing the switch, how long will it take for the capacitor voltage to be 45 % of
the battery voltage?
Express your answer in seconds (s)
Answers
The time taken for the capacitor voltage to be 45 % of the battery voltage is 5,750.3 s.
Discharge of the capacitor voltage
The rate at which the capacitor voltage discharges is given by the following formula;
\(V = V_0(1 - e^{-t/RC})\)
Where;
V₀ is the initial voltageV is the final voltaget is the time of dischargeR is resistanceC is capacitanceThe final voltage = 0.45 x 5 V = 2.25 V
\(2.25 = 5(1 - e^{-t/RC})\\\\(1 - e^{-t/RC}) = \frac{2.25}{5} \\\\(1 - e^{-t/RC}) = 0.45\\\\e^{-t/RC} = 1- 0.45\\\\e^{-t/RC} = 0.55\\\\\frac{-t}{RC} = ln(0.55)\\\\\frac{-t}{RC} = -0.597\\\\t = 0.597 (RC)\\\\t = 0.597(3440 \times 2.8)\\\\t = 5,750.3 \ s\)
Thus, the time taken for the capacitor voltage to be 45 % of the battery voltage is 5,750.3 s.
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an old 59 rpm record rotates through an angle of 300° as it slows down uniformly from 59.0 rpm to 17.0 rpm. what is the magnitude of the angular acceleration of the record?
Answers
Answer:
3.34
Explanation:
The relationship between final angular speed, initial angular speed, angular acceleration, and change in radians is given by
\(\omega^2_f=\omega^2_i+2\alpha(\theta_f-\theta_i)\)Now in our case
\(\begin{gathered} \omega_i=59rpm \\ \omega_i=59\times\frac{2\pi}{60}\text{rad}/s \\ \end{gathered}\)\(\omega_f=17\times\frac{2\pi}{60}\text{rad}/s\)\(\theta_f-\theta_i=300^o=\frac{5}{3}\pi(radians)\)Therefore, the above equation gives
\((17\times\frac{2\pi}{60})^2=(59\times\frac{2\pi}{60})^2+2(\frac{5}{3}\pi)\alpha\)subtracting (17 2pi/ 60 )^2 from both sides gives
\((17\times\frac{2\pi}{60})^2-(59\times\frac{2\pi}{60})^2=2(\frac{5}{3}\pi)\alpha\)dividing both sides by 2 * 5 / 3 pi gives
\(\frac{(17\times\frac{2\pi}{60})^2-(59\times\frac{2\pi}{60})^2}{2(\frac{5}{3}\pi)}=\alpha\)simplifying the above gives
\(\alpha=3.34\)which is our answer!
Most space lawyers agree that the barrier between airspace and outer space lies somewhere between where
the highest planes fly and the lowest satellites orbit.
True
False
Answers
True. The majority of space lawyers concur that the line dividing airspace from outer space is located halfway between the altitude at which airplanes fly and the orbital altitude of satellites.
What purposes do satellites serve?They serve a variety of functions, including that of the Satellite Navigation System, amateur radio, television transmission, and weather forecasting. In order to conduct study and acquire data, they also employ telescopes to view outward somewhere at solar system.
Do satellites provide internet access?Over 99% of Americans have access to satellite internet, along with most other (but certainly not all) rural residents. You do not need to have a home internet connection because the broadband signal is transmitted from satellites.
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Which fundamental force increases with the mass of an object?A. Weak nuclearB. GravitationalC. Electromagnetic. D. Strong nuclear
Answers
We know that all fundamental forces have a fundamental charge and that each of them is responsible for some fundamental phenomenon. In the case of the gravitational force, we know that it is responsible of all gravitational interactions and that its magnitude is proportional to the mass.
Therefore, gravitational force increases with the mass of an object and the answer is B.
Describe how to demonstrate the thermal energy is dissipated from a cup of hot tea
Answers
Answer:
Explanation:
1. Place a cup of hot tea on a flat surface.
2. Place a thermometer in the tea and record the temperature.
3. Place a fan in front of the cup of tea and turn it on.
4. Place the thermometer in the tea again and record the temperature.
5. Compare the two temperatures and observe the difference.
6. The difference in temperature is an indication of the thermal energy that has been dissipated from the cup of hot tea.
A small truck has a mass of 2085 kg. How much work is required to decrease the speed of the vehicle from 22.0 m/s to 13.0 m/s on a level road?
Answers
Answer:
Work required is 328387.5 Joules.
Explanation:
Given the following data;
Mass = 2085kg
Initial velocity, Vi = 13m/s
Final velocity, Vf =22m/s
To find the workdone;
We know that from the workdone theorem, the workdone by an object or a body is directly proportional to the kinetic energy possessed by the object due to its motion.
Mathematically, it is given by the equation;
W = Kf - Ki
Where;
W is the work required.
Kf is the final kinetic energy possessed by the object.
Ki is the initial kinetic energy possessed by the object.
But Kinetic energy = ½MV²
W = ½MVf² - ½MVi²
Substituting into the equation, we have;
W = ½(2085)*22² - ½(2085)*13²
Simplifying the equation, we have;
W = 1042.5 * 484 - 1042.5 * 169
W = 504570 - 176182.5
W = 328387.5J
Therefore, the work required to decrease the speed of the vehicle is 328387.5 Joules.
Describe the change to the graph of Y= X +3 when Y=2X -3 is graphed 
Answers
Answer: a stretch of 2
Explanation: because it 2 (x) - 3
How do supersonic flights create sonic boom? Please explain in detail.
Answers
Supersonic flights are moving with speed greater than that of sound. This speed through air will combine the pressure waves and creates shock waves. Continuation of shock waves leads to sonic boom in air.
What is sonic boom ?Sonic booms are sound created on the ground by overpressure in the air generated by fastly moving objects. Similar to someone dumping goods from a moving car, an aircraft travelling at supersonic speeds continuously produces shock waves that cause sonic booms to travel throughout its flight path.
The boom seems to be swept rearward as it moves away from the aeroplane from its point of view. The boom will strike the ground in front of the aircraft if the aircraft makes a rapid turn or pulls up.
The abrupt start and release of pressure following the building by the shock wave or "peak overpressure" is what is heard as a "sonic boom" on the ground. Only a few pounds per square foot change in pressure results from a sonic boom, which is about equivalent to the pressure shift we experience in an elevator.
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A ball is dropped from the top of a building. When does the ball have the least potential energy?
A. as it is released
B. after it has hit the ground
C. just before it hits the ground
D. half way through the fall
Answers
Answer:
it would be before it hits the ground
Explanation:
potential enrgy is energy that will be turned into something
Answer: The answer is B. "After it hits the ground"
Explanation: When you drop a ball it gains speed, and after it hits the ground it looses half of that speed or more. Then it keeps on bouncing until it stops completely. (You can even try it yourself if you don't believe me.) HOPE THIS HELPS!!
A dog starts from point A and moves 15m toward the east, then turns 90 degrees south and moves 3m. His displacement is
Answers
The displacement of the dog is 15.3 meters at a bearing of 339.4 degrees (or about 20.6 degrees west of due north).
Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position. It is the straight-line distance and direction between these two points.
To calculate the displacement, we need to find the straight-line distance and direction between the starting point A and the final point where the dog ends up.
The dog first moves 15m toward the east. This means that its position changes in the x-direction by 15m. We can represent this as a vector:
d1 = 15i
where i is the unit vector in the x-direction.
Next, the dog turns 90 degrees south and moves 3m. This means that its position changes in the y-direction by -3m (since south is in the negative y-direction). We can represent this as another vector:
d2 = -3j
where j is the unit vector in the y-direction.
To find the displacement, we can add these two vectors:
d = d1 + d2
= 15i - 3j
The magnitude of this vector is:
|d| = sqrt(15^2 + (-3)^2)
= sqrt(234)
≈ 15.3
So the dog's displacement is approximately 15.3 meters. To find the direction, we can calculate the angle that this vector makes with the positive x-axis:
theta = arctan(-3/15)
≈ -0.197
Since the angle is negative, we know that the vector points in the fourth quadrant. To express the direction as a compass bearing, we can add 360 degrees to the angle and convert to degrees:
theta_degrees = (-0.197 + 2*pi) * 180/pi
≈ 339.4
Hence, the dog's displacement is approximately 15.3 meters at a bearing of 339.4 degrees (or about 20.6 degrees west of due north).
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A fireman standing on a 6.4 m high ladder operates a water hose with a round nozzle of diameter 2.27 inch. The lower end of the hose (6.4 m below the nozzle) is connected to the pump outlet of diameter 3.7 inch. The gauge pressure of the water at the pump is (attached file)
Calculate the speed of the water jet emerging from the nozzle. Assume that water is an incompressible liquid of density 1000 kg/m3 and negligible viscosity. The acceleration of gravity is 9.8 m/s^2. Answer in units of m/s.
Answers
The speed of the water jet emerging from the nozzle is 25.9 m/s.
Speed of water jet calculation.We can solve this problem using Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a closed system. For a fluid with negligible viscosity, the equation can be simplified to:
P + 1/2ρv^2 + ρgh = constant
where P is the pressure, ρ is the density, v is the velocity, h is the height, and g is the acceleration due to gravity.
We can apply this equation to two points in the system: the nozzle and the pump outlet. Since the pressure gauge is attached to the pump outlet, we know the pressure at that point. We can assume that the velocity at the pump outlet is negligible, so the second term in the equation can be dropped.
At the nozzle, we don't know the pressure or the velocity, but we do know the height difference between the nozzle and the pump outlet. We can use this to write the Bernoulli equation as:
P + 1/2ρv^2 + ρgh_n = P_0 + ρgh_p
where h_n is the height of the nozzle above the pump outlet, P_0 is the pressure at the pump outlet (as given by the gauge), and h_p is the height of the pump outlet above some reference level (which we can choose to be zero).
Solving for v, we get:
v = sqrt(2*(P_0-P)/ρ + 2gh_n)
where P is the unknown pressure at the nozzle.
To find P, we can use the gauge pressure and the density of water:
P = P_0 + ρgh_p - ρgh_n
Plugging in the given values and converting units, we get:
h_n = 6.4 m
d_n = 2.27 in = 0.0577 m
A_n = pi*(d_n/2)^2 = 0.0026 m^2
d_p = 3.7 in = 0.09398 m
A_p = pi*(d_p/2)^2 = 0.00696 m^2
P_0 = 600 kPa
ρ = 1000 kg/m^3
g = 9.8 m/s^2
First, we need to find the height of the pump outlet:
h_p = h_n + d_n/2 + d_p/2 = 6.4 + 0.02885 + 0.04699 = 6.46684 m
Then, we can find the pressure at the nozzle:
P = P_0 + ρgh_p - ρgh_n = 600000 + 10009.86.46684 - 10009.86.4 = 33768 Pa
Finally, we can find the velocity of the water jet:
v = sqrt(2*(P_0-P)/ρ + 2gh_n) = sqrt(2*(600000-33768)/1000 + 29.86.4) = 25.9 m/s
Therefore, the speed of the water jet emerging from the nozzle is approximately 25.9 m/s using Bernoulli equation.
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formula for percentage error
Answers
Answer:
PE = (|accepted value – experimental value| \ accepted value) x 100%
Explanation: