(a) The height of the roller coaster at 120,000 potential energy is 122.45 m.
(b) The velocity of the roller coaster at 0 J kinetic energy is 0.
(c) The height of the roller coaster at 60,000 potential energy is 61.23 m.
(d) The velocity of the roller coaster at 60,000 J kinetic energy is 34.64 m/s.
(e) The height of the roller coaster at 40,000 potential energy is 40.82 m.
(f) The velocity of the roller coaster at 80,000 J kinetic energy is 40 m/s.
The given parameters:
mass of the roller coaster, m = 100 kgWhen the kinetic energy = 0 and potential energy = 120,000 J
The height of the roller coaster is calculated as follows;
P.E = mgh
[tex]h = \frac{P.E}{mg}\\\\h = \frac{120,000}{100 \times 9.8} \\\\h = 122.45 \ m[/tex]
Since the kinetic energy = 0, the velocity of the roller coaster = 0
When the potential energy, P.E = 60,000 J, the kinetic energy, K.E is calculated as;
P.E + K.E = M.A
P.E + K.E = 120,000
60,000 + K.E = 120,000
K.E = 120,000 - 60,000
K.E = 60,000 J
The height of the roller coaster at 60,000 potential energy is calculated as follows;
[tex]h = \frac{P.E}{mg} \\\\h = \frac{60,000}{100 \times 9.8} \\\\h =61.23 \ m[/tex]
The velocity of the roller coaster at 60,000 J kinetic energy is calculated as follows;
[tex]K.E = \frac{1}{2} mv^2\\\\v^2 = \frac{2K.E}{m} \\\\v = \sqrt{ \frac{2K.E}{m}} \\\\v = \sqrt{ \frac{2\times 60,000}{100}}\\\\v = 34.64 \ m/s[/tex]
When the potential energy, P.E = 40,000 J, the kinetic energy, K.E is calculated as;
P.E + K.E = M.A
40,000 + K.E = 120,000
K.E = 120,000 - 40,000
K.E = 80,000
The height of the roller coaster at 40,000 potential energy is calculated as follows;
[tex]h = \frac{P.E}{mg} \\\\h = \frac{40,000}{100 \times 9.8} \\\\h = 40.82 \ m[/tex]
The velocity of the roller coaster at 80,000 J kinetic energy is calculated as follows;
[tex]v = \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2\times 80,000}{100} } \\\\v = 40 \ m/s[/tex]
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A vessel with an unknown volume is filled with 10 kg of water at 90oC. Inspection of the vessel at equilibrium shows that 8 kg of the wateris in the liquid state. What is the pressure in the vessel, and what is the volume of the vessel
In this case, it is possible to solve this problem by using the widely-known steam tables which show that at 90 °C, the pressure that produces a vapor-liquid mixture at equilibrium is about 70.183 kPa (Cengel, Thermodynamics 5th edition).
Moreover, for the calculation of the volume, it is necessary to calculate the volume of the vapor-liquid mixture, given the quality (x) it has:
[tex]x=\frac{m_{steam}}{m_{total}}[/tex]
Thus, since 8 kg correspond to liquid water, 2 kg must correspond to steam, so that the quality turns out:
[tex]x=\frac{2kg}{10kg} =0.20[/tex]
Now, at this temperature and pressure, the volume of a saturated vapor is 2.3593 m³/kg whereas that of the saturated liquid is 0.001036 m³/kg and therefore, the volume of the mixture is:
[tex]v=0.001036m^3/kg+0.2(2.3593-0.001036 )m^3/kg=0.4727m^3/kg[/tex]
This means that the volume of the container will be:
[tex]V=10kg*0.4727m^3/kg\\\\V=4.73m^3[/tex]
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https://brainly.com/question/23339302https://brainly.com/question/15081976a convex mirror and a plane mirror both give virtual and erect images still a convex mirror is used in vehicles. why?
Pls answer thiss
Answer:Convex mirrors are used because these mirrors provide a wider viewing angle than a plane mirror. This wide angle will help you getting more information/overview than what is happening at a narrow spot right behind the car if you use a plane mirror.
With a convex mirror you are for example able to detect an overtake (by the car behind you) early, if you for some reason wanted to turn left into another lane at the same moment the overtake took place - so you then can prevent a collision. Convex mirrors are simply covering a much larger area behind the car than plane mirrors do. And in the US, on the mirrors there is a text explaining that the vehicle behind you is closer than it appears - some kind of an idiot explanation in case some driver took the mirror image literally….because in the mirror image of a convex mirror, everything looks smaller and further away than they actually are.
Explanation: mark me as brainliest this is my best answer till now
describe the motion of objects that are viewed from your reference frame both inside and outside while you travel inside a moving vehicle
Answer:
The objects outside the reference frame aren't moving. It appears this way since the vehicle you are inside is moving, but unless the objects are people, animals, or other vehicles, the objects aren't moving.
what is the acceleration of the cart at t=8 seconds?
a) 0 m/s^2
b) 10 m/s^2
c) 20 m/s^3
d) -20m/s^2
What is the acceleration of the cart at t=8 seconds?
a) 0 m/s^2b) 10 m/s^2c) 20 m/s^3d) -20m/s^2Hence the answer us letter a) 0 m/s^2.
That's all I know, Hope it help :)
A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope that is wound on the wheel and attached to it (see figure). The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope. The tension in the rope during the descent of the block is 20 N. What is the moment of inertia of the wheel?
The moment of inertia of the wheel is 4.27 kg.m²
The kinematics equation explains the variables associated and related of motion.
From the information given, applying the kinematic equation of motion to determine the acceleration of the block, we have:
[tex]\mathbf{y = ut + \dfrac{1}{2}at^2}[/tex]
[tex]\mathbf{y = (0)t + \dfrac{1}{2}at^2}[/tex]
[tex]\mathbf{y = \dfrac{1}{2}at^2}[/tex]
Making acceleration (a) the subject, we have:
[tex]\mathbf{a = \dfrac{2y}{t^2}}[/tex]
where;
y = 1.5 mt = 2.0 s[tex]\mathbf{a = \dfrac{2\times 1.5 }{2.0^2}}[/tex]
a = 0.75 m/s²
The angular acceleration of the wheel can be estimated by the formula:
[tex]\mathbf{\alpha = \dfrac{a}{r}}[/tex]
[tex]\mathbf{\alpha = \dfrac{0.75 \ m/s^2}{0.40 \ m}}[/tex]
[tex]\mathbf{\alpha = 1.875 \ rad/s^2}[/tex]
Finally, the torque acting on the wheel is:
[tex]\mathbf{\tau = I \alpha}[/tex]
[tex]\mathbf{Tr = I \alpha}[/tex]
where;
T = tensionr = radiusI = moment of inertia∝ = angular acceleration∴
[tex]\mathbf{I =\dfrac{T\times r}{\alpha} }[/tex]
[tex]\mathbf{I =\dfrac{20 \ N\times 0.40 \ m}{1.875 \ rad/s^2} }[/tex]
I = 4.27 kg.m²
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The center of mass of a 1600 kg car is midway between the wheels and 0.7 m above the ground. The wheels are 2.6 m apart. (a) What is the minimum acceleration A of the car so that the front wheels just begin to lift off the ground
Answer:
Explanation:
I guess we are ASSUMING that this is a rear wheel drive car as a front wheel drive car will never get the front wheel normal force to zero
If we consider it as a statics problem and choose our moment center carefully...say 0.7 m above the rear wheel to ground contact point.
Call the traction force at the rear wheels F
The normal force on the front wheels will be zero, so no moment generated by the front wheels.
Summing moments about our chosen point to zero
1600(9.8)[2.6 / 2] - F[0.7] = 0
F = 291,200
this force will create an acceleration of
a = F/m
a = 291200/1600
a = 182 m/s²
which is about 18.6 times gravity acceleration
a body of mass 15 kg accelerates from rest of the rate of 4.0 ms^-2. determine the distance with the body travel in 25 seconds
The distance traveled by the body in the given time is 1,250 m.
The given parameters;
mass of the body, m = 15 kgacceleration of the body, a = 4 m/s²time of motion, t = 25 sinitial velocity, u = 0The distance traveled by the body in the given time is calculated as follows;
[tex]s =ut + \frac{1}{2} at^2\\\\s = 0 \ + \ \frac{1}{2} (4)(25^2)\\\\s =1,250 \ m[/tex]
Thus, the distance traveled by the body in the given time is 1,250 m.
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How is the wavelength of a sound affected when (a) a sound source moves toward a stationary observer and (b) the observer moves away from a stationary sound source
Answer:
If the observer is stationary but the source moves toward the observer at a speed vs, the observer still intercepts more waves per second and the frequency goes up. This time it is the wavelength of the wave received by the observer that is effectively shifted by the motion, rather than the speed.
I need help been struggling on this question
Answer:
440 m
Explanation:
S=(u+v) t / 2
S = (11+33) × 20/2
S= 44× 20/2
S=440 m
Goal statement write a positive statement that includes your desired outcome and your imagine preferred future after development
A goal statement may involve how to develop physical skills in a given outdoor activity (e.g., soccer) in order to reach my maximum potential. It involves a statement of purpose.
A goal statement is a statement of purpose that describes long-term professional and/or motivational objectives.
A goal statement involves writing a statement about how to reach personal objectives, i.e., how to accomplish a career, job title, sports skills, educational training, etc.
An excellent statement of purpose should ideally be clear, specific, acceptable, time-bound and realistic.
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Does it appear that true average HAZ depth is larger for the high current condition than for the nonhigh current condition
Answer:
The data suggest that the true mean HAZ depth is larger when the current setting is higher.
What type of equilibrium maintains body position during sudden motion?
dynamic
rotational
static
balanced
I think static is the correct answer
The symbol delta x (x) is used to find what value?
Answer:
Explanation:
Δx means a change in the magnitude of the x variable, often used in reference to a number line on the horizontal axis of a plot.
numerical problems:
a.) convert 300K into the celsius scale.
b.) convert 220 centigrade scale into kelvin scale.
c.) convert 20 ventigrade scale into Fahrenheit scale.
d.) convert 260 Fahrenheit into centigrade. pls help me to solve this problems
define heterotrophic
Answer:
Heterotrophic requiring complex organic compounds of nitrogen and carbon (such as that obtained from plant or animal matter) for metabolic synthesis.
Answer -:
⟹ It is a mode of nutrition in which organism are unable to synthesize organic substance by themselves and obtain part of whole of organic substance from external environment. the organism that obtain their food by this method are called heterotphs.
tha organism which lack green pigments chlorophyll are included in this group.all animal ,fungi and most of bacteria belong to this group.a large number of higher plant also Lack chlorophyll . they are also unable to synthesize their organic substance food .On the basis of types of food and feeding habit's nutrition classified into following group -:
(1) Holozoic Nutrition -:
nutrition and animal consumes a plant or an animal us whole or a part of it in solid or liquid form most of free living a cellular protist and all animal show Holozoic Nutrition
(2) Herbivores -:
animal eating grass or other plant material are called Herbivores.
Example - Grazers- horse , cow , goat etc .(3) Carnivorous
flesh eating animal are called carnivorous.
Example -: Lion , tiger , Wolf etc(4) Omnivorous
animal eating food or plant us well us animal origin are called omnivorous.
(5) Insectivorous
insect eating animal are calledinsectivorous .
(6) Frugivores
animal which mainly depend on fruit are called frugivores.
Make one comparison between the moral condition of the world at the time of the Flood with our day. Only One Short explanation.
The moral condition of the world today appears to be worse than it was in the antediluvian era.
The biblical account of the flood records that the world delved into apostasy in the days of Noah so much so that God regretted the fact that he created man. Some of the evils of the antediluvian world include; sodomy, drunkenness, lewdness and several forms of immorality.
We can see that these vices that led to the destruction of the world due to moral bankruptcy in the antediluvian era is still very much prevalent in our world today. The moral condition of the world today appears to be worse than it was in the antediluvian era.
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Why is it important for the community to take action
Answer:
Why is community action important? ... Involving communities in the design and delivery of services can help to achieve a number of objectives, including: Building community and social capacity – helping the community to share knowledge, skills and ideas. Community resilience – helping the community to support itself
The current in a resistor is 2.0 A, and its power is 78 W. What is the voltage?
Answer:
39 volts
Explanation:
Use the equation [tex]P=VI[/tex]
[tex]78=V(2)[/tex]
[tex]V=39[/tex]
Standing at a crosswalk, you hear a frequency of 550 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 475 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.)
a box has a mass of 4 kg and surface area 4 metre square calculate the pressure exerted by the box on the floor
- BRAINLIEST answerer ❤️✌
Answer:
9.8
Explanation:
we know ,
f=m.g(g=9.8m/s^2)
now,
p=force/area
p=m.g/a
p=4×9.8/4
p=4 pascal.
if u put g as 10 then ypu will get 10 pascal
What is the cause of plate tectonics on Earth?
The magnetic field
Tides in the ocean
Convection in the mantle
Volcanic eruptions
Answer:
im pretty sure the answer is C
Which of the following is a fundamental unit of the SI system of units?
A) kilometer
B) joule
C) kilogram
D) gram
E) newton
The answer is C) kilogram
The SI unit in the given options is kilogram, the correct option is C.
What is SI unit?The most common unit of measurement is the standard unit. These units are standardized, which means that everyone understands an object's size, weight, and other properties.
Standard Units of Measurement have fixed values that cannot be changed.
The International System of Units, abbreviated SI in all languages and sometimes pleonastically as the SI system, is the modern version of the metric system and the world's most widely used measurement system.
The SI is a coherent system of units of measurement that begins with seven base units: the second (symbol s, the unit of time), the metre (m, length), the kilogram (kg, mass), the ampere (A, electric current), and so on.
Thus, the correct option is C.
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A race car, starting from rest, travels around a circular turn of radius 22.5 m. At a certain instant the car is still speeding up, and its angular speed is 0.541 rad/s. At this time, the car’s total acceleration vector (centripetal plus tangential) makes an angle of 39.0 with respect to the car’s velocity. What is the magnitude of the car’s total acceleration
Answer:
Explanation:
The answer:
https://www.chegg.com/homework-help/questions-and-answers/race-car-starting-rest-travels-around-circular-turn-radius-247-m-certain-instant-car-still-q402991
Total acceleration of car is 148.31 m/s².
What is centripetal acceleration?Centripetal acceleration is a characteristic of an object's motion along a circular path. Centripetal acceleration applies to any item travelling in a circle with an acceleration vector pointing in the direction of the circle's center.
Given parameters:
Radius of the circular path: r = 22.5 m.
Angular speed: ω = 0.541 rad/s.
So, centripetal acceleration; α = ω²r = (0.541)² × 22.5 m/s² = 6.58 m/s².
Tangential acceleration: [tex]\alpha_t[/tex] = αr = 6.58 × 22.5 = 148.16 m/s².
Hence, total acceleration = √(α² + [tex]\alpha_t[/tex]²) = √(6.58² +148.16²) = 148.31 m/s².
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A 20-N falling apple encounters a 4-N of air resistance. The magnitude of the net force on the apple is?
A. 0n
B.4n
C.16n
D. 20n
E. None of the above
Answer:
C
Explanation:
Pls brainliest
How does friction help us in walking.
what memory are you using to remember who the president of the united states is
Answer:
The First 8 Presidents
For this exercise, we're going to use a silly story made of silly sentences. The letters that represent the last names of these presidents are W, A, J, M, M, A, J, V. One silly sentence to help you remember this sequence is: Wilma and John made merry and just vanished
working memory.
sensory memory.
short-term memory.
long-term memory.
A race car traveling at 100 m/s enters an unbanked turn of 400 m radius. The coefficient of (static) friction between the tires and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct
Answer:
The race car will crash into the outer wall
Explanation:
max fr = μsN = 1.1 mg = 11 m
mv2/R = m(100)2/(400) = 25 m > fr
How is heat transferred by convection?
Answer:
Convective heat transfer is the transfer of heat between two bodies by currents of moving gas or fluid. In free convection, air or water moves away from the heated body as the warm air or water rises and is replaced by a cooler parcel of air or water.
Explanation:
Hope this helped and have a great day
Heat can be transferred by convection through liquids. Heat travels where warmer liquid rises and cooler liquid sinks. An example of this can be heating up a pot of water. Hope this helps!
Saturn's mass is 5.68 x 1024 kg and its radius is 6.03 x 107 m. A. Calculate the gravitational field strength at Saturn's surface. (2 marks) B. Calculate the force of gravity at Saturn's surface on an object with a mass of 50 kg.
Hi there!
A.
We can calculate the gravitational field strength using the following equation:
[tex]g = \frac{Gm_p}{r^2}[/tex]
G = Gravitational Constant
mp = mass of planet (kg)
r = radius (m)
Plug in the given values:
[tex]g = \frac{(6.67*10^{-11})*(5.68*10^{24})}{(6.03*10^7)^2} = \boxed{0.104 N/kg}[/tex]
B.
The force can be calculated using:
[tex]F_g = \frac{Gm_1m_2}{r^2}[/tex]
Plug in the values:
[tex]F_g = \frac{(6.67*10^{-11})(5.68*10^{24})(50)}{(6.04*10^7)^2} = \boxed{5.209N}[/tex]
Answer:
[tex]\boxed {\boxed {\sf g=0.104 \ N/kg \ and \ F_g= 5.2 \ N }}[/tex]
Explanation:
A. Gravitational Field Strength
The gravitational field strength can be calculated using the following formula:
[tex]g= \frac{Gm}{r^2}[/tex]
G, or the universal gravitational constant, is 6.67 × 10⁻¹¹ N*m²/kg². The mass of Saturn is 5.68 × 10²⁴ kilograms. The radius of Saturn is 6.03×10⁷ meters.
Substitute these values into the formula.
[tex]g= \frac{ (6.67 \times 10^{-11} \ N*m^2/kg^2) (5.68 \times 10^{24} \ kg)}{(6.03 \times 10^{7} \ m )^2}[/tex]
Multiply the numerator and square the denominator.
[tex]g= \frac{ 3.78856 \times 10^{14} \ N *m^2/kg }{3.63609 \times 10^{15} \ m^2}[/tex]
Divide.
[tex]g= 0.1041932405 \ N/kg[/tex]
The original measurements of mass and radius have 3 significant figures, so our answer must have the same. For the number we found, that is the thousandth place. The 1 in the ten-thousandth place tells us to leave the 4 in the thousandth place.
[tex]\boxed {g \approx 0.104 \ N/kg}[/tex]
B. Force of Gravity
The force of gravity is calculated using the following formula:
[tex]F_g= mg[/tex]
The mass of the object is 50 kilograms. We just calculated the gravitational field strength, which is 0.104 Newtons per kilogram. Substitute these values into the formula.
[tex]F_g= (50 \ kg)(0.104 \ N/kg)[/tex]
Multiply. The units of kilograms cancel.
[tex]\boxed {F_g=5.20 \ N}[/tex]
Four small 0.600-kg spheres, each of which you can regard as a point mass, are arranged in a square 0.400 m on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane at point O.
Answer:
.192 kg x m^2
Explanation:
I= mass of a times radius of a squared + mass of b times radius of b squared +...
I= .6 kg x .4m^2 + .6 kg x .4m^2
= .192 kg x m^2
Hope this helps :)