Answers
I don't know if there is other given information that's missing here, so I'll try to fill in the gaps as best I can.
Let m be the mass of the object and v₀ its initial velocity at some distance x up the plane. Then the velocity v of the object at the bottom of the plane can be determined via the equation
v² - v₀² = 2 a x
where a is the acceleration.
At any point during its motion down the plane, the net force acting on the object points in the same direction. If friction is negligible, the only forces acting on the object are due to its weight (magnitude w) and the normal force (mag. n); if there is friction, let f denote its magnitude and let µ denote the coefficient of kinetic friction.
Recall Newton's second law,
∑ F = m a
where the symbols in boldface are vectors.
Split up the forces into their horizontal and vertical components. Then by Newton's second law,
• net horizontal force:
∑ F = n cos(θ + 90º) = m a cos(θ + 180º)
→ - n sin(θ) = - m a cos(θ)
→ n sin(θ) = m a cos(θ) ……… [1]
• net vertical force:
∑ F = n sin(θ + 90º) - w = m a sin(θ + 180º)
→ n cos(θ) - m g = - m a sin(θ)
→ n cos(θ) = m (g - a sin(θ)) ……… [2]
where in both equations, a is the magnitude of acceleration, g = 9.80 m/s², and friction is ignored.
Then by multiplying [1] by cos(θ) and [2] by sin(θ), we have
n sin(θ) cos(θ) = m a cos²(θ)
n cos(θ) sin(θ) = m (g sin(θ) - a sin²(θ))
m a cos²(θ) = m (g sin(θ) - a sin²(θ))
a cos²(θ) + a sin²(θ) = g sin(θ)
a = g sin(θ)
and so the object attains a velocity of
v = √(v₀² + 2 g x sin(θ))
If there is friction to consider, then f = µ n, and Newton's second law instead gives
• net horizontal force:
∑ F = n cos(θ + 90º) + f cos(θ) = m a cos(θ + 180º)
→ - n sin(θ) + µ n cos(θ) = - m a cos(θ)
→ n sin(θ) - µ n cos(θ) = m a cos(θ) ……… [3]
• net vertical force:
∑ F = n sin(θ + 90º) + f sin(θ) - w = m a sin(θ + 180º)
→ n cos(θ) + µ n sin(θ) - m g = - m a sin(θ)
→ n cos(θ) + µ n sin(θ) = m g - m a sin(θ) ……… [4]
Then multiply [3] by cos(θ) and [4] by sin(θ) to get
- n sin(θ) cos(θ) + µ n cos²(θ) = - m a cos²(θ)
n cos(θ) sin(θ) + µ n sin²(θ) = m g sin(θ) - m a sin²(θ)
and adding these together gives
µ n (cos²(θ) + sin²(θ)) = m g sin(θ) - m a (cos²(θ) + sin²(θ))
µ n = m g sin(θ) - m a
m a = m g sin(θ) - µ n
m a = m g sin(θ) - µ m g cos (θ)
a = g (sin(θ) - µ cos (θ))
and so the object would instead attain a velocity of
v = √(v₀² + 2 g x (sin(θ) - µ cos (θ)))
Related Questions
what are the laws of newton
Answers
Answer:
Explanation:
These are the laws of Newton
Answer:
the first law, an object will not change its motion unless a force acts upon it. the 2nd one, the force of an object is equal to its mass times it acceleration. the 3rd one is when 2 objects interact, they apply forces to each other of equal magnitude and opposite direction.
During a baseball game, a batter hits a popup to a fielder 83 m away.
The acceleration of gravity is 9.8 m/s
2
.
If the ball remains in the air for 5.7 s, how
high does it rise?
Answer in units of m
Answers
Answer:
The height risen by the ball is 39.8 m.
Explanation:
Given;
total time spent in air by the ball, t = 5.7 s
time to rise to maximum height, t = 5.7 /2 = 2.85 s
The initial velocity of the ball is given by;
v = u - gt
where;
v is the final velocity at maximum height = 0
u is the initial velocity of the ball
0 = u - gt
u = gt
u = (9.8 x 2.85)
u = 27.93 m/s
The vertical height traveled by the ball is given by;
v² = u² - 2gh
where;
v is the final velocity of the ball at maximum height = 0
g is acceleration due to gravity = 9.8 m/s²
0 = u² - 2gh
2gh = u²
h = u² / 2g
h = (27.93)² / ( 2 x 9.8)
h = 39.8 m
Therefore, the height risen by the ball is 39.8 m.
In the concluding paragraph, how does the author make the conflicting point of view that vegetarianism is strange and unnatural seem less reasonable?
Answers
Answer:
By pointing out that vegetarianism isn't contagious
Explanation:
I got this right on iready!
Answer:
by point out how food isn't contagious
Explanation:
got it right
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 is the force of a 1500 kg car accelerating at 45 m/s2 ?
Answers
Answer:
67500
Explanation:
F=ma
F = 1500 × 45
F = 67500
A system of 4 electrons, 18 protons, and 4 neutrons has a net charge of?
Answers
Answer:
+ 14
Explanation:
18 protons make a positive 18 charge (+18)
4 electrons make a negative 4 charge (-4)
both combined give + 18 - 4 = + 14
The four neutrons don't carry net charge, so the addition of the electrons doesn' affect the net charge found above which still gives + 14.
A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced.What is the average fluid velocity in m/s for a 4.25 cm diameter pipe, if a 0.575 T field across it creates a 60.0 mV Hall voltage?
Answers
Answer:
The velocity is [tex]v =2.455 \ m/s[/tex]
Explanation:
From the question we are told that
The diameter of the pipe is [tex]d = 4.25 \ cm = 0.0425 \ m[/tex]
The magnetic field is [tex]B = 0.575 \ T[/tex]
The hall voltage is [tex]V_H = 60.0 mV = 60 *10^{-3} \ V[/tex]
Generally the average fluid velocity is mathematically represented as
[tex]v = \frac{V}{ B * d }[/tex]
=> [tex]v = \frac{60*10^{-3}}{ 0.575 * 0.0425 }[/tex]
=> [tex]v =2.455 \ m/s[/tex]
What is the relevant similarity in the following argument?
"If a single cell, under appropriate conditions, becomes a person in the space of a few years, there can surely be no difficulty in understanding how, under appropriate conditions, a cell may, in the course of untold millions of years, give origin to the human race"
a.
The human race is composed of many humans in the same way a human is composed of many cells
b.
understanding human biology is difficult and understanding the existence of the human race is difficult
c.
both involve biological processes of great complexity taking place under “appropriate conditions” and commencing with a single cell
d.
a person starts from a single cell and an animal life starts from a single cell
Answers
Select all correct answers....Covalent compounds
Answers
When lightning occurs, it produces a sound wave and a light wave at the same exact time. If u are watching a faraway storm, which wave gets to you first?
Answers
Light travels faster than sound and is around 300000000 m/s which is faster than sound waves. And by experience, when you are looking out the window, you can see a quick flash of light (lightning), light moves very fast
How many turns are needed in a solenoid of radius 10 cm and length 20 cm for its self-inductance to be 6.0 H?
A) 30
B) 74
C) 500
D) 550
E) 5500
Answers
Answer:
B
Explanation:
74 turns are needed in a solenoid of radius 10 cm and length 20 cm for its self-inductance to be 6.0 H
what is solenoid?The solenoid is a type of electromagnet and the main purpose of the solenoid is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
The solenoid is a coil structure of wire, and the plunger is made of soft iron. The magnetic field is formed around it when an electric current passes through it and draws the plunger in.
the solenoid is responsible for converting electrical energy into mechanical work, these were the results of the development of an efficient and greater strength offering magnets which was discovered in the year 1823.
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a car accelerates at a constant rate from 15 m/s to 25 m/s while it travels a distance of 125 m. How long does it take to achieve this speed?
Answers
25m/s -15m/s/ 125m
10m/s /125m
=0.08s
I hope it’s correct !
The time taken by the car to achieve the final speed is 6.25 seconds.
What is the equation of motion?The equations of motion can be defined as the equation that represents the relationship between the time, velocity, acceleration, and displacement of a moving object.
The mathematical expressions for the equations of motions can be written as:
[tex]v= u+at\\S=ut+(1/2)at^2\\v^2-u^2=2aS[/tex]
Given, the initial speed of the car, u = 15 m/s
The final speed of the given car, v = 25m/s
The distance covered by car, S = 125 m
From the third equation of motion: v² = u²+ 2aS
(25)² = (15)² + 2×a× 125
a = 1.6 m/s²
From the first equation of motion we can find the time to achieve the final speed:
v = u+ at
25 = 15 + (1.6) × t
t = 6.25 sec
Therefore, 6.25 seconds will be taken by the car to catch the final speed.
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Sona wants to install room heater in her living room. She had only two options, either to install heater at the top of the window or near the ground level. . Which method of installing room heater would be the effective way . Why or Why not ?
Answers
The chemical equation below shows that hydrogen and oxygen chemically react to form water.
Which of these is true?
A.
Water is a pure substance and has the same properties as oxygen.
B.
Water is a pure substance and has the same properties as hydrogen.
C.
Hydrogen and oxygen are pure substances that have identical properties to each other.
D.
Hydrogen, oxygen, and water are pure substances that each have different properties.
Answers
Answer:
D
Explanation:
Hydrogen, oxygen, and water are pure substances that each have different properties.
Although the 3 of them are pure substances, but they nonetheless have different properties. These properties could either be their physical properties, or their chemical properties. This is particularly so because since Oxygen and Hydrogen the major components in water have different properties, it is only right if their product, water, has different properties also.
Answer:
D
Explanation:
got it right on study island
What unbalanced force is needed to give a 976 kg vehicle an acceleration of 2.50 m/s2? ASAP
Answers
Answer:
2440 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question we have
force = 976 × 2.5
We have the final answer as
2440 NHope this helps you
please help i will mark brainliest
what does a speedometer measure?
a. accerlation
b. velocity
c. speed
d. average speed.
Answers
Answer:
c. speed
Explanation:
Speedometer is a device used to measure the speed of a vehicle. I am pretty sure this is the correct option.
If the peak wavelength of a star at rest is 615 nm, then what peak wavelength is observed when the star is traveling 2,500,000 m/s toward the Earth.
Answers
Answer:
1612903nm
Explanation:
Doppler effect can be regarded as the change in frequency of a wave with respect toobserver that move relative to the wave source
We can expressed as
(λo - λs)/λs = v/s
λo= peak wavelength
λs= peak wavelength observed
C= speed of light
(λo -615×10^9 )/615×10^9 = 2,500,000/(3×10^8)
1.5375=3×10^8λo -184.5
1.5375+184.5=3×10^8λo
186=3×10^8λo
λo=1612903nm
Therefore the peak wavelength that is observed when the star is traveling away from the eart to the velocity given is 1612903nm
A footballer kicks a ball from rest. The foot is in contact with the ball for 0.30s and the final velocity of the ball is 15ms-1 .What is the average acceleration of the ball?
Answers
Answer:
50m/s^2Explanation:
Step one:
given data
initial velocity u= 0m/s since the ball is at rest
time of contact t= 0.3s
final velocity v=15m/s
Required
acceleration a
from the first law of motion
v=u+at
substitute our given data
15=0+a*0.3
15=0.3a
divide both sides by 0.3
a=15/0.3
a=50m/s
The average acceleration is 50m/s^2
An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. At what horizontal distance away from the target should the package be released so that it lands on the target
Answers
Answer:
The
Explanation:
The horizontal distance covered is known as the range expressed as;
R = U√2H/g
U is the speed = 200m/s
H is the max height = 800m
g is the gravity = 9.8m/s²
R = 200√2(800)/9.8
R = 200√1600/9.8
R = 200√163.27
R = 200(12.78)
R = 2555.54
Hence the package should be released at a distance of 2555.54m
A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring it to rest.
(a) 0.019 s
(b) 54s
(c) 4.2Ã106s
(d) 2.4Ã10â7s
Answers
Answer:
54 s
Explanation:
Given that,
Mass of a car, m = 15000 kg
Initial speed, u = 5.4 m/s
Final speed, v = 0 (it comes to rest)
Force, F = 1500 N
We need to find time when it comes to rest. Let it is t. Net force is given by :
F = ma, a is acceleration of the car
[tex]F=\dfrac{m(v-u)}{t}\\\\t=\dfrac{m(v-u)}{F}\\\\t=\dfrac{15000\times (0-5.4)}{1500}\\\\t=54\ s[/tex]
So, it will take 54 seconds to come to rest.
The time required to bring the car to rest is 54 s and the right option is (b) 54 s.
To calculate the time required for the force to bring the car to rest, we use the formula below.
Formula:
F = m(v-u)/t............ Equation 1Where:
F = Force applied to the carm = mass of the carv = final velocity of the caru = initial velocity of the cart = time.Make t the subject of the equation
t = m(v-u)/F............. Equation 2From the question,
Given:
F = -1500 N (stopping force)m = 15000 kgv = 0 m/s (to rest)u = 5.4 m/sSubstitute these values into equation 2
t = [1500(0-5.4)]/-1500t = -81000/-1500t = 54 secondst ≈ 54 sHence, The time required to bring the car to rest is 54 s and the right option is (b) 54 s.
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A T-shirt cannon mounted at the top of an arena needs to fire a t-shirt into the first row, a horizontal distance of 39 meters away. If the cannon launches t-shirts at 12 m/s, how high is the cannon mounted?
A.) 8.9 m
B.) 3.3 m
C.) 53.4 m
D.) 16.2 m
Answers
At what speed does a 2000 kg compact car have the same kinetic energy as a 18000 kg truck going 21 km/hr?
Answers
Answer:
v = 17.5 m/s = 63 km/h
Explanation:
The general expression for the kinetic energy of one moving object is as follows:[tex]K = \frac{1}{2}*m *v^{2} (1)[/tex]
where m = mass of the object, v= speed of the object.
In order to get the value of the kinetic energy of the truck in Joules, we need to convert km/hr to m/s first, as follows:[tex]21 km/hr * \frac{1 hr}{3600s}*\frac{1000m}{1 km} = 5.83 m/seg (2)[/tex]
Now, replacing (2) and m = 18000 kg in (1), we get:[tex]K = \frac{1}{2}*18000 kg *(5.83m/s)^{2} = 306250 J (3)[/tex]
This value must be the same for the 2000 kg compact car, so we can write:[tex]K = 306250 J = \frac{1}{2}*2000 kg *v^{2} (4)[/tex]
Solving for v, we get:[tex]v = \sqrt{\frac{306250}{1000} (m/s)2} = 17. 5 m/s = 63 km/h (5)[/tex]
Suppose the microphone on an AM radio is not working properly. Which best explains how this will affect the
process of amplitude modulation?
The frequency of the carrier wave will be modified instead of the amplitude.
Sound waves will not be transformed into electrical signals.
Electrical signals will not be transformed into sound waves.
The pulse of the carrier wave will be modified instead of the amplitude.
Answers
Answer:
B. Sound waves will not be transformed into electrical signals.
Explanation:
edge2021
Sound waves will not be transformed into electrical signals is the reason that microphone on an AM radio is not working properly.
What is a sound wave?It is a type of mechanical wave composed of the disturbance caused by the movements of the energy. A sound wave travels through compression and rarefaction in an elastic medium such as air.
The microphone on an AM radio is not working properly means sound waves are not transforming into electrical signals.
Learn more about sound waves
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The diagram below shows two bowling balls, A and B, each having a mass of 7.0 kg, placed 2.00 m apart between their centers.
Answers
Answer:
F = 1.63 x 10⁻⁹ N
Explanation:
Complete question is as follows:
The diagram below shows two bowling balls, A and B, each having a mass of 7.0 kg, placed 2.00 m apart between their centers. Find the magnitude of Gravitational Force?
Answer:
The gravitational force is given by Newton's Gravitational Law as follows:
F = Gm₁m₂/r²
where,
F = Gravitational Force = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = m₂ = mass of each ball = 7 kg
r = distance between balls = 2 m
Therefore,
F = (6.67 x 10⁻¹¹ N.m²/kg²)(7 kg)(7 kg)/(2 m)²
F = 1.63 x 10⁻⁹ N
Which statement explains how it is possible to carry books to school without changing the kinetic or potential energy of the books or doing any work?
a. by moving the book without acceleration and keeping the height of the book constant
b. by moving the book with acceleration and keeping the height of the book constant
c. by moving the book without acceleration and changing the height of the book
d. by moving the book with acceleration and changing the height of the book
Answers
Answer:
a. by moving the book without acceleration and keeping the height of the book constant
Explanation:
FOR CONSTANT KINETIC ENERGY:
The kinetic energy of a body depends upon its speed according to its formula:
ΔK.E = (1/2)mΔv²
So, for Δv = 0 m/s
ΔK.E = 0 J
So, for keeping kinetic energy constant, the books must be moved at constant speed without acceleration.
FOR CONSTANT POTENTIAL ENERGY:
The potential energy of a body depends upon its height according to its formula:
ΔP.E = mgΔh
So, for Δh = 0 m/s
ΔP.E = 0 J
So, for keeping potential energy constant, the books must be moved at constant height.
So, the correct option is:
a. by moving the book without acceleration and keeping the height of the book constant
''The Evolution Of Sakura And Hinata''
Who looks better?! Who do you think has improved a lot in the Naruto Series?
Answers
Answer:
hinata
Explanation:
unlike sakura she has not change at all
In my opinion, Sakura looks prettier and she developed way more than Hinata. Personally, I dislike the both of them because of their Tsundere side, but there's no doubt Sakura developed way more than Hinata. In the original Naruto series, Sakura was honestly a burden. There were some missions where Team 7 had to rescue Sakura. However, after the training with Tsunade, she gained monster strength and healing abilities. Additionally, throughout Naruto Shippuden she learned new jutsu like Yin Seal: Release.
However with Hinata, it's a bit more different. In the original Naruto series, I feel believe she was stronger than Sakura. She relied on her infamous visual prowess--the Byakugan. However in Naruto Shippuden, she improved slightly compared to Sakura. In my opinion, she would have been the most useless shinobi out of the eleven characters (YES, more useless than Tenten) if it weren't for her visual prowess. She's fortunate that she was born into the Hyuga clan. Every jutsu that's in her arsenal relies heavily on the Byakugan. And if Sakura and Hinata were to battle each other, it's most likely that Sakura would win. It's true that Hinata can block Sakura's chakra points, but I think she could dodge her attacks. And even if her chakra points are blocked, Sakura can rely on Taijutsu and raw strength to win.
Though both kunoichi are honorable, I believe Sakura is more prettier and stronger than Hinata.
Describe why you are doing the experimen?
Answers
Answer:
An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated.
Explanation:
What is exerted when atoms collide with the walls of their container?
O gravity
O pressure
O stress
O friction
Answers
Answer:
B
Explanation:
Answer:
Pressure
Explanation: I took a test
A series RCL circuit contains a 65.2-Ω resistor, a 2.26-μF capacitor, and a 2.08-mH inductor. When the frequency is 2400 Hz, what is the power factor of the circuit?
Answers
Answer:
The power factor of the circuit is 0.99
Explanation:
Given;
resistance of the resistor, R = 65.2 ohms
capacitance of the capacitor, C = 2.26 μF = 2.26 x 10⁻⁶ F
inductance, L = 2.08 mH = 2.08 x 10⁻³ H
frequency of the AC, f = 2400 Hz
The angular frequency is given by;
ω = 2πf
ω = 2π(2400) = 15081.6 rad/s
The inductive reactance is given by;
XL = ωL
XL = (15081.6 x 2.08 x 10⁻³)
XL = 31.37 ohms
The capacitive reactance is given by;
[tex]X_c = \frac{1}{\omega C} \\\\X_c = \frac{1}{(15081.6)(2.26*10^{-6} )}\\\\X_c = 29.34 \ ohms[/tex]
The phase difference is given by;
[tex]tan\phi = \frac{X_l - X_c}{R}\\\\ tan\phi =\frac{31.37-29.34}{65.2} \\\\tan\phi = 0.0311 \\\\\phi = tan^{-1} (0.0311)\\\\\phi = 1.78^0[/tex]
The power factor is given by;
CosФ = Cos(1.78) = 0.99
Therefore, the power factor of the circuit is 0.99
Prove that you can do a one foot spin.