A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant, but starts at 0.100 at P and increases linearly with distance past P, reaching a value of 0.600 at 12.5 m past point P.
(a) Use the work energy theorem to find how far this box slides before stopping.
(b) What is the coefficient of friction at the stopping point?
(c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?
Answers
Answer:
(a). The value of distance is 5.043 m
(b). The coefficient of friction is 0.302.
(c). The distance is 10.33 m
Explanation:
Given that,
Speed = 4.50 m/s
Minimum friction = 0.1
Maximum friction = 0.6
Distance = 12.5 m
We know that,
The newton's second law
\(F_{net}=-\mu N\)
\(F_{net}=-\mu mg\)
We know that,
The frictional coefficient is directly proportional to the distance.
We need to calculate the value of coefficient
Using general equation of frictional coefficient
\(\mu(x)=Ax+B\)....(I)
At x= 0,
\(\mu(0)=0+B\)
Put the value into the formula
\(B=0.1\)
Now for value of A
Put the value in equation (I)
\( 0.6=A12.5+0.1\)
\(A=\dfrac{1}{25}\)
Put the value in equation (I)
\(\mu(x)=\dfrac{x}{25}+0.1\)......(II)
We need to calculate the work done
Using work energy theorem
\(W=\int_{0}^{x}{F_{net} dx}\)
\(W=\int_{0}^{x}{-\mu_{x}mgdx}\)
\(W=-mg\int_{0}^{x}{(\dfrac{x}{25}+0.1)dx}\)
\(W=-mg(\dfrac{x^2}{50}+0.1x)\)....(III)
(a). We need to calculate the distance
Using difference of kinetic energy
\(W=\dfrac{1}{2}m(v_{f}^2-v_{0}^2)\)
\(-mg(\dfrac{x^2}{50}+0.1x)=\dfrac{1}{2}m(0-(4.50)^2)\)
\(\dfrac{x^2}{50}+0.1x=1.013\)
\(x^2+5x=50.65\)
\(x^2+5x-50.65=0\)
\(x=5.043\ m\)
(b). We need to calculate the coefficient of friction at the stopping point
Using equation (III)
\(\mu(5.043)=\dfrac{5.043}{25}+0.1\)
\(\mu(5.043)=0.302\)
(c). We need to calculate the distance
Using formula work done
\(W=-fx_{2}\)
\(W=-\mu mgx_{2}\)
\(-\dfrac{1}{2}mv_{0}^2=-\mu mgx_{2}\)
\(x_{2}=\dfrac{v_{0}^2}{2\mu g}\)
Put the value into the formula
\(x_{2}=\dfrac{(4.5)^2}{2\times0.1\times9.8}\)
\(x_{2}=10.33\ m\)
Hence, (a). The value of distance is 5.043 m
(b). The coefficient of friction is 0.302.
(c). The distance is 10.33 m
Related Questions
How much time will it take an armadillo traveling 0.1 m/s to go 2010 meters?
Answers
Answer:
20100s
Explanation:
the ratio of "diameter over distance" for the Sun, then, must be __________ [bigger than, smaller than, or the same as] the ratio of "diameter over distance" for the Moon
Answers
The ratio of "diameter over distance" for the Sun must be smaller than the ratio of "diameter over distance" for the Moon.
This is because, although the Sun is much larger than the Moon, it is also much farther away. The diameter of the Sun is approximately 1.39 million kilometers, while the diameter of the Moon is approximately 3,476 kilometers. However, the distance from the Earth to the Sun is approximately 149.6 million kilometers, while the distance from the Earth to the Moon is approximately 384,400 kilometers. To calculate the ratio of "diameter over distance," we divide the diameter of the celestial body by the distance from Earth to that body. For the Sun, the ratio is 0.0093 (1,390,000/149,600,000), while for the Moon, the ratio is 0.0090 (3,476/384,400). Therefore, the ratio of "diameter over distance" for the Sun is smaller than that of the Moon.In summary, the ratio of "diameter over distance" for the Sun is smaller than that of the Moon because although the Sun is much larger than the Moon, it is also much farther away. This is demonstrated by the calculations of the respective ratios, which result in a smaller ratio for the Sun.For more questions on Moon
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. A boy wishes to make a catapult out of a rubber band of width 9mm and thickness 1.55mm. Determine the length of the band that he must use so that when he stretches it by 0.25 of its natural length and releases it the velocity of pebble of mass 0.006kg will be 30m/s. Take young modulus of the rubber to be 4×10^7 N/m^2
Answers
The length of the rubber band that the boy must use is 0.024 m or 24 mm.
What will be the length of the rubber required?To determine the length of the rubber band, we can use the formula for the potential energy stored in a stretched spring, which is also applicable to a stretched rubber band:
U = 1/2 kx²where U is the potential energy stored in the rubber band, k is the spring constant (or in this case, the rubber band constant), and x is the displacement of the rubber band from its natural length.
Since the rubber band is stretched by 0.25 of its natural length, the displacement x is 0.25 times the natural length of the rubber band.
We can solve for the rubber band constant k by using the formula for the velocity of a projectile launched by a spring (or in this case, a rubber band):
v = √(2mk/M)where v is the velocity of the projectile, m is the mass of the rubber band, M is the mass of the projectile, and k is the spring constant. We can rearrange this equation to solve for k:
k = (v² M) / (2 m)
We can now combine the two equations to solve for the length of the rubber band, L:
U = 1/2 k x²
U = 1/2 ((v² M) / (2 m)) (0.25 L)²
U = (v² M L²) / (32 m)
The potential energy stored in the rubber band must be equal to the kinetic energy of the projectile when it is launched:
U = 1/2 M v²
(v² M L²) / (32 m) = 1/2 M v²
L = ((16 m v²) / (k M))
L = ((16 m v²) / ((v² M) / (2 m) M))
L = √(32 m^2 / M)
L = (0.032 M)
Substituting the given values, we get:
L = √(0.032 * 0.006)
L = 0.024 m
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what is atomic weight
Answers
Answer:
Its also know as atomic mass its the mass of isotopes.
Explanation:
relative atomic masses of sources in the local environment of the Earth's crust and atmosphere as determined by the atomic weight.
need help asap, thank you !
In the absence of air resistance, a projectile launched at an angle of 33 above the horizontal will have the same range as a projectile launched at which of the following angles? O 38 O 57⁰ 0:45. 07
Answers
A projectile is launched at an angle of 33⁰ above the horizontal, then the projectile launched at an angle of 90 - 33 = 57⁰ will have the same range as the projectile launched at 33⁰. The correct option is (B) 57⁰.
In the absence of air resistance, a projectile launched at an angle of 33 above the horizontal will have the same range as a projectile launched at an angle of 57⁰.
The range of a projectile can be determined by using the range formula.
R = ((v^2 * sin(2θ))/g) Where
R is the range of the projectile,
v is the velocity of the projectile,
θ is the angle at which the projectile is launched, and
g is the acceleration due to gravity.
In the absence of air resistance,
the horizontal component of velocity of a projectile remains constant throughout the flight.
So, the range of a projectile depends only on its initial velocity and the angle at which it is launched.
If a projectile is launched at an angle θ,
the time of flight of the projectile can be calculated by using the following formula:
T = (2v * sin(θ))/g
The maximum height reached by the projectile is given by the formula:
H = (v^2 * sin^2(θ))/2gIf a projectile is launched at an angle θ, then the range of the projectile will be the same as the range of the projectile launched at an angle of (90 - θ).
So, if a projectile is launched at an angle of 33⁰ above the horizontal, then the projectile launched at an angle of 90 - 33 = 57⁰ will have the same range as the projectile launched at 33⁰.
Therefore, the correct option is (B) 57⁰.
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A paved blacktop parking lot was built on what was
once a soil-covered field. This area will now
experience increased runoff when rain occurs because
the paved parking lot has
A) less capillarity B) less permeability
C) greater infiltration D) greater porosity
Answers
Answer:
The answer is B. less permeability.
Explanation:
someone please helppp :|||
Answers
Answer:
b
Explanation:
Answer:
its c
Explanation:
i have asked my teacher
define resistivity ?
what is the range of resistivity for metal and alloys
Answers
Answer:
The resistivity of an exceedingly good electrical conductor, such as hard-drawn copper, at 20° C (68° F) is 1.77 × 10-8 ohm-metre, or 1.77 × 10-6 ohm-centimetre. At the other extreme, electrical insulators have resistivities in the range 1012 to 1020 ohm-metres.
a speeder traveling at a constant speed of 85 km/h races past a billboard. a patrol car pursues from rest with constant acceleration of (6 km/h)/s until it reaches its maximum speed of 112 km/h, which it maintains until it catches up with the speeder. how long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes? answer in units of s
Answers
Therefore, it takes approximately 58.57 seconds for the patrol car to catch up with the speeder if it starts moving just as the speeder passes.
To find the time it takes for the patrol car to catch up with the speeder, we need to analyze the motion of both vehicles.
First, let's convert the speeds to m/s to have a consistent unit for calculations.
The speed of the speeder is 85 km/h, which is equal to 85 * (1000 m / 1 km) / (3600 s / 1 h) = 23.6 m/s.
The maximum speed of the patrol car is 112 km/h, which is equal to 112 * (1000 m / 1 km) / (3600 s / 1 h) = 31.1 m/s.
Now, let's calculate the time it takes for the patrol car to reach its maximum speed.
The acceleration of the patrol car is given as (6 km/h)/s. Since the unit of the speed is km/h, we need to convert it to m/s.
(6 km/h) * (1000 m / 1 km) / (3600 s / 1 h) = 1.67 m/s².
We can use the formula:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values:
31.1 m/s = 0 m/s + (1.67 m/s²) * t.
Simplifying the equation, we find:
t = 31.1 m/s / 1.67 m/s² = 18.6 s.
Therefore, it takes 18.6 seconds for the patrol car to reach its maximum speed.
Next, let's calculate the distance traveled by the speeder during this time.
The distance is equal to the speed multiplied by the time:
Distance = Speed * Time = 23.6 m/s * 18.6 s = 439.3 meters.
Now, let's calculate the time it takes for the patrol car to catch up with the speeder.
The relative speed between the patrol car and the speeder is the difference in their speeds:
Relative speed = 31.1 m/s - 23.6 m/s = 7.5 m/s.
The time it takes to cover the distance between the two vehicles is given by:
Time = Distance / Relative speed = 439.3 meters / 7.5 m/s = 58.57 seconds.
Therefore, it takes approximately 58.57 seconds for the patrol car to catch up with the speeder if it starts moving just as the speeder passes.
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( t ^ s ) v ( ~t^ ~s ) is true or false
Answers
The statement (t ^ s) v (~t ^ ~s) is always true. Assuming t and s are Boolean variables, "~" represents the negation operator (i.e., NOT), "^" represents the conjunction operator (i.e., AND), and "v" represents the disjunction operator (i.e., OR).
The true value of this statement depends on the truth values of t and s.
Assuming t and s are Boolean variables, "~" represents the negation operator (i.e., NOT), "^" represents the conjunction operator (i.e., AND), and "v" represents the disjunction operator (i.e., OR).
If t is true and s is true, then the statement simplifies to:
(true ^ true) v (~true ^ ~true)
= true v false
= true
If t is false and s is false, then the statement simplifies to:
(false ^ false) v (~false ^ ~false)
= false v true
= true
In all other cases, the statement simplifies to:
(false) v (true)
= true
Therefore, the statement (t ^ s) v (~t ^ ~s) is always true.
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Describe when the chemical
reaction occurs in a dry-cell
battery
Answers
Answer:
For a dry-cell battery to operate, oxidation will occur from the zinc anode and reduction will take place in the cathode. The most common type of cathode is a carbon graphite. Once reactants have been turned into products, the dry-cell battery will work to produce electricity.
Explanation:
The battery operates through electrochemical reactions called oxidation and reduction. These reactions involve the exchange of electrons between chemical species. If a chemical species loses one or more electrons, this is called oxidation. The opposite process, the gain of electrons, is called reduction.
I dropped a wet bar of soap on the ground is the bar of soap dirty or is the floor clean???
Answers
Answer:
the floor is clean and the soap is dirty. lol
The Earth orbits the Sun because of the competing forces of _________________ and _______________________.
Answers
Scientists are studying a pond. Which property can the scientists measure to understand the amount of energy held by the lake water?
A. the depth of the lake
B. the color of the water
C. the volume of the lake
D. the temperature of the water
Answers
suppose that the magnitude of the charge on the yellow sphere is determined to be 2q2q . calculate the charge qredqredq red on the red sphere. express your answer in terms of qqq , d1d1d 1 , d2d2d 2 , and θθtheta .
Answers
To calculate the charge qred on the red sphere, we need to use the concept of Coulomb's Law. According to Coulomb's Law, the electric force between two charges is given by the equation:
F = k * (q1 * q2) / r^2
Where F is the force between the charges, k is the electrostatic constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges. In this case, we have the yellow sphere with charge magnitude 2q, and the red sphere with charge magnitude qred. The distance between the spheres can be expressed as d1 + d2.
Now, let's assume that the force between the charges is zero when the charges are in equilibrium. Therefore, we have: F = 0
k * (2q * qred) / (d1 + d2)^2 = 0
Now, solving for qred:
2q * qred = 0
qred = 0 / (2q)
Therefore, the charge qred on the red sphere is 0.
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It is a force that acts in a direction opposite to the motion of the moving object
Answers
The force that acts in a direction opposite to the motion of the moving object is called drag or air resistance.
Drag or air resistance is a force that acts on a moving object in a fluid medium, such as air or water, opposing its motion. It acts in a direction opposite to the motion of the object and is caused by the friction and pressure differences between the fluid and the object's surface. Drag force increases with the velocity of the object and its surface area, and it's usually modeled as a quadratic function of the velocity. For example, when a car is moving, the air resistance acts in the opposite direction of the car's motion, slowing it down. The drag force is not the only force that acts on the object, but it's one of the most significant forces acting on it, especially for objects moving at high speeds.
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An electron enters the magnetic field at right angle from left B into paper. The electron will be deflected?
Answers
Answer:
According to this direction of force is perpendicular to the direction of current and magnetic field. Therefore force is opposite to electron into the paper at 90°.
How much kinetic energy does a baseball with a mass of 0.143 kg have it it is traveling at a velocity of 41.1 m/s?
89.7 Joules
108 3 Joules
156.6 Joules
120.8 Joules
Answers
Answer:
E = 120.77 J
Explanation:
Given that,
Mass of a baseball, m = 0.143 kg
Velocity of a baseball, v = 41.1 m/s
We need to find the kinetic energy of the baseball. We know that the kinetic energy of an object is associated with its motion. It can be given by the formula as follow :
\(E=\dfrac{1}{2}mv^2\\\\E=\dfrac{1}{2}\times 0.143\ kg\times (41.1\ m/s)^2\\E=120.77\ J\)
So, the kinetic energy of the baseball is 120.77 J.
The kinetic energy of the baseball is 120.8 J.
What is kinetic energy?The kinetic energy of an object is associated with its motion. It can be related to the mass and velocity as
K.E = 1/2 mv²
Given is the Mass of a baseball, m = 0.143 kg and Velocity of a baseball, v = 41.1 m/s
substitute the values, we have
K.E = 1/2 x 0.143 x (41.1)²
K.E = 120.77 J
Hence, the kinetic energy of the baseball is 120.8 J.
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The boat's 'echo sounder' could not be used in an aeroplane to measure its heigh
above the ground unless it had been modified.
Answers
True, this is because the echo sounder that is applicable to boats cannot be used directly for airplanes
How does an echo sounder work?By sending out sound waves and timing how long it takes for them to bounce back, an echo sounder, sometimes referred to as a sonar, is a device frequently used in boats to gauge the depth of the water beneath the craft.
When a sound pulse from an echo sounder strikes a solid item in the water, such as fish, vegetation, or other objects, the signal is reflected back to the surface.
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Select the correct answer. Which feature of a wave determines its color in the visible spectrum? A. Amplitude B. Composition C. Temperature D. Wavelength.
Answers
Answer:
D. Wavelength
Explanation:
Explanation: the colour of visible light depends on the wavelength of the wave. The visible light spectrum goes approximately from wavelength of 380 nm (corresponding to violet light) to 750 nm (corresponding to red light), and the different colours in between correspond to different wavelengths.
A 1.96-kg particle has a velocity (2.09 î − 3.05 ĵ) m/s, and a 2.98-kg particle has a velocity (1.08 î + 5.91 ĵ) m/s.
(a) Find the velocity of the center of mass
( ) î + ĵ m/s
(b) Find the total momentum of the system
( ) î + j kg · m/s
Answers
(a). The velocity of the center of mass is (4.32 î + 6.43 ĵ) m/s.
(b). The total momentum of the system is:
\(p_{total\) = \(p_1 + p_2\) = (4.10 î − 6.00 ĵ) kg · m/s + (3.22 î + 17.62 ĵ) kg · m/s = (7.32 î + 11.62 ĵ) kg · m/s
(a) The velocity of the center of mass can be found using the formula:
\(v_cm = (m_1v_1 + m_2v_2) / (m_1 + m_2)\)
where\(m_1\) and \(v_1\) are the mass and velocity of the first particle, and \(m_2\) and \(v_2\) are the mass and velocity of the second particle. Substituting the given values, we get:
\(v_{cm\) = (1.96 kg)(2.09 î − 3.05 ĵ) m/s + (2.98 kg)(1.08 î + 5.91 ĵ) m/s / (1.96 kg + 2.98 kg)
\(v_{cm\) = (4.32 î + 6.43 ĵ) m/s
(b) The total momentum of the system can be found by adding the momentum of each particle. The momentum of a particle is given by:
p = mv
where m is the mass of the particle and v is its velocity. Substituting the given values, we get:
\(p_1\) = (1.96 kg)(2.09 î − 3.05 ĵ) m/s = (4.10 î − 6.00 ĵ) kg · m/s
\(p_2\) = (2.98 kg)(1.08 î + 5.91 ĵ) m/s = (3.22 î + 17.62 ĵ) kg · m/s
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Ajdaifsgodtistizhxtsgoachoach
Answers
Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm maybe
A ball is thrown horizontally at a speed of 7.9 m/s. When the ball is released, it is 1.8 m off the ground. How far (horizontally) will the ball travel?
Answers
If a ball is tossed horizontal at a speed of 7.9 m/s, it will travel 4.8 meters (horizontally).
What exactly does it entail to speed?Teenagers, young adults, and others take various stimulant medications collectively referred to as "speed" to feel more focused and alert, as well as occasionally to get high. Additionally, some people take various forms or speed to suppress their appetite.
How fast is relativistic motion?Relativistic speed is the rate at which relativity effects matter for the desired level of measurement precision of the phenomenon being examined. Relativistic effects are the differences between values calculated using models that take relativity into account and those that do not.
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Question 7 Points 2
The bicycle lamp glows when the bicycle's generator touches the wheel. This is because
Answers
Answer:
The dynamo has a wheel that touches the back tyre. As the bicycle moves, the wheel turns a magnet inside a coil. This induces enough electricity to run the bicycle's lights. The faster the bicycle moves, the greater the induced voltage - and the brighter the lights.
Because of the bicycle's actions, the wheel turns a magnet internal a coil. This induces enough strength to run the bicycle's lighting fixtures. The faster the bicycle movements, the greater the caused voltage - and the brighter the lights.
What type of modern is produced with the aid of a bicycle dynamo?A trendy dynamo creates an instantaneous modern-day (DC) – a one-directional waft of electrical rate. A bicycle dynamo creates an alternating current (AC), which reverses course from time to time.
A dynamo is a tool normally positioned inside the hub of a motorcycle's wheel that converts the energy generated by means of the wheel spinning to electric power. That energy is then used to run front and rear dynamo lights at the bike, offering constantly-on illumination without the want to change the lighting.
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A car is traveling constant spoed ol 12 12 m/s When the driver accelerates, the car reaches a speed of 26 m/s in s What is the average acceleration of the
Answers
Answer:
Average acceleration of the car is 1.167 m/s^2
Explanation:
The speed of car with which it is travelling is 12 m/s
As the driver accelerates the car, the speed reaches 26 m/s
The change in speed in 12 seconds is
26 -12 = 14 m/s
Average acceleration is change in speed divided by time
\(\frac{14}{12} \\1.167\) m/s^2
What are the parts of a wedge and their function?
Answers
Answer:
A wedge is a machine that consists of two inclined planes, giving it a thin end and thick end. A wedge is used to cut or split apart objects. Force is applied to the thick end of the wedge, and the wedge applies force to the object along both of its sloping sides. This force causes the object to split apart
What does this tell you about the direction and magnitude of the acceleration acting on the cannonball throughout its duration of flight?
Answers
Answer:
Direction remains the same but velocity changes.
Explanation:
This tell us about the direction and magnitude of the acceleration acting on the cannonball throughout its duration of flight that its direction remains the same but its magnitude of the acceleration is continuously changing. The cannonball moves in the direction in which the cannon was fired while the velocity is highest after the fire but decreases when goes higher and when it comes back to the ground so its velocity increases against so we can say that both positive and negative acceleration occurs. Positive acceleration means increase in the magnitude of velocity whereas negative acceleration means decrease in velocity.
The intensity of the distributed lood acting on the beams 25 kN/m.) Determine the magnitude of reaction at Express your answer to three significant figures and include the appropriate units O ? N Value Units Submit Request Answer Figure Part 6 1 of 1 Delane te zand y components of reaction all sing scalar notation Express your answers using three significant figures separated by a comma HV AED vec ?
Answers
The magnitude of reaction at the beam due to the distributed load of 25 kN/m is 625 N.
What is the magnitude of reaction to the distributed load?The magnitude of reaction at the beam can be determined by calculating the total force exerted by the distributed load. In this case, the distributed load is given as 25 kN/m. To find the magnitude of reaction, we multiply the distributed load by the length of the beam.
Therefore, the magnitude of reaction is 25 kN/m multiplied by the length of the beam in meters. By performing the calculation, we obtain the value of 625 N as the magnitude of reaction at the beam due to the distributed load. This represents the total force exerted by the distributed load on the beam.
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How is spring force different in a compressed spring versus a stretched spring?
Answers
Answer:
if you pull on a spring and stretch it, then you do work. that's bc you're applying a force over a displacement. your pull is the force and the amount that you stretch the spring is the displacement. a spring can be stretched or compressed.
A 15kg child and a 25kg child sit at opposite end of a 4m seesaw pivoted at its center. Where should the third child whose mass is 20kg sit in order to balance the seesaw?
Answers
The position the 20 kg child should seat in order to balance the seeesaw is determined as 1 m.
What is the position of the 20 kg child?Let the position of the 20 kg child from the center of the seesaw = x
Apply the principle of moment, taking moment about the pivot as shown below;
clock wise moment = antilock wise moment
15(2m) + (20x) = 25 (2m)
30 + 20x = 50
20x = 50 - 30
20x = 20
x = 20/20
x = 1 m
Thus, when the 20 kg child seats at 1 m from the end of the 15 kg child the seesaw will balance.
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