A 5 kg block is moving at v0 = 6 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that is attached to a wall. (a) Find the maximum distance that the spring will be compressed. (b) If the spring is to be compressed no more than 0.15 m, what is the maximum value of v0.
Answers
(a) The maximum distance that the spring will be compressed is 0.6928 m.
(b) The maximum value of v0 when the spring is compressed no more than 0.15 m is 3.8729 m/s.
(a) The maximum distance that the spring will be compressed can be found using the conservation of energy principle, which states that the initial kinetic energy of the block is converted into potential energy stored in the spring when the block is brought to rest. The maximum compression of the spring occurs when all the initial kinetic energy of the block is converted into potential energy stored in the spring.
The initial kinetic energy of the block is given by:
KE = (1/2)mv0^2 = (1/2)(5 kg)(6 m/s)^2 = 90 J
When the block comes to rest, all the initial kinetic energy is stored as potential energy in the spring. The potential energy stored in a spring is given by:
PE = (1/2)kx^2
where x is the compression of the spring.
Equating the initial kinetic energy and the potential energy stored in the spring, we get:
KE = PE
(1/2)mv0^2 = (1/2)kx^2
Solving for x, we get:
x = sqrt[(mv0^2)/k] = sqrt[(5 kg)(6 m/s)^2/500 N/m] = 0.6928 m
Therefore, the maximum distance that the spring will be compressed is 0.6928 m.
(b) To find the maximum value of v0 when the spring is compressed no more than 0.15 m, we can use the same equation as before, but solve for v0 instead of x:
v0 = sqrt[(kx^2)/m] = sqrt[(500 N/m)(0.15 m)^2/5 kg] = 3.8729 m/s
Therefore, the maximum value of v0 when the spring is compressed no more than 0.15 m is 3.8729 m/s.
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Related Questions
a wheel of radius 30.0 cm is rotating at a rate of 4.20 revolutions every 0.0510 s. through what angle does the wheel rotate in 1.00 s?
Answers
The angle of the rotation of the wheel in 1.0 seconds is 164.7 radians.
Does a free-body diagram include centripetal force?
Because F = ma is the net force and the net force has the unique form when dealing with uniform circular motion, you should not include a centripetal force on a free-body diagram for the same reason that ma should not be included.
The given parameters;
radius of the wheel, r = 30 cm = 0.3 m
angular speed of the wheel, ω = 4.20 rev for 0.0510 s
The angle of the rotation in 1.0 seconds is calculated as;
Ф = ωt
Ф ={ 4.20 / 0.0510 × \(\frac{2}{1 rev}\)} × 1
Ф = 164.7 rad .
Hence, the angle at which the wheel rotates in 1 s is 164.7 rad.
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a car travels 11.8 m north and then travels 13.3 m east. what is the magnitude of the car's displacement?
Answers
The magnitude of car's displacement is 17.78 m.
Given that, distance travelled due north is 11.8 m
Distance travelled due east is 13.3 m
As it is said that the car travels north and then east, it forms the two sides of a right-angled triangle. The magnitude of third side is the magnitude of car's displacement.
From Pythagoras theorem, the expression for car's displacement can be written as,
AC² = AB² + BC²
where, AB and BC are the sides of the right triangle
AC is the displacement of the car
Making AC as subject, we have,
AC = √(AB² + BC²) = √(11.8² + 13.3²) = √(139.24 + 176.89) = 17.78 m
Thus, the magnitude of car's displacement is 17.78 m.
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Gravity is not considered matter.
A. True
B. False
Answers
Answer:
false gravity is not considered matter
In the winter months the number of daylight hours decreases. What accounts for this change?
A. The sun travels faster when the time between sunrise and sunset is shorter
B. The sun is further away when the time between sunrise and sunset is shorter
C. The size of the sun and its revolution around the solar system results in this difference in time
D. The tilt of theEarth and its revolution around the sun results in this difference in time
Answers
Answer:
B
Explanation:
four massâ€""spring systems oscillate in simple harmonic motion. rank the periods of oscillation for the massâ€""spring systems from largest to smallest.
Answers
The ranking of periods of oscillation for the four mass-spring systems, from largest to smallest, is:
System with the largest mass and smallest spring constant. System with the largest mass and larger spring constant. System with the smallest mass and largest spring constant. System with the smallest mass and smallest spring constant.
To rank the periods of oscillation for the four mass-spring systems, we need to know the formula for the period of a mass-spring system, which is given by:
\(T = 2π√(m/k)\)
where T is the period, m is the mass, and k is the spring constant.
Based on this formula, we can see that the period of oscillation is directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant. Therefore, the larger the mass or the smaller the spring constant, the longer the period of oscillation.
We can rank the periods of oscillation for the four mass-spring systems as follows:
System with the largest mass and smallest spring constant: This system will have the longest period of oscillation because the mass is the largest and the spring constant is the smallest, making the denominator of the equation the smallest.
System with the largest mass and larger spring constant: This system will have a shorter period of oscillation than the first system, but still longer than the remaining two systems.
System with the smallest mass and largest spring constant: This system will have a shorter period of oscillation than the first two systems because the mass is the smallest and the spring constant is the largest, making the denominator of the equation the largest.
System with the smallest mass and smallest spring constant: This system will have the shortest period of oscillation because the mass is the smallest and the spring constant is the smallest, making the denominator of the equation the largest.
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A child holds a sled on a frictionless, snowcovered hill, inclined at an angle of 29◦
. If the sled weighs 82 N, find the force exerted on the rope by the child.
Answer in units of N.
Answers
The force exerted on the rope by the child is 71.8 N.
Weight of the sled holding by the child, W = 82 N
Angle of inclination, θ = 29°
The component of weight acting downwards,
Wx = mg sinθ
Wx = 82 x sin 29°
Wx = 82 x 0.485
Wx = 39.8 N
Given that the surface of the hill is frictionless. So, the force of friction will be zero.
Therefore, force exerted on the rope by the child,
F = mg cosθ
F = 82 cos29°
F = 82 x 0.875
F = 71.8
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what type of matter is always made up of only one kind of atom
Answers
It is impossible to break down an element into a simpler substance since it is a pure material made up of only one type of atom.
An element is a pure substance and is made of only one type of atom; it cannot be broken down into a simpler substance.
What is the net force on a water bottle?
Answers
Answer:
if it is not moving it is zero, like all things that aren't in motion
Explanation:
Answer:
Note that net force on the bottle is zero.
Explanation:
Which watch is used by scientists for correct measurement of time?
Simple watch
Digital watch
Atomic watch
Quarta watch
Answers
Answer:
It’s the atomic clock
Explanation:
Describe the relationship between speed and thinking distance. Physics Paper 2
Answers
While there is no direct relationship between speed and thinking distance, higher speeds can result in longer thinking distances due to the increased reaction time needed by the driver.
The relationship between speed and thinking distance is not a direct one, as thinking distance is primarily influenced by the driver's reaction time rather than the actual speed of the vehicle. Thinking distance refers to the distance traveled by a vehicle during the driver's reaction time after perceiving a hazard.
However, there is an indirect relationship between speed and thinking distance in the sense that higher speeds generally result in longer thinking distances. When a vehicle is traveling at a higher speed, the driver needs more time to process information, make decisions, and react to potential hazards. Therefore, a higher speed can lead to a longer thinking distance.
It is important to note that thinking distance is just one component of the total stopping distance, which also includes braking distance. Braking distance is directly influenced by the speed of the vehicle. Higher speeds require longer braking distances to bring the vehicle to a stop.
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This is an earth science question about Issac Newton’s laws and I need some major help
Answers
A calorimeter for which mc = 25 J K−1 contains
140 g of a liquid. An immersion heater is used to
provide energy at a rate of 40 W for a total time of
4.0 min. The temperature of the liquid increases by
15.8 °C. Calculate the specific heat capacity of the
liquid. State an assumption made in reaching this
result.
Answers
The liquid's specific heat capacity is 4.2 kJ kg⁻¹ K⁻¹.
In a calorimeter, mc = 25 J K⁻¹.
The calorimeter contains m(l) = 140 g = 140 × 10⁻³ kg of liquid.
The energy is provided at a rate of Q = 40 W for a time of 4 minutes.
The liquid's temperature increases by ΔT = 15.8° C = 15.8° K.
Q = mcΔT
The equation tells you how much heat is given (Q or E), how much of that heat changes the material's temperature T, and how much of that heat is applied to a mass-m material with a specific heat capacity (c).
Now, the heat supplied will be:
Q = mcΔT + m(liquid) c(liquid)ΔT
Q = mcΔT + m(l) c(l)ΔT
c(l) = ( Q - mcΔT ) / m(l)ΔT
Now, the heat supplied is Q = 40 W = 40 J/s = 40 × 4 × 60s = 9600 J
c(l) = { ( 9600 - 25 × 15.8 ) / [ (140 × 10⁻³) × 15.8 ] }
c(l) = ( 9600 - 395 ) / [ 2212 × 10⁻³ ]
c(l) = 9205 / 2212 × 10⁻³
c(l) = 4.1614 × 10³ = 4.2 kJ kg⁻¹ K⁻¹
The specific heat capacity of the liquid is 4.2 kJ kg⁻¹ K⁻¹.
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PLEASE HELP!!! Predicting the Characteristics of images formed What are the characteristics of the image formed by the object? I F 2F 2F F
Answers
Answer:
Real, inverted, equal to body size .
Answer:
Sample Response: The image created by the object is located on 2F behind the lens, real, inverted, and the same size as the actual object.
Explanation:
Edge 2021-2022 :)
When the positively charged rod Q is brought close to rod R, rod R moves away from rod Q.
Which conclusion can be made from this observation?
A Rod R is charged, but it is not possible to identify the sign of the charge.
B Rod R must be positively charged.
C Rod R must be negatively charged.
D Rod R is uncharged.
Answers
Answer:
B rod r is positively charged
_____ is the force of attraction between objects that have mass.
Answers
Explain the ways to change
momentum.
Answers
Two 0.55-kg basketballs, each with a radius of 14 cm , are just touching. How much energy is required to change the separation between the centers of the basketballs to 1.1 m? (Ignore any other gravitational interactions.)
Answers
Answer:
The amount of energy required is 4.08 J.
Explanation:
Given,m1 = m2 = 0.55-kgR = 14 cm = 0.14 m The distance between the two basketballs d = 1.1 m
Energy required to change the separation between the centers of the basketballs to 1.1 m is given by the formula; E = K1 + K2 - U where K1 = kinetic energy of ball 1K2 = kinetic energy of ball 2U = potential energy
Let's calculate K1,K2, and U: K1 = 0.5 mv²where m = mass of ball v = velocity of ball Initial velocity of ball = 0 m/s Final velocity of ball v = 0.5 m/sK1 = 0.5 × 0.55 × (0.5)²= 0.069 JK2 = 0.5 mv² Initial velocity of ball = 0 m/s .
Final velocity of ball v = - 0.5 m/sK2 = 0.5 × 0.55 × (- 0.5)²= 0.069 J Let's find out the potential energy; U = (kQ1Q2) / d
where Q1 = Q2 = Q d = distance between the centers of two balls U = (kQ²) / d where k = Coulomb's constant = 8.99 × 10⁹ Nm²/C²Q = charge on a ball = 0 (because it is an uncharged object) U = 0.
Therefore, E = K1 + K2 - U= 0.069 + 0.069 - 0= 0.138 J Therefore, the amount of energy required is 4.08 J.
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Highlight the correct answer.
A.) An object with more mass has more/less gravitational force than an object with a smaller mass.
B.) Objects that are closer together have more/less of a gravitational force between them than objects that are further apart.
Answers
The correct answer is B. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
In simpler terms, as objects get closer together, the gravitational force between them increases.
When the distance between two objects decreases, the denominator of the equation (distance squared) becomes smaller, resulting in a larger force. Conversely, when the distance increases, the denominator becomes larger, resulting in a smaller force.
It is important to note that the mass of an object does not directly affect the strength of the gravitational force between two objects. However, a higher mass will lead to a greater gravitational force when compared to a lower mass, but only because the force is being exerted on a more massive object. The mass of an individual object doesn't directly affect the gravitational force it experiences from another object. option B
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An air-track glider of mass 0.25 kg moving at 0.60 m/s collides with and sticks to a glider of mass 0.50 kg at rest. How much kinetic energy is converted into other forms of energy as a direct result of this collision?
Answers
Answer:
0.03 Joules have been converted into other forms of energy as the direct result of the collision.
Explanation:
Let's start studying the conservation of momentum for the system:
\(P_i=P_f\\(0.25\,kg)\,{0.6\,m/s)+(0.5\,kg)\,(0\,m/s)=(0.25\,kg+0.5\,kg)\, v_f \\\\\\ 0.15\,kg\,m/s=0.75\,kg\,\,v_f\\v_f=0.15/0.75\,\,m/s\\v_f=0.2\,\,m/s\)
Now that we know the speed of the newly created object, we can calculate how the final kinetic energy differs from the initial one:
\(K_i=\frac{1}{2} (0.25)\,(0.6)^2+\frac{1}{2} (0.5)\,(0)^2=0.045\,\,J\\ \\K_f=\frac{1}{2} (0.75)\,(0.2)^2=0.015\,\,J\\\)
Then, when we subtract one from the other, we can estimate how much kinetic energy has been converted into other forms of energy in the collision:
0.045 J - 0.015 J = 0.03 J
Why is light referred to as an electromagnetic wave.
Answers
they have oscillating electric and magnetic fields
is the total momentum before the collision equal the total momentum after the collision. if not, what are the possible differences as to why
Answers
The overall momentum of the system can be thought of as being conserved because the total momentum before and after the collision is the same. As a result, the system receives no net external impulse.
Momentum is a vector quantity that is influenced by the object's direction. During collisions between objects, momentum is a relevant concept. The total momentum before a collision between two objects equals the total momentum after the impact (in the absence of external forces).
The law of conservation of momentum is this. It holds true in every collision. According to the principle of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.
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How long does it take to fly 108 km east if you are travelling at 270 km/h?
Answers
Answer:
0.4 hour or 24 minutes
Explanation:
Knowing the formula:
\( \displaystyle{ \vec v = \dfrac{ \vec s}{t}}\)
v is velocity, s is displacement and t is time. We know two values which are s = 108 km and v = 270 km/h. Substitute in the formula:
\( \displaystyle{ 270 \ \text{km/h} = \dfrac{108 \ \text{km}}{t}}\)
Solve for t:
\( \displaystyle{ 270 \ \text{km/h} \cdot t= 108 \ \text{km}} \\ \\ \displaystyle{t= \dfrac{108 \ \text{km}}{270 \ \text{km/h}}} \\ \\ \displaystyle{t= 0.4 \ \text{h}}\)
Therefore, it will take around 0.4 hour or converting to minutes. We know that 1 hour = 60 minutes. Multiplying 0.4 both sides, hence:
0.4 hour = 0.4 × 60 minutes = 24 minutes.
Select the correct answer. If the resistance remains constant and the voltage doubles, what effect will that have on the power? A. The power will remain the same. B. The power will decrease by a factor of 2. C. The power will decrease by a factor of 4. D. The power will increase by a factor of 2. E. The power will increase by a factor of 4.
Answers
If the resistance remains constant and the voltage doubles, the power will increase by a factor of 4 (option E)
How do i determine the new power?The following data were obtained from the question:
Initial power (P₁) = PInitial voltage (V₁) = VResistance = ConstantNew voltage (V₂) = 2VNew power (P₂) =?P = V² / R
Resistance is constant, we have
V₁² / P₁ = V₂² / P₂
V² / P = (2V)² / P₂
V² / P = 4V² / P₂
Cross multiply
V² × P₂ = P × 4V²
Divide both side by V²
P₂ = P × 4V² / V²
P₂ = P × 4
From the above, we can conclude that the power will increase by a factor of 4 (option E)
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Arrange the following phyla in increaing order of evolution
arthopodo, platyhelminthe, annelide, echinodemata
Answers
Phyla in increaing order of evolution is Platyhelminthes, Annelidia, Arthopoda and Echinidermata.
What is meant by Annelidia?
The coelomate, triploblastic, bilaterally symmetric Annelids are invertebrates. For movement, they also have parapodia.This system has undergone a significant modification as a result of cladistic study since 1997, which views leeches as a subgroup of oligochaetes and oligochaetes as a subgroup of polychaetes.Additionally, previously recognized as distinct phyla, the Pogonophora, Echiura, and Sipuncula are now considered to be subgroups of polychaetes. The Lophotrochozoa, a "super-phylum" of protostomes that also includes molluscs, brachiopods, and nemerteans, is thought to include annelids.The fundamental annelid form is divided into several sections. In most polychates, each segment has the same set of organs and a pair of parapodia that many species use for locomotion.To learn more about Annelidia refer to
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Find the density of a 2 cm x 2 cm x 2 cm cube with a mass of 64 g.
Answers
Answer:
8 g/cm³
Explanation:
density=mass/volume
volume=2*2*2=8 cm³
mass=64 g
density=64/8=8 g/cm³
The density of a 2 cm x 2 cm x 2 cm cube with a mass of 64 g is equal to 8 g/cm³.
What is the density?Density can be defined as the material mass per unit of volume. The symbol commonly used to represent density ρ and the letter 'D' can also be used.
The mathematical equation of the density can be represented as written below:
Density = Mass /Volume
or, ρ = m/V
The density of a material varies with pressure and temperature. There is a small variation for solids and liquids of any material but much larger for gases. Increasing the pressure of material decreases the volume and thus increases its density.
Given the volume of the cube = 2 cm x 2 cm x 2 cm
V = 8 cm³
The mass of the cube, m = 64 g
The density of the cube can be calculated from the above-mentioned formula:
Density = Mass of cube/volume
D = 64/8
D = 8 g/cm³
Therefore, the density of the cube is 8 g/cm³.
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a ball is thrown vertically upward with a speed of 12.0 m/s. (a) how high does it rise? m (b) how long does it take to reach its highest point? s (c) how long does the ball take to hit the ground after it reaches its highest point? s (d) what is its velocity when it returns to the level from which it started? m/s need help?
Answers
To find answer to all the questions asked, we can use the equations of motion.
When a ball is thrown vertically upward, it follows a projectile motion. The velocity of the ball decreases as it moves upward due to gravity, until it reaches its highest point. At the highest point, the velocity of the ball becomes zero, and then it starts to fall back to the ground with an increasing velocity.
(a) To find the height the ball rises, we can use the equation:
v² = u² + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
At the highest point, the final velocity is zero, the initial velocity is 12.0 m/s, and the acceleration is -9.8 m/s² (due to gravity).
0² = 12.0² + 2(-9.8)s
s = (12.0²)/(2×9.8)
s = 7.35 m
So, the ball rises to a height of 7.35 m.
(b) To find the time taken to reach the highest point, we can use the equation:
v = u + at
At the highest point, the final velocity is zero, the initial velocity is 12.0 m/s, and the acceleration is -9.8 m/s².
0 = 12.0 + (-9.8)t
t = 12.0/9.8
t = 1.22 s
So, it takes 1.22 s to reach the highest point.
(c) The time taken to hit the ground after reaching the highest point is the same as the time taken to reach the highest point, because the motion is symmetrical. So, the ball takes 1.22 s to hit the ground after reaching the highest point.
(d) The velocity of the ball when it returns to the level from which it started is the same as the initial velocity, but in the opposite direction. So, the velocity is -12.0 m/s.
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Whay are derived quantity?
Answers
derived quantity are those that may be expressed in terms of base or derived quantities by means of the mathematical symbols of multification and division
John doesn't think that skepticism should play an important role in the scientific process. He says that skepticism interferes with scientific consensus. Which statement best describes John's conclusion
Answers
Answer: it is incorrect because skepticism helps scientists recognize when ideas are not supported by evidence.
Explanation:
Skepticism is simply the understanding that there can be uncertainty when it comes to knowledge in certain areas.
From the question, we are informed that John doesn't think that skepticism should play an important role in the scientific process and that he says that skepticism interferes with scientific consensus.
The statement that best describes John's conclusion is that it is incorrect because skepticism helps scientists recognize when ideas are not supported by evidence.
a pulse covers a distance of 5m in 15seconds . Calculate the sped of the pulse.
Answers
According to the question the speed of pulse is = 0.33m/s
What does "speed" in science mean?Velocity is the pace and direction of either an object's movement, whereas speed is now the time rate which an object is travelling along a path. In other words, velocity is a vector, whereas speed would be a scalar value. If you determine how far an object travels in a certain amount of time, you can calculate its speed.For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour .
How is speed measured?The equation for speed can be obtained by simply dividing time by distance.
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Р
The densities of two metals are 6.3 g/cm³ and 3.7 g/cm³ respectively. The two metals
are of equal mass, and are melted to form an alloy.
What is the new density of the alloy?
A) 4.0 g/cm³ B) 4.7 g/cm³
C) 5.0 g/cm³
D) 10.0 g/cm³
Answers
Solution:- let d1 and d2 be their respective densitiesd1= 6.3 gram/cm³ , d2 = 3.7 gram/cm³let us consider taking m mass of both substance as it is given masses are equalLet their volumes be V1 and V2
Now ,
☯︎Density= Total Mass / Total Volume
➪\(density = \dfrac{m + m}{V1 + V2} \)
➪\( \dfrac{2m}{ \frac{m}{d1} + \frac{m}{d2} }\)
\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (Volume=\frac{mass}{density}) \)
➪\( \dfrac{2\cancel{m}}{ \cancel{m}(\frac{1}{d1} + \frac{1}{d2}) }\)
➪\( \dfrac{2}{ \frac{1}{d1} + \frac{1}{d2} }\)
➪\( \dfrac{2.d1.d2}{ d1+d2 }\)
Putting Values -
✰\( \dfrac{2\times 6.3\times 3.7}{ 6.3+3.7 }\)
➪\( \dfrac{46.62}{ 10}\)
➪\( 4.662\)
≈\( 4.7 gram/cm^3\)