The cyclist will accelerate because he changed his direction from west to south.
Is acceleration a scalar or vector quantity?
Acceleration is a vector quantity. It has both magnitude and direction.
Given is a bicyclist bikes to the west at a constant speed for 30 minutes before turning South and continuing at the same speed for an hour.
As learned above, acceleration is a vector quantity. This means that it has both the magnitude and the direction. If any one of that changes the acceleration will change. Now, since the direction changed from west to south, the resultant acceleration of the cyclist will change. Hence, the cyclist will accelerate.
Therefore, the cyclist will accelerate because he changed his direction from west to south.
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A helicopter is ascending vertically with a constant speed of 5.20 m/s. At a height of 125
m above ground, a package is dropped from the helicopter.
a) How much time does it take to reach the ground?
b) How far above ground is the helicopter when the package lands?
According to the given statement:
a)It take time to reach the ground is 3.69 s.
b)The helicopter when the package lands far above the ground is 144.18 m.
What is constant speed and example ?Constant speed refers to a speed that remains constant throughout the duration of the motion. Constant speed is demonstrated in our example of using cruise control while driving a car.
Briefing:Using this formula:
t= √(h/g)
h= 125m
g= 9.2 m/s
t = √(125/9.2)
t = √13.59
t= 3.69 s
The package must touch the ground in 3.69 seconds.
From equation of motion s = u t + 1/2 a t².
Here a= 0, then s= ut
s= 5.2x 3.69 = 19.18 m.
Total height = 19.18 + 125 = 144.18 m.
Helicopter is 144.18m far above from the ground when the package lands.
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How much work is done when a car is pushed 8 m with 160 N of force?
Answer: 1280 J
Explanation: Work is calculated by multiplying the displacement (8m) by the force (160 N) which will give you 1280 J (joule)
a railroad car collides and couples with a second railroad car that is standing still. if the external forces acting on the two cars are negligible, how will the velocity of the first car change after the collision?
velocity of the first car will decrese after the collision.
Momentum is conserved so when the mass of the moving system is increased by the addition of the second car the velocity will be less than that of the first car before the collision.
Most often, the collision between the objects is described in terms of conservation of momentum. In the event of an isolated system interacting with the objects, the momentum is preserved. The starting and ultimate momentum of an isolated system will be the same since there is no external force operating on the system.
When a collision happens between the two objects in the isolated system, the total momentum before the collision and the total momentum after the collision are identical. Elastic and inelastic collisions are the two forms of collision.
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a car is traveling driving at 80 km/h when the driver sees an accident 50 meters ahead and applies the brakes. what constant deceleration is required to stop the car in time to avoid hitting the vehicles ahead? express your answer in m/s2.
The correct answer is -4.937284m/s^2 constant deceleration is required to stop the car in time to avoid colliding with the vehicles ahead.
u= 80km/h= 22.22m/s
s= 50m
a=? , v=0
According to newton's third equation:
2as= v^2-u^2
a= v^2-u^2/2s
a= 0-(22.22)^2/2*50
a= -493.7284/100
a= -4.937284m/s^2 (solution)
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the work function of silver metal is 6.9 × 10-19 j. if a crystal of silver is exposed to a pulse of blue light with a wavelength of 450 nm, will electrons be ejected, and if so, what kinetic energy will they have?
Determine the energy of an ultraviolet photon with a wavelength of 250 nm using E = hc/(wavelength) . After that, deduct the Cs work function energy, e* (work function in volts)
The entire mass of a nucleus is described in Section 44.1's discussion of 12C is smaller than the total of each nucleon's separate masses. The confined system's (the nucleus') energy is lower than the sum of the rest energies of the nucleon separation. The binding energy of this difference in energy the nucleus and can be understood as the additional energy required for a nucleus.
To separate it into its constituent parts. Consequently, to divide a nucleus into protons and neutrons, the system needs to be supplied with energy. Energy conservation and the mass-energy equivalence principle of Einstein demonstrate that any nucleus's binding energy, measured in MeV, is where mn is the mass of the neutral hydrogen atom and M(H) is its atomic mass.
nuclear, M(AZX) is a representation of the isotope A's atomic mass.
and the ZX Atomic mass units are used for all masses. The weight of the Z electrons in M (H) within a narrow range, cancels the mass of the Z electrons in the phrase M(AZX).
Discrepancy related to the electrons' atomic binding energy. Because
nuclear binding energies and atomic binding energies are both generally several electron volts.
With energies in the millions of electrons volts range, this difference is small.
Using the formula E = hc/(wavelength), calculate the energy of a UV photon having a wavelength of 250 nm (wavelength). Subsequently, subtract the Cs work function energy, e* (work function in volts)
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prove that cubic expansivity is equal to 3 linear expansivity
The relationship between Linear Expansivity and Cubic Expansivity is as follows: Cubic / Volume expansivity = 3 Linear expansivity
Now, consider a sheet of metal of Length (l), Breadth (b), and Height (h). Let the initial Length be (l₁), the initial Breadth be (b₁) and the initial Height be (h₁). Let the final Length be (l₂), the final Breadth be (b₂) and the final Height be (h₂) after the metal is heated through a temperature change of θ.
Considering,
the initial volume of the metal be V₁ = l₁*b₁*h₁
and, the final volume of the metal be V₂ = l₂*b₂*h₂
Then,
Using the formula of linear expansivity,
l₂ = l₁ (∝∆θ + 1 )
b₂ = b₁ (∝∆θ + 1 )
h₂ = h₁ (∝∆θ + 1 )
Remember that Volume = l * b*h
Therefore,
V₁ = l₁*b₁*h₁
V₂ = l₂*b₂ *h₂
V₂ =l₁ (∝∆θ + 1 ) * b₁ (∝∆θ + 1 ) * h₁ (∝∆θ + 1 )
V₂ = l₁* b₁*h₁ (∝∆θ + 1 ) * (∝∆θ + 1 ) * (∝∆θ + 1 )
V₂ = l₁* b₁*h₁ ((∝∆θ * (∝∆θ + 1 ) + 1 * (∝∆θ + 1 ) ) * (∝∆θ + 1 )
Let's open the brackets, now we get,
V₂ = l₁* b₁*h₁(∝²(∆θ)² + ∝∆θ + ∝∆θ + 1 ) * (∝∆θ + 1 )
V₂ = l₁* b₁*h₁(∝²(∆θ)² + 2∝∆θ +1 ) * (∝∆θ + 1 )
V₂ = l₁* b₁*h₁(∝²(∆θ)² * (∝∆θ + 1 ) + 2∝∆θ * (∝∆θ + 1 ) +1* (∝∆θ + 1 ) )
V₂ = l₁* b₁*h₁(∝³(∆θ)³ +∝²(∆θ)² + 2∝²(∆θ)² + 2∝∆θ +∝∆θ + 1 )
V₂ = l₁* b₁*h₁(∝³(∆θ)³ +∝²(∆θ)² + 2∝²(∆θ)² + 3∝∆θ + 1 )
V₂ = V₁(∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 )
Remember that ,
V₂ = V₁ ( ϒ * ∆θ + 1 )
Let us substitute for V₂ in the above formula. Then we will get,
V₁ ( ϒ * ∆θ + 1 ) = V₁(∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 )
ϒ * ∆θ + 1 = ∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ+1 (V₁ canceled V₁ and the brackets are removed)
ϒ * ∆θ = ∝³(∆θ)³ + 2∝²(∆θ)² + 3∝∆θ ( 1 cancelled 1 )
At this point,∝ tends to be zero because its value starts from 0.0000... Upward. Therefore,∝² and ∝³ are approximately zero. i.e. ∝² and ∝³ are = 0.
Therefore, we put zero in place of ∝² and ∝³. Now we get,
ϒ * ∆θ = 0*(∆θ)³ + 2*0*(∆θ)² + 3∝∆θ
ϒ * ∆θ = 0 + 0 + 3∝∆θ
ϒ * ∆θ = 3∝∆θ
ϒ = 3∝ ( ∆θ cancelled. ∆θ )
Therefore,
Cubic / Volume expansivity = 3 Linear expansivity
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pingus pingus pingus pingus pingus pingus
Answer: pingus
Explanation: pingus
Which of the following equations illustrates the law of conservation of
matter?
A. 2H₂ + O₂ → H₂O
OB. 2H₂ + 202 → 2H₂0
OC. H₂ + O2 → H₂O
D. 2H₂ + O₂ → 2H₂O
SUBMO
Answer:
Explanation:
Answer : D that’s the answer
Please help me with this
Kinetic energy is a type of energy that is present in a particle or object in motion. When work, which entails the transfer of energy, is done on an object by applying a net force, that object acquires kinetic energy.
What does the term "kinetic energy" mean?The energy of motion is known as kinetic energy, and it can be observed in the motion of a particle, an object, or a collection of particles. A person walking, a baseball being thrown, a piece of food falling from a table, or a charged particle in an electric field are all examples of moving objects that consume kinetic energy.
There are five different types of kinetic energy: radiant, thermal, acoustic, electrical, and mechanical.
The kinetic energy unit is kg m 2 /s2, or mass times the square of speed. However, the units of kinetic energy are also the units of work, or joules, which are the units of force times distance. However, force is measured as mass times acceleration, or kg m/s2 kg m/s2.The Greek verb "to move" is the root of the term "kinetic." The word has more specific definitions in the realms of art and science, but when used in a generic sense, it may simply indicate "animated," "dynamic," or "lively" linguistically. Kinetic drawings, sculptures, and installations all make use of moving parts.To Learn more About Kinetic energy here-
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Pls help with the questions in the photo, any of them will help :)
Answer: The velocity of the bird is 7m/s
Explanation: Since momentum is the total quantity of the motion which is contained in the body.
It is defined as the multiply of mass and velocity of the body
It is given in the question that mass of bird is 2.5 kg and momentum is 17.5 kg/s.
a new car is tested on a 290-m-diameter track. part a if the car speeds up at a steady 1.3 m/s2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration? express your answer with the appropriate units.
After 11 seconds the tangential acceleration becomes equal to the centripetal acceleration.
What is tangential acceleration?
Similar to linear acceleration, tangential acceleration is directed only in that direction. This has to do with rotational motion. As a result, tangential acceleration is the rate at which a particle's tangential velocity changes in a circular orbit. It always points in the direction of the body's tangent.
ac, also known as centripetal acceleration.
at is acceleration along a tangent.
The frictional force between the car wheel and the road surface supplies the necessary centripetal force when the vehicle moves in a circular motion over a curved path.
at=1.2m/sec2
The centripetal acceleration equation is given by,
ac=V2r
V2r=at
V2=at×r
V=√at×r ... (1)
Think of the equation for motion.
V=u+at×t
V=0+at×t
V=at×t
t=Vat
t=√at×ra2t
t=√rat
t=√1451.2
t=11seconds
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a 14.0-kg bucket is lowered vertically by a rope in which there is 163 n of tension at a given instant. what is the acceleration of the bucket? is it up or down?
A 14.0-kg bucket is vertically dropped by a rope with 163 n of tension at any given time. The acceleration of the bucket is upward-directed and has a value of 2.06 ms^-2.
Let's imagine that two bodies are attached by a rope, causing the system to move with an acceleration an in opposition to the force of gravity acting on one of the bodies. By dividing a body's mass (m) by the net force (F n e t) exerted on it, one can calculate the acceleration (a) of the body.
Please direct the bucket's acceleration in an upward direction.
The tension T supplied to the bucket is resisted by the weight mg acting downward, which causes the bucket to rise with an acceleration.
Applying the force balance we have as a result,
ma = T-mg
14a = 163-14 x 9.8
a = 1.84 m/s²
We can see that the acceleration is 1.84 m/s² times larger than the speed and since a has a positive sign, we can infer that the direction is upward.
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A block of mass m = 5.3 kg is pulled up a 0 21° incline as in the figure below with a force of magnitude F = 36 N.
(a) Find the acceleration of the block if the incline is frictionless. (Give the magnitude of the acceleration.)
3.28
m/s²
(b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.11. (Give the magnitude of the acceleration.)
The acceleration the block if the incline is frictionless is 3.28m/s² and the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.11 is 2.26 m/s².
what is newtons law of motion?
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
given:
mass of the block (m) = 5.3kg
angle of incline (x)= 21°
force exerted on the block up the incline (F) = 36 newtons
coefficient of kinetic friction = 0.11 u
a)
the sine component of the weight will act as the resistive force and will act against the 36 newtons force that is acting parallel to the incline.
i.e.
net force = 36 - (m × g × sin 21°)
m × net acceleration = 36 - 18.6
net acceleration = 17.4/5.3
net acceleration = 3.28 m/s²
b)
now in this case similarly the friction will also act against the intention of motion, such that:
net force = 36 - (m × g × sin 21°) - coefficient of kinetic friction ×m × g × cos 21°
net force = 36 - 18.6 - 5.33
net force = 12
net acceleration = 12/5.3
net acceleration = 2.26 m/s²
therefore, the acceleration the block if the incline is frictionless is 3.28m/s² and the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.11 is 2.26 m/s².
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A rocket is fired with an initial velocity of 100m/s at angle of 55degree above the horizontal it expodes on the mountain side 12 second after it's firing what is the x and y coordinates of the rocket relative to it's final point
The coordination of the rocket relative to its firing point is 688.32m and 277.44m.
What is coordination?
The purpose of organizing people or groups so they work together properly.
Sol-
The X and Y coordinates of the rocket relative of firing
As per the given question
Velocity (vi)=100ms-1
Angle=55.0
Time (t)=12
The horizontal range of projectile at X is
X=vxi×t
x=vi×cos×t
Now substituting the required value we get
X=300×cos 55×12
X=100×0.5756×12
X=688.32 m
Now substituting the recauird value
We get
Y= 983.04-705.6
Y=277.44m
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use triangle,parallelogram and polygon method determine the resultant vector of a) 10km left,20km up b) 150km north,50km west c) 7km east,14km north
The resultant forces in each case is;
a) 22.3 Km
b) 158 Km
c) 15.7 Km
What is the resultant force?Let us note that the resultant force is the force that would have the same effect in magnitude and direction as the the two force that are acting together.
In this case we have been asked to find the resultant of the forces and we would use the triangle method.
a) R = √(10)^2 + (20)^2
R = 22.3 Km
b) R = √(150^2) + (50)^2
R = 158 Km
c) R = √(7)^2 + (14)^2
= 15.7 Km
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the eye works similar to a camera in the sense that it has an ideal framerate for visualizing motion. for instance, the monitor on your laptop has a refresh rate of 60 hz so that image transitions look smooth to the human eye. given the formula for the frequency output of a 555 timer and using only the values you have available to you, what is a possible combination of resistors and capacitors that will get you as close as possible to this value (note: you may use resistor values that could be made if you configure a set of resistors in series or parallel)?
The brain, not the eye, is what actually sees. Information is sent from the eye to the brain, but certain aspects of the signal are lost or changed in the process.
How fast can the human eye see?The human eye can perceive between 30 and 60 frames per second, according to some scientists. Some claim that the human eye cannot actually comprehend more than 60 frames per second.
Higher rates are seen as motion by the human visual system, which can process 10 to 12 pictures per second and perceive each one separately. The majority of participants in studies see modulated light (such a computer display) as steady when the rate is more than 50 Hz.
The screen will look smoother to the human eye the higher the number. This implies that a 120Hz display, which updates itself 120 times per second, would seem noticeably smoother and more natural than your typical 60Hz screen, which refreshes itself just 60 times each second.
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A cold duck slides down a snow covered hill inclined at an angle of 35° to the horizontal. If the ducks speed is a constant 5m/s, determine the horizontal and vertical components of its velocity.
Given data:
* The angle of the inclined plane is,
[tex]\theta=35^{\circ}[/tex]* The speed of the duck along the inclined plane is v = 5 m/s.
Solution:
The diagrammatic representation of the given case is,
From the triangle ABO,
[tex]\angle ABO=180^{\circ}-\angle AOB-\angle OAB[/tex]Substituting the known values,
[tex]\begin{gathered} \angle ABO=180^{\circ}-90^{\circ}-35^{\circ} \\ \angle ABO=55^{\circ} \end{gathered}[/tex]Thus, the inclined plane makes an angle of 55 degrees with the negative of the y-axis.
Similarly, the angle of the velocity of the duck along the inclined plane with the negative y-axis is 55 degrees.
Thus, the vertical component of the velocity is,
[tex]\begin{gathered} v_y=-v\cos (55^{\circ}) \\ v_y=-5\times\cos (55^{\circ}) \\ v_y=-2.88\text{ m/s} \end{gathered}[/tex]The horizontal component of the velocity is,
[tex]\begin{gathered} v_x=v\sin (55^{\circ}) \\ v_x=5\sin (55^{\circ}) \\ v_x=4.096\text{ m/s} \end{gathered}[/tex]Thus, the horizontal component of velocity is 4.096 meters per second, and the vertical component of velocity is -2.88 meters per second.
alice and bill are at the top of a cliff of height h. both throw a ball with initial speed v0, alice straight down and bill straight up. the speeds of the balls when they hit the ground are va and vb. if there is no air resistance, which is true?
Alice and bill throw the ball with same speed [tex]V_{A}[/tex]=[tex]V_{B}[/tex].
What is the speed ?The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.
Okay, so let's imagine that there are two persons, Bob and Alice, standing on the edge of a cliff. We want to know how the speeds compare when the balls strike the ground so that as throws her ball downward at a speed of v and bill throws his ball upward at a speed of v from the same height.
Bill's will therefore rise to this height, strike 0 at that point, and then descend again. When it reaches this height, it will really be moving at the same speed as when it left Bill's hand, just in the opposite direction.
As a result, it will appear as though you tossed it straight down at the same speed, which implies When they both strike the ground, Alice's and Bill's balls will do so at the same pace.
The trajectory of Bill's ball will be symmetrical about this point in terms of the velocity or have the same speed going up as it did coming down or coming down as it did up, if you look at it because there is essentially no air resistance or anything.
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The complete question is:
"Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed v0, Alice straight down and Bill straight up. The speeds of the balls when they hit the ground are [tex]V_{A}[/tex] and [tex]V_{B}[/tex]. If there is no air resistance, which is true? A)[tex]V_{A}[/tex] <[tex]V_{B}[/tex] B) [tex]V_{A}[/tex]=[tex]V_{B}[/tex] C) [tex]V_{A}[/tex]>[tex]V_{B}[/tex] D) impossible to tell"
What is the mass of an object that has a weight of 61.1 N?
Answer:
6.23kg
Explanation:
61.1/9.8 = 6.23kg
9.8 is the amount of gravity acting on the object so divide the weight by the gravity to get mass.
The temperature of jordan lake is determined to be 13. 9ºc when an iron block is dropped in. The iron block is at 400 k and has a mass of 60 kg. Determine the heat transfer in kj of this process that is allowed to reach equilibrium.
This study reveals that only if the flow conditions in the holding tube are provided for comparison with commercial HTST systems can continuous laboratory and pilot-scale pasteurizers be utilized to evaluate the inactivation of microorganisms.
In order to make sure that laboratory or pilot-scale HTST apparatus meets the Pasteurized Milk Ordinance standards for pasteurizing milk and can be used for obtaining thermal inactivation data, we present a method in this study for calculating the fastest moving particle (FMP) and residence time distribution (RTD) in a pilot-scale high temperature, short time (HTST) pasteurizer.
The plate used in the pasteurizer had overall measurements of 75 x 115 mm, a thickness of 0.5 mm, and an effective diameter of 3.0 mm. The pasteurizer had standard hold tubes measuring 21.5 and 52.2 seconds, and its variable flow capacity ranged from 0 to 20 L/h.
FMP durations were established using tracer investigations, and flow parameters were established using RTD data. In comparison to the nominal timings of 21.5 and 52.2 s, respectively, the FMP times for the short and long holding sections using brine milk as the tracer were 18.6 and 36 s, respectively, at 72 degrees C.
According to the RTD investigation, the short hold section for whole milk at 72 degrees C had 45% back mixed and 55% plug flow.
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a stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. find the rate (in cm2/s) at which the area within the circle is increasing after each of the following.
Area of circular ripple is increasing after 2sec is 6400π cm²/s,
after 3 sec is 9600π cm²/s and after 6 sec is 19200π cm²/s
An individual who throws a pebble into a body of water will likely see a splash and hear the booming plop of the pebble. He might observe a center point where the stone struck the water, with concentric circles spreading outward from it. Other outcomes of the tossed pebble could include frightening a nearby duck that jumps out of the water, hitting another rock and rebounding, or frightening a school of fish as it sinks into the pond. The individual who throws the rock is linked to the pebble, the water, and the duck and fish through his deeds. Through a single, straightforward action, he has sparked change. The ripple effect is the term used to describe this idea in education.
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what quantity of heat energy is needed to melt 120g of ice at -20°C to water at 30°c? (SHC of water = 4200J/kg/k, SHC for ice = 2100J/kg/K, Specific latent heat of fusion of ice = 3.36x10^5 J/kg)
Answer:
59, 720 Joules
Explanation:
[tex]q = mc(t2 - t1) + m(lf) + mc(t2 - t1)[/tex]
first term=ice to 0 degrees
second term=water to ice
third term-water to 30 degrees
[tex]q = 0.12 \times 2100 \times 20 + 0.12 \times 3.36 \times {10}^{5} + 0.12 \times 4200 \times 30[/tex]
[tex]q = 59720 \: joules[/tex]
adjacent antinodes of a standing wave on a string are 15.0 cmcm apart. a particle at an antinode oscillates in simple harmonic motion with amplitude 0.850 cmcm and period 0.0750 ss. the string lies along the xx-axis and is fixed at xx
D = 15 cm , b) λ = 30.0 cm , c) 0.0850 cm, d) v = 400 cm / s , e) v = 80.43 cm / s , v = -80.43 cm / s, f) D₂= 7.5 cm
Standing waves form when two waves of the same frequency traveling in opposite directions,
A) in the waves the distance of the nodes and antinode is the same since the wavelength is constant
D = 15 cm
B) the wavelength is the distance for which the wave repeats itself, in the case of a standing wave, the distance between two nodes is the lamina of the wavelength.
D = λ / 2
λ= 15 2
λ = 30.0 cm
C) the amplitude of each wave is 0.0850 cm, and the amplitude of the standing wave is double A = 0.17 cm
D) Let's use the speed ratio
v = λ f
f = 1 / T
v = λ / T
v = 30.0 /0.0750
v = 400 cm / s
E) the transverse speeds are the speed of the oscillatory movement
y = A cos (wt)
w = 2π f = 2π / T
w = 2π / 0.0750
w = 83.78 rad / s
y = 0.850 cos (83.78 t)
Speed is
v = dy / dt
v = -A w cost wt
v = - 0.850 83.78 cos (83.78 t)
v = -80.43 cos (83.78 t)
The maximum speed when the cosine values ±1
v = 80.43 cm / s
v = -80.43 cm / s
F) if we draw a drawing, the distance between two nodes is half the wavelength, at the distance between an antinode synod is half this, it occupies a quarter of the wavelength
D₂ = ¼ λ
D₂ = 30.0/4
D₂= 7.5 cm
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sound waves have entered natalie’s ear and traveled through to her auditory nerve. what process that will now take place in which she identifies what the sound is?
Sound waves have entered Natalie’s ear and traveled through to her auditory nerve. The process of perception took place in which she identifies what the sound is.
Perception is the ability to see, hear and become aware of something through the senses.
The process of interpreting a present stimulus based on past experience is called as perceptionSound waves from the environment enter the outer ear and are directed to the ear drum
The eardrum vibrates when sound waves are received, and the vibrations are sent to the oval window through the ossicles of the ear, .
From the oval window, these vibrations are transmitted to the fluid of the cochlea, where waves are generated in the lymph.
These waves generate vibrations in the basilar membrane that bends the hair cells and push them against the tectorial membrane, and hence are sent to the brain which gives signal to the organ to react.
Hence perception is used by Natalie to react.
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A clay ball (mass = 0.25kg) has a rightward momentum of +1.75 kg∙m/s. A second clay ball (mass = 0.25 kg) has a leftward momentum of -1.75 kg∙m/s. The two collide, stick together, and come to a complete stop after the collision.1) What was the total energy of the system before the collision?a- Not enough information to determineb- 6.13 Jc- 0 Jd- 12.25 J2) What was the total energy of the system after the collision?a- 6.13 Jb- 12.25 Jc- Not enough information to determined- 0 J3) What was the total momentum before the collision?a- 6.13 kg∙m/sb- 12.25 kg∙m/sc- Not enough information to determined- 0 kg∙m/s4) What was the total momentum after the collision?a- Not enough information to determineb- 0 kg•m/sc- 6.13 kg•m/sd- 12.25 kg•m/s
1)
[tex]\begin{gathered} E1=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_1v_2^2 \\ where: \\ m_1=m_2=0.25kg \\ v_1=7m/s \\ v_2=-7m/s \\ so: \\ E1=\frac{1}{2}0.25(7^2)+\frac{1}{2}0.25(7^2) \\ E1=6.125+6.125 \\ E1=12.25J \end{gathered}[/tex]Answer:
d. 12.25J
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2)
According to the conservation of energy:
[tex]\begin{gathered} E1=E2 \\ so: \\ E2=12.25J \end{gathered}[/tex]Answer:
b. 12.25
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3)
[tex]P1=m_1v_2+m_2v_2=+1.75-1.75=0[/tex]
Answer:
d. 0 kg∙m/s
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4)
Using conservation of momentum:
[tex]\begin{gathered} P1=P2 \\ so: \\ P2=0 \end{gathered}[/tex]Answer:
b. 0 kg•m/s
it takes a car 6.o seconds to slow down to a stop, and it travels 90 meters during this time. What was its initial velocity?
The initial velocity of the car, given that it takes 6.0 seconds to slow down to a stop is 30 m/s
How do I determine the initial velocity?The initial velocity of the car can be obtained by doing the following:
First, we list out the given parameters from the question. This is given below:
Time (t) = 6 secondsDistance (s) = 90 mFinal velocity (v) = 0 m/sInitial velocity (u) = ?Finally, we shall determine the initial velocity of the car as illustrated below:
s = (v + u)t / 2
90 = [(0 + u) × 6] / 2
90 = [u × 6] / 2
90 = 6u / 2
Cross multiply
6u = 90 × 2
6u = 180
Divide both sides by 6
u = 180 / 6
u = 30 m/s
From the calculations made above, we can conclude that the initial velocity of the car is 30 m/s
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An automobile travels for 90 minutes along a highway. The graph shows the progress of the automobile, with its start point designated as distance = 0 km.
As shown on the graph, at which two points does the automobile change speed?
points P and Q
points B and P
points A and B
points A and P
The change in the speed of the automobile occurred at points A to B.
What is change in speed of an object?
The change in the speed of an object is the rate at which the distance traveled by the object changes with time.
The change in speed of the object from point O to A is calculated as follows;
ΔV = Δx/Δt
where;
Δx is change in position of the objectΔt is change in timeΔV = (5 - 0) / (15 - 0)
ΔV = 0.333 km/min
The change in speed of the object from point A to B is calculated as follows;
ΔV = (15 - 5) / (30 - 15)
ΔV = 0.67 km/min
From this we can conclude that speed of the automobile changed at points O to A, A to B and B to P.
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An airplane at 70 m/s in the direction 133 degrees counterclockwise from east. What are the east and north components of the plane's velocity?
Answer:
See below
Explanation:
East is 70 cos 133 = -47.7 m/s East
North is 70 sin 133 = 51.2 m/s North
A small plane, starting from rest, much reach a speed of 33 m/s for takeoff.
A.) How long of a runway is needed if the plane has a constant acceleration of 3.0 m/s^2 during takeoff?
B.) How much time does it take for the plane to take off?
A.) Runway has to be 181.5 long.
B.) Plane takes 11 second for the plane to take off.
What is acceleration?Change in velocity (Δv) divided by the change in time (Δt), is called acceleration that can be represented by the equation
a = Δv/Δt.
This lets you measure how fast a velocity changes in (m/s^2). Acceleration a vector quantity, that is it has both magnitude and direction
Meter per second squared is the SI unit of acceleration.
Given, a small plane must reach a speed of 33m/s for takeoff, starting from rest and constant acceleration is 3.0m/s^2
Let the time be 't'
hence,
(33-0 )/t = 3
33 = 3t
t = 11 sec
Time taken by the plane to take off is 11sec.
Average velocity = (33 + 0)/t
= 16.5 m/sec
Distance = speed * time
= 16.5 * 11
= 181.5 m
Runway has to be at least 181.15 meters long.
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a spring with an mm-kg mass and a damping constant 5 (kg/s) can be held stretched 1 meters beyond its natural length by a force of 2 newtons. if the spring is stretched 2 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping.
A spring with a damping constant 5 (kg/s) can be held stretched 1 meters beyond its natural length by a force of 2 newtons. The mass m = 3.12 kg that would produce critical damping
From hooke's law, force required to stretch the spring is
k (1) = 2
Spring Constant, k = 2
For critical damping, c²-4mk =0
m = c² / 4 k
c= damping constant (from question)
m = Mass to produce critical damping
There fore, m = (5²/4*2) = 3.12 kg
According to Hooke's law, the restoring force is equal to -kx, where k is a positive number known as the spring constant. Since c is a positive constant that is also known as the damping constant, we assume that the damping force is -c(dx/dt). Robert Hooke, an English scientist, developed the law of elasticity in 1660. According to Hooke's law, for relatively minor deformations of an item, the displacement or amount of the deformation is directly proportional to the deforming force or load.
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