1. The force of gravity on the ship at that orbit be using the early measurements be 5.435 × 10^5 N..
2. The acceleration of your lander due to gravity be 4.94 m/s^2..
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Given that:
Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.
colony ship lander has a mass of approximately 1.1x10^5 kg.
stable orbit radius of 9000000 m from the center of planet Proxima Centauri B.
1. Using Newton's Law of Universal Gravitation, the force of gravity on the ship at that orbit be using the early measurements = GMm/r²
= (6.67 × 10⁻¹¹)×(6x10^24)(1.1x10^5)/(9000000)² N
= 5.435 × 10^5 N.
2. the acceleration of your lander due to gravity: a = F/m
= 5.435 × 10^5 N/ 1.1x10^5 kg.
= 4.94 m/s^2.
3.The possible causes that would account for the difference in expected vs. actual values are:
mass distribution of the planet may not be uniform. So, the center of mass of the planet does not locate at the geometrical center.Path of orbiting does not circular, it may be elliptical.Learn more about force here:
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determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point o.
The definition of moment of inertia allows for the following results for the moment of inertia with respect to each axis:
1-Iₓ = m r²
2-Iy=9m r²
3-Iz=10m r².
What exactly is moment interia?
The expression yields the moment of interia as a scalar quantity.
Sol-
I =∫ r² dm
Where I is the moment of inertia, m is the body's mass, and r is the distance from the axis of rotation.
In the case of point particles, the expression is as follows:
I = m r²
In this case, we calculate along each coordinate axis.
a) The distance is x = r with respect to the x axis, and the moment of inertia is
Iₓ = m r²
indicate the distance in relation to the y-axis
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two particles of mass m and 3m are moving with the same speed v in a vacuum at right angles with the particle of mass m moving in the x-direction and the particle of mass 3m moving in the negative y-direction. a
The kinetic energy of the two particles will be equal if they are travelling at the same speed in a vacuum. The equation: gives the particle's kinetic energy.
KE = (1/2)mv^2
m is the particle's mass, v is its speed, and KE is its kinetic energy.
In this instance, the particle with mass m will have the following kinetic energy:
KE = (1/2)m*v^2
And the kinetic energy of the particle with mass 3m will be:
KE = (1/2)3mv^2
= (3/2)mv^2
The two equations may be made to equal one another and we can solve for v because the particles have the same kinetic energy.
(1/2)mv^2 = (3/2)mv^2
(1/2)*v^2 = (3/2)*v^2
1/2 = 3/2
Since there is no solution to this equation, two particles travelling in a vacuum cannot be moving at the same speed if one of them has a mass.
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Nuclear decay occurs according to first-order kinetics. What is the rate constant for radon-220, which has a half-life of 55. 6 seconds?.
The rate constant for radon-220, which has a half-life of 55. 6 seconds is 0.012.
We know that half life of first order reaction is : [tex]t_{1/2} = 0.693/k[/tex]
where k = rate of reaction.
Given half life = 55.6 sec
Putting this value in above equation we get k = 0.012
i.e. The rate constant for radon-220, which has a half-life of 55. 6 seconds is 0.012.
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given a diffraction grating with 300 lines per mm, what is the spacing d between lines? as- suming that the lines in the grating are manufactured with a tolerance of 1%, what is the estimated uncertainty in the line spacing d
The spacing between the lines is 3.33 X 10⁻³ mm and the estimated uncertainty in the line spacing is 3.33 X 10⁻⁵ mm.
Diffraction grating = 300 lines/mm
Thus,
The spacing between the lines = d =
= d = 1/300 lines/mm
= d = 3.33 X 10⁻³ mm
A grating consists of many slits, or lines, close together. In a grating, the spacing between adjacent lines is constant. Gratings are also used to produce interference patterns. When waves are incident on a grating all of the lines act as coherent sources of the waves.
Now, the uncertainty in the lines spacing is = Δ d =
= Δd = d (tolerance)
= Δd = 3.33 X 10⁻³ X 1%
= Δd = 3.33 X 10⁻⁵ mm
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what step in the laser printing process is responsible for conditioning the imaging drum in preparation for receiving an electrical charge?
Yes this information is correct about electrical resistance.
What is electrical resistance?Electrical resistance is a force that counteracts the flow of current.
Sol- when two lamps are connected in parallel to a battery, the total electrical resistance that the battery senses is more than the resistance of either . Beacuse In a parallel circuit each bulb is in its own circuit. As bulbs are added the resistance in the circuit decreases since each circuit is another pathway for electrons to move from one end of the circuit to the other.when two lamps are connected in series to a all the battery the electricals resistance that the battery's senses is the more than the resistence of either lamp.
As each bulb is connected in parallel to the battery of the , each has thatbsame potential difference across by to the it as the all of voltage of across the battery of to the terminals. All of other to the potential by differences are zero, as we know all the wires have to the zero resistance.
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A current-carrying ohmic metal wire has a cross sectional area that gradually becomes smaller from one end of the wire to the other. The current has the same value for each section of the wire, so charge does not accumulate at any one point. How does the resistance per unit length vary along the wire as the area becomes smaller?.
The cross-sectional area decreases, so the resistance per unit length, increases
What is resistance ?The limitation of current flow in an electrical circuit is measured in terms of resistance. The ohm, or the Greek letter omega, stands for the unit of measurement for resistance.
According to the given information
We know that
Resistance of the wire is directly proportional to length of the wire and inversely proportional to the area of the wire
So,
R ∝ [tex]\frac{L}{A}[/tex]
Proportionality constant ρ = resistivity constant
R = ρ[tex]\frac{L}{A}[/tex]
So If the cross sectional area decreases , Resistance per unit length increases
a 4 kg ball is thrown straight up in the air. what is the net force acting on the ball when it reaches its maximum height?
A 4 kg ball is launched vertically into the air. The net force exerted on the ball at its highest point is 39.24N.
What is net force?
In mechanics, the net force is the vector sum of forces acting on a particle or object. The net force is a single force that replaces the effect of the original forces on the particle's motion.
Given data
Ball mass m=4 kilogram
Gravitational acceleration is 9.81 m/s^2 , or g.
The location of the ball has no bearing on the net force applied to it in vertical projectile motion. As a result, the ball experiences a net downward force throughout its travel, and the size of this force is equal to the mass times the acceleration caused by gravity.
[tex]\begin{aligned}& F_{\text {net }}=m g \\& F=4 * 9.81 \\& F=39.24 N\end{aligned}[/tex]
Therefore, the ball is subject to a net force of 39.24 N.
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Two units of measurement for energy are calories and joules. The measurement of 355 J is the same amount of energy as ___________.
Two units of measurement for energy are calories and joules. The measurement of 355 J is the same amount of energy as 84.84 calories.
Energy in physics is the ability to perform work. Different shapes, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc., may be assumed by it. Other examples of energy being transferred from one body to another include heat and work. Energy is always distributed after it has been transported in accordance with its type. Thus, heat transfer could result in thermal energy, whereas work could result in mechanical energy.
Motion is a trait shared by all forms of energy. For instance, if a body is moving, it has kinetic energy. Due to the object's design, which incorporates potential energy, a tensioned object, like a spring or bow, has the ability to move even when at rest.
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if a household appliance is operating on 110 volts and electricity is flowing with a current of 0.2 amperes in this appliance, how many watts are consumed?
The electric power consumed by the household appliance is determined as 22 watts.
What is the electrical power consumed in the household?The electrical power consumed by the household appliance that is operating on 110 volts and whose electricity is flowing with a current of 0.2 amperes is calculated as follows;
P = IV
where;
I is the current flowing in the household applianceV is the voltage supplied to the household applianceP = 0.2 A x 110 V
P = 22 W
Thus, the electric power consumed by the household appliance is a function of current and voltage.
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(a) is positive or negative work done by a constant force f with arrow on a particle during a straight-line displacement d with arrow if the angle between f with arrow and d with arrow is 27°?
The work done by a constant force f with arrow on a particle during a straight-line displacement d with arrow if the angle between f with arrow and d with arrow is 27° is positive.
Paintings done are elaborated in one way it consists of both forces exerted on the frame and the whole displacement of the frame. This block is preceded via a steady pressure F. The cause of this force is to move the frame a sure distance d in a direct route in the direction of the force.
To express this concept mathematically, the paintings W is identical to the pressure f times the gap d, or W = fd. If the force is being exerted at an attitude θ to the displacement, the paintings completed is W = FD cos θ.
The paintings accomplished through pressure are described to be the product of thing of the pressure inside the route of the displacement and the value of this displacement. formula. work can be calculated with the aid of multiplying force and Distance in the route of pressure as follows. W = F × d.
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What can one say about the size of the magnification of a single convex mirror?
It is greater than one It is equal to one. It is less than one.
A convex mirror can never provide more than one in magnification effect. This is so because a convex mirror's image of the thing is smaller than the object itself.
When an object is held 30 cm away from a convex mirror, the image it creates is half the size of the actual object. A convex mirror is a kind of spherical mirror in which the reflecting surface is the protruded portion of the sphere; in other words, the reflecting surface of these mirrors protrudes outward in the direction of the incident light source. Enlarging something's seeming size—rather than its actual size—is known as magnification. A calculated value known as "magnification" is used to measure this enlargement.
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sort the galaxy rotation curves according to whether they would support or refute the hypothesis that galaxies are made up only of visible matter.
The claim is refuted -rotation curve 1, -rotation curve 3, -rotation curve 2 -supports Rotation Curve 4, Rotation Curve 6, and Rotation Curve 5
Curves is a particular kind of workout.You can work every significant muscle area with Curves since it combines stretching, cardio, and upper- and lower-body strength training routines. It may be done by people of all fitness levels and employs hydraulic resistance gym equipment created specifically for ladies.
To Curves, may guys go?Although males are permitted to join in some jurisdictions, Curves fitness and weight reduction facilities are focused solely on and built for women. Competitors of the clubs include Spa Lady and Lucille Roberts, two chains that cater only to women.
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initially, the translational rms speed of a molecule of an ideal gas is 461 m/s. the pressure and volume of this gas are kept constant, while the number of molecules is doubled. what is the final translational rms speed of the molecules
The stated statement states that the molecules' final maximum rate of translation is 270 m/s.
What does physics define as speed?The rate at which the position of an object shifts in any direction. Speed is described as the ratio of the area traveled to the time required to cover that distance. Time is a scalar number since it just has a heading but no magnitude.
Briefing:temperature at the start = T
v = √(3RT/M) = 467 m/s
temperature = T' later
note PV = mRT/M = NRT/NA
so NT = constant,
now N is tripled, T reduces to T' = T/3
so v will change to v' = √(3RT'/M) = v*√(T'/T) =v*√(1/3) = 270 m/s
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the resistance in a series rcl circuit is doubled. (a) does the resonant frequency increase, decrease, or remain the same? (b) does the maximum current in the circuit increase, decrease, or remain the same?
The resistance in a series rcl circuit is doubled.:
(a) The resonant frequency will decrease. The resonant frequency of an RLC circuit is inversely proportional to the total resistance. As the resistance increases, the total resistance increases and the resonant frequency decreases.
(b) The maximum current in the circuit will remain the same. The maximum current in an RLC circuit is determined by the magnitude of the source voltage and the total resistance. As the resistance increases, the total resistance increases, but the source voltage remains the same, so the maximum current remains the same.
What is resistance?
The opponents to current flowing through an electrical circuit is measured by resistance. The Greek letter omega (Ω) represents the unit of measurement for resistance, known as ohms. Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance. Ohm's Law is attributed to him as its creator.
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is the total momentum before the collision equal the total momentum after the collision. if not, what are the possible differences as to why
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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calculate the maximum force, in newtons, exerted by the blood on an aneurysm (a ballooning in a major artery), given that the effective area of the aneurysm is 18.5 cm2.
36.99N
Given
Maximum blood pressure P = 150 mm
Effective area of the aneurysm a = 18.5 cm2.
Expression for the maximum force exerted by blood on an aneurysm is,
f =P * a = (150 mm Hg* (133.322 N/m²/ 1 mmHg)) * ( 18.5 cm² * (1 m² /10000cm²)) = 36.99N
The pressure is computed as the ratio of acting force on an object and the surface area of the object where the force is directed. The pressure is usually measured in terms of Pascal and blood pressure in mm of Hg.
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light of intensity so and polarized horizontally passes through three polarizes. the first and third are horizontal, but the second is oriented 0.62832 rad to the horizontal. in terms of so , what is the intensity of the light that passes through the set of polarizers?
The Light Intensity that passes through the set of polarizers is 9.99939871 W/m
It takes complicated mechanisms to control how light moves through media. As an electromagnetic wave, light interacts with the electric charge that permeates all matter. The oscillatory motion of electric charges along a single dimension can actually be significantly restricted by creating a solid substance.As a result, charges respond to electric fields in one direction—or more specifically, to their individual components in one direction—while not responding in the opposite direction.[tex]I=icos\alpha[/tex]
I=10 cos 0.62832
=9.99939871 W/m
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a proton is at rest at the plane vertical boundary of a region containing a uniform vertical magnetic field b. an alpha particle moving horizontally makes a head-on elastic collision with the proton. immediately after the collision, both particles enter the magnetic field, moving perpendicular to the direction of the field. the radius of the proton's trajectory is 4.0 r. find the radius of the alpha particle's trajectory as a factor of r. the mass of the alpha particle is four times that of the proton, and its charge is twice that of the proton.
The radius of the alpha particle's trajectory is 4.0 r.
What is elastic collision?An elastic collision is one in which the system does not experience a net loss of kinetic energy as a result of the collision.
Given: the mass of the alpha particle is four times that of the proton, and its charge is twice that of the proton.
After elastic collision, the speed of the proton and the alpha particle will be in a ratio of 2: 1.
Let, the speed of the proton be2 v then the speed of the alpha particle be v.
So, the proton's trajectory is = 2mv/qB = 4.0 r
Hence, alpha particle's trajectory is = (4m×v)/(2qB)
=2mv/qB
=4.0 r
= 4.0r.
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during an isothermal compression of an ideal gas, 200 j of heat must be removed from the gas to maintain constant temperature. how much work is done by the gas during the process?
Work done by the gas during the process is -200J.
Work done can be defined as the product of force and distance travelled by the force.
For an isothermal process, temperature is constant and thus the heat transfer into and out of the system happens slowly so that the system is in thermal equilibrium.
Also, from the first law of thermodynamics, the change in internal energy (ΔU) of a closed system is equal to the sum of the heat transferred (Q) and the work done (W) by the system. i.e
ΔU = W + Q
The internal energy is dependent on the temperature of the system and since this temperature is constant the change in internal energy is zero (0).
i.e
ΔU = 0
putting the values in the equation of FLOT
⇒ 0 = W + Q
⇒ W = -Q
Therefore, for such process, the work done is the negative of the heat transferred (heat removed in this case).
Q = 200J
W = -200J
Therefore, the work done is -200 J
The value is negative to show that the process is a compression meaning that work is done by the surrounding on the gas.
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g a 4 kg ball is thrown straight up in the air. what is the net force acting on the ball when it reaches its maximum height? what is the ball's acceleration at this point?
The weight of the ball is the only force pushing down on a ball that has been tossed into the air approximately half its maximum height.
How does science define force?At this point, referring to a force as a push or a pull is perfectly appropriate. An object does not "have in it" or "contain" a factorOne thing experiences a force from another. The idea of a force encompasses both living and non-living things.
What is an example of force?An illustration would be to push or forcefully shove a door. As a vector quantity, effort has both magnitude and a direction.. According to Newton's second law, force equals the "net of a body's natural mass and acceleration."
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a 915 kg car goes over a hill of circular arc. if the radius of the curve is 43 m, how fast can the car travel without leaving the road at the top of the arc?
The car can travel at 20.5 m/s (74 km/hr). Any faster, and it will leave the road.
What is speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object travels along a path. In other words, velocity is a vector, whereas speed is a scalar value.
According to the question:
Two forces—gravity and the normal force of the road—are acting on the car as it crests the hill. These combined exert a net centripetal force, which will cause the car to travel in a circular arc.
[tex]$$\vec{F}_c=\vec{F}_g+\vec{F}_N$$[/tex]
Next, realize that "without leaving the road" actually refers to "just at the point where the car is going to leave the road" and that this corresponds to the condition FN = 0.
This means that our equation becomes
[tex]$$F_c=F_g$$[/tex]
and that gravity alone will determine the radius of the path the car will follow.
Substituting [tex]$F_c=\frac{m v^2}{r}$[/tex] and [tex]$F_g=m g$[/tex], we get
[tex]$$\frac{m v^2}{r}=m g$$[/tex]
Since we don't observe small, light automobiles flying airborne more frequently than larger ones, we can cancel the mass, which means that all cars traveling at this speed will follow the same course regardless of mass.
[tex]$$\begin{aligned}& \frac{v^2}{r}=g \\& v=\sqrt{g r}\end{aligned}$$[/tex]
After Substituting the values:
[tex]$$v=\sqrt{(9.8)(43)}=20.5 m/s}$$[/tex]
So, the car can travel at 20.5 m/s (74 km/hr).
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a noisy machine in a factory produces a decibel rating of 72 db. how many identical machines could you add to the factory without exceeding the 85 db limit?
There are 10 identical machines could you add to the factory without exceeding the 85 dB limit.
Calculation:-
sound leve in decibel is:
β dB = 10 log ( I / Io )
where I is the intensity of sound
It is the relative intensity
72 = 10 logs ( I /10⁻¹²)
8 = log ( I /10⁻¹²)
10⁸ = I / 10⁻¹²
I = 10⁸ . 10⁻¹² = 10⁻⁴ W /m2
If the sound level is 85 dB, the number of identical machines is n.
85 = 10 logs ( n I / Io )
= 10 logs ( n . 10⁻⁴ / 10⁻¹² )
9 = log ( n . 108 )
10⁹ = n. 10 8
n = 10.
so n = 10 .
Sounds below 70 dB are considered safe for hearing. This is the sound of a normal conversation between two people. A noise level of 80 or 85 dB will damage your hearing over time. 70 decibels is as loud as a washing machine or dishwasher. Medium noise level. 70 dB of noise is not considered harmful to human hearing.
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A glass has some ice and some liquid water in it. What happens if this glass is heated?.
If this glass is heated ice will turn into water
Explain forms of water.
Ice, water, and gas are all forms of water that can exist (vapour or gas). Ice, a solid, can melt into water with the addition of heat (a liquid). Ice forms when heat is removed from water, a liquid (a solid). We refer to a shift in a substance's state as occurring when liquid water becomes a solid or a gas. The molecules of the water don't change, even when its physical appearance does.
Solid water is what an ice block is. The ice turns into liquid water when heat (an energy source) is introduced. It's melted since it's at 0 degrees Celsius. If you keep heating the water, it will transform into water vapour, which is water that has turned gaseous.
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brainly a child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25°. what is the maximum speed of the child as she swings?
Maximum speed of the child as she swings is 2.23 m/s.
Step by Step Calculation:T=3.3 s is the oscillation's time period.
The swing's greatest angle is 25° (max).
The swing's bottom will have the following kinetic energy:
k=12mv2...........(1)
The mass in this situation is m, and the speed is v.
The potential energy change is expressed as,
∆U=mgL1-cosθmax...............(2)
Here, L is a string's length and g is the acceleration caused by gravity. L is given as,
L=gT24π2
Combine equation (1) with (2)
12mv2=mgL1-cos, maxv=2g, maxv=gT24, maxv=g2T22, maxv=9.8 m/s
22.33 m/s, 22.31 s22.31 cos25°
Therefore, the child's top speed is 2.23 m/s.
What is Oscillation ?The process of any quantity or measure fluctuating repeatedly about its equilibrium value in time is known as oscillation.A periodic change in a substance's value between two values or around its central value is another way to define oscillation.To learn more about Oscillation refer to:
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A pulse is created on a spring with a fixed end. What happens to the wave after it hits the fixed end? a. It reflects, remains upright, and maintains the same velocity. B. It reflects, inverts, and maintains the same velocity. C. It reflects, remains upright, and changes velocity. D. It reflects, inverts, and changes velocity.
It reflects, inverts, and maintains the same velocity.
What is velocity?
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
"It reflects , reverts and maintains the same velocity" is the one among the following that describes what happens to the wave after it hits the fixed end. The correct option among all the options that are given in the question is the second option or option "b". I hope the answer has come to your help.
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a projectile is thrown upward with speed v by the time its speed has decreased to 3v/4 it has risen a height h what is the maximum height reached by the projectile if it is projected at an angle of 60 with the horizontal
The maximum height attained by the projectile in terms of h is 12h/7.
What is the maximum height reached by the projectile?
The maximum height attained by the projectile is calculated by applying the following formula as shown below.
H = v² sin²θ / 2g
where;
v is the initial speed of the baseballg is the acceleration due to gravityθ is the angle of projection of the ballH = ( v² ( sin 60 )² ) / 2g
H = ( v² x ³/₄ ) /2g
H = 3v² / 8g
To solve for the maximum height attained by the projectile in terms of h is calculated as follows;
vf² = vi² - 2gh
2gh = vi² - vf²
h = (vi² - vf²) /2g
where;
vi is the initial velocity of the projectile = vvf is the final velocity of the projectile = 3v/4g is acceleration due to gravityh = (v² - (3v/4)²) / 2g
h = (v² - 9v²/16) / 2g
h = (7v²/16) / 2g
h = 7v² / 32g
7v² = 32gh
v² = 32gh/7
The maximum height becomes;
H = 3v² / 8g
H = 3(32gh / 7) / 8g
H = (3 x 32 gh) / (7 x 8g)
H = 12 h / 7
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A descending elevator of mass 1,000 kg is uniformly decelerated to rest over a distance of 8 m by a cable in which the tension is 11,000 N. The speed v_1 of the elevator at the beginning of the 8 m descent is most nearly (A)4 m/s (B) 10 m/s (C) 13 m/s (D) 16 m/s E) 21 m/s
The speed [tex]V_{i}[/tex] of the elevator at the beginning of the 8 m descent is nearly 4 m/s. Hence, option A is the correct answer.
We are given that-
the mass of the elevator (m) = 1000 kg ;
the distance the elevator decelerated to be y = 8m ;
the tension is T = 11000 N;
let us determine the acceleration 'a' by using Newton's second law of motion.
∑Fy = ma
W - T = ma
(1000kg x 9.8 m/s² ) - 11000N = 1000 kg x a
9800 - 11000 = 1000
a = - 1.2 m/s²
Using the equation of kinematics to determine the initial velocity.
[tex]V_{f}[/tex] ² = [tex]V_{i}[/tex]² + 2ay
[tex]V_{i}[/tex] = √ ( 2 x 1.2m/s² x 8 m )
[tex]V_{i}[/tex] = √19.2 m²/s²
[tex]V_{i}[/tex] = 4.38 m/s ≈ 4 m/s
Hence, the initial velocity of the elevator is 4m/s.
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A long narrow uniform stick of length D and mass ms = m lies motionless on frictionless surface of ice puck of mass Mlp m slides without spinning on the ice with a velocity Vo toward the stick; collides elastically with one end of the stick, and rebounds in the opposite direction with velocity Vf After the collision, the center of mass of the stick moves with velocity V$, and the stick rotates about the center of mass with angular velocity Ws . Throughout the process, from finite time before the collision to finite time after the collision, the angular momentum of the rod and puck system is constant bout which of the following points? Select that apply; The center of mass of the rod-puck system The center of mass of the rod The center of mass of the puck The fixed point on the ice where the center of mass of the system was located when puck collided with the rod Any fixed point in space Angular momentum is not constant around any point
Throughout the process, from a finite time before the collision to a finite time after the collision, the angular momentum of the rod and puck system is constant about any fixed point in space.
The condition of conservation of angular momentum of a system about a point is that net torque about that point of the system must be zero. The point that has zero net torque is any fixed point in space.
τ = I α
I = L / ω
τ = L ω / ω t
τ = L / t
Since L is constant, τ = 0
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a 1,325 kg car rolls from rest down a 10.0 m tall hill. it then moves across a level surface and runs into a spring-loaded
To find maximum spring compression we assume no energy losses due to friction.
Here, the initial and final kinetic energy of the car is zero.
We know that, Total Energy= kinetic energy+ Potential Energy
Since the initial and final kinetic energy of the car is zero, here initial potential energy of the car-spring-earth system completely converts to elastic potential energy.
By the law of conservation of energy,
K1 +U1 = K2 + U2
i.e, (KE+PE, + PE) = (KE + PEg+PES) =
Here KE=0 and Potential energy after reaching ground(PE, = 0) =
0 + mgh + 0 = 0+0+1/2kx- 0
mgh = (1/2kx2) =
2= 2mgh/k
mg = 1325.(9.8) = mg = 1325.(9.8) = 12985N ) = =
We can round off 12985N to 13000N for easy calculation.
-2 2 = 2 * 13000 * 10 1.0 * 106 0.51m
(b) To find the maximum acceleration of the car after contact with the spring,
We apply Newton's 2nd law,
ma= (-kx = )
a = (-kx/n -m)
Multiply the above equation with g/g
a = a= (-kug/mg) = (-kxg/u
a = -(1.0 * 10%) * (0.51) * (9.8)/13000 = -380m/s? = *
a = 380m/s
A level curve is a plane curve where f has a constant value. A plane is a surface in XYZ space where f has a constant value. A level curve or surface is sometimes called a level set. The plane is the equipotential surface of the Earth's gravitational field. It is a curved surface and all its elements are perpendicular to the vertical line.
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he three blocks (from left to right in the figure) have masses of 3.38 kg, 0.702 kg and 7.80 kg. the leftmost block has a velocity of 3.51 m/s toward the right, the center block is stationary, and the rightmost block as a velocity of 2.79 m/s toward the left. assuming movement toward the right is positive, what is the velocity of the center-of-mass of this system as pictured (prior to collision)? give your answer with the appropriate sign.
-0. 833m/s is the velocity of the centre-of-mass of this system, prior to the collision.
What is Centre-of-mass?
The unique location where the weighted relative position of the distributed mass accumulates to zero is known as the centre of mass of a distribution of mass in space (also known as the balance point). At this location, a force can be applied to produce a linear acceleration alone, not an angular acceleration.
What is Collision?
In physics, the abrupt, violent meeting of two bodies in direct contact is referred to as an impact. Examples of such bodies are two pool cues, a golf club and a ball, a hammer and a nail head, two railroad cars when linked, or a falling object and a floor. The force and the amount of time the objects are in touch, in addition to the materials the two objects are made of, have an impact on the outcome of the impact. It is generally knowledge that a hard steel ball dropped on a steel plate would rebound almost to the original position from where it was dropped, while a ball made of putty or lead will not.
What are the Calculations?
There are typically 3 masses named
m1= 3.38kg
m2= 0.702kg
m3= 7.80kg
Here m2 stays stationary hence its velocity (v2= 0)
Let the final velocity be V
Value of m1 + m2 + m3 = 3.38 + 0.702 + 7.8 = 11.882kg
A/Q V= m1v1/11.882 + m2v2/11.882 + m3v3/11.882
m1v1/11.882= 3.38 * 3.51/11.882= 0.998
m3v3/11.882= 7.8 * (-2.79) /11.882= -1. 831 ( here -ve sign is taken as the velocity of m3 is towards the left which is negative)
Hence, after simplifying V= m1v1/11.882 + m2v2/11.882 + m3v3/11.882 the final answer is -0. 833m/s
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