The speed of the three couple car after the collision is 1.8 m/s and the total loss in kinetic energy of the system during the collision is 2.16 x 10⁴ J.
The mass M of the each railroad car is given to be 2 x 10³ kg and the speed U of the each railroad car is 3m/s. The speed V of the coupled car is given to be 1.20 m/s.
(a) According to the law Conservation of Linear Momentum, the linear momentum before and after the collision is always conserved.
So, we can write here,
MU + 2MV = (M+2M)V'
Where,
V' is the speed after collision.
U + 2V = 3V'
V' = (U+2V)/3
V' = (3+2.4)/3
V' = 1.8m/s.
(b) The loss in kinetic energy of the system can be calculated as,
∆K = final kinetic energy - initial kinetic energy
∆K = (1/2MU²+1/2×2MV²) - 1/2 × 3MV'²
Putting values,
∆K = (0.5×2.00×10⁴×(3.00)2+0.5×2(2.00×10⁴)(1.20)2)−0.5×3(2.00×10⁴)(1.8)2
∆K = 2.16 x 10⁴ J.
So, the loss in kinetic energy of the system after the collision is 2.16x10⁴ J.
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two 20.-nwewton forces act concurrently on an object. What angle between these forces will produce a resultant force with the greatest magnitude?
These forces will produce a resultant force with the greatest magnitude when angle between them is 0° .
What is force?When an object with mass is pushed or pulled, it changes its velocity, according to the definition of force in physics.
Force is an external agent that has the power to alter a body's resting or moving condition. It has a size and a movement. The direction of the force is referred to as the force's direction, and the application of force is the place at which the force is applied.
Given that: two 20. newton forces act concurrently on an object.
If the angle between the forces is α then resultant force be:
= √(20² + 20² +2.20.20cosα)
Hence, these forces will produce a resultant force with the greatest magnitude when angle between them is 0° and the the greatest magnitude of resultant force be 40 N.
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Sound 1 has an intensity of 40.0 W/m^2 . Sound 2 has an intensity level that is 2.0 dB greater than the intensity level of sound 1.
What is the intensity of sound 2?
l2= ? W/m^2
The intensity level of sound 2 is 63.386 W/m².
Intensity of sound 1 = 40.0 W/m²
Intensity of sound 2 = 2.0 dB
We know that I₁ = 10⁻¹² W/m²
Intensity level of sound 2 =
= Using the equation of the sound level intensity
= Iₓ = 10log (I/I₁)
= Iₓ = 10 log(40/ 10⁻¹²)
= Iₓ = 136.02 dB
Given that intensity of sound 2 is greater than sound 1 by 2.0 dB
Thus,
= Iₙ = 136.02 + 2.0
= Iₙ = 138.02 dB
To calculate intensity of sound 2 =
= I₂ = 10log(Iₙ / 10⁻¹²)
= I₂ = 63.386 W/m²
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Two charged particles repel each other with a force f. If the charge on only one of the particles is doubled and the distance between them is also doubled, then the force will be.
With a force of f, two charged particles repel one another. The force will be F/2 if only one particle's charge is doubled and the distance in them is likewise doubled.
What does the word "force" mean in science?A force of this magnitude can be described as a push or a pull, which is perfectly fine. A force does not "exist in" or "contain" an object. A force from another can exert pressure on something. The concept of a force makes no distinction across living creatures and inanimate objects.
what is In one words, define force.The definition of force is an external cause that, when applied, modifies or tends to modifies the state of the body. The body comes to rest while it is in motion, and it will go into motion when it is at rest.
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A 10.0 kg block is released from rest down a 30° ramp.
It slides 6.0m along the ramp against a frictional force
of 16N. What is its speed after sliding 6.0m along the ramp?
*SOLVE USING ENERGY
Answer:
6.298 m/s
Explanation:
[tex]F_{net} =ma[/tex]
[tex]F_F=u_k*F_N[/tex] friction force equation
[tex]ma=mgsin(x)-umgcos(x)[/tex]
We are given
[tex]m=10\\g=9.81\\F_F=16\\V_i=0[/tex]
[tex]umgcos(x)=F_F[/tex]
[tex]u*10*9.81*cos(x)=16[/tex]
[tex]u=0.18833036[/tex]
[tex]ma=mgsin(x)-umgcos(x)[/tex]
[tex]10*a=10*9.81*sin(30)-0.18833036*10*9.81*cos(30)[/tex]
[tex]a=3.305[/tex]
[tex]V_{f} ^{2} =V_{i} ^{2}+2ax[/tex]
[tex]V_{f} ^{2} =0 ^{2}+2*3.305*6[/tex]
[tex]V_f=6.298[/tex]
what is the difference between the pressure on the bottom of a pool and the pressure on the water surface?
Due to the weight of the water on the body that is submerged, the pressure is higher at the bottom and lower at the surface.
How does pressure change with ocean depth?Our bodies experience a 14.7 pound per square inch air pressure while we are at sea level. Since your body's internal fluids are also pushing outward with equal force, you cannot feel it.But if you go even a few feet under the surface of the water, something changes. The pressure in your ears is getting worse. The hydrostatic pressure, or the force a liquid exerts on an object per unit area, has increased, which is the cause of this. The pressure of the water pressing down on you increases the deeper you go under the water. As you descend, the pressure rises by one atmosphere for every 33 feet (10.06 meters).Numerous sea creatures can withstand high pressure with no problems at all. Because of their more flexible bodies, whales, for example, can withstand extreme pressure changes. The loose, bendable cartilage that holds their ribs together prevents their rib cage from collapsing at pressures that would easily snap our bones.In order to prevent rupturing, a whale's lungs can also safely collapse under pressure. As a result, sperm whales can now go in search of giant squid at depths of up to 7,000 feet.To Learn more About pressure refer to:
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PLEASE HELP WILL MARK BRAINLIEST IF YOU EXPLAIN HWK YOU GOT THE ANSWER!!!!
Answer:
A A A A. a. a a a a a a a
Explanation:
a is the answer
in the figure, unpolarized light with an intensity of 28.0 w/m^2 is sent into a system of four polarizing sheets with polarizing directions at angles
Intensity of light is a measurement of the amount of power either emitted or reflected by a source, and it can be calculated using either the total wave output, luminosity, or brightness. passing through polarized sheets
How to calculate intensity of light passing through polarized sheet ?
The intensity of unpolarized light , Iⁿ = 28 W/m²
The intensity of light passing through, I¹= 0.5 × Iⁿ
I¹ = 14 W/m²
The intensity of light passing through the second polarizer , I² = I¹ × (cos(theta1 + 90 - theta2) )²
I² = 14 × cos^2(40 + 90 - 20) W/m²
I² = 1.64 W/m²
The intensity of light passing through the third polarizer , I³ = I²× (cos(180 - theta2 - theta1) )²
I³ = 1.64 × cos^2(180 - 20 - 20) W/m²
I³= 0.962 W/m²
The intensity of light passing through the fourth polarizer , I⁴= I³ ×(cos(theta3 + 90 + theta4) )²
I⁴ = 0.962 * cos^2(28 + 90 + 20) W/m²
I⁴ = 0.53 W/m²
The intensity of the light that emerges from the system is 0.53 W/m²
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The supplied statement states that perhaps the system's light output has a 0.53 W/m² intensity.
What does intensity mean according to science?The rate at which a wave moves over just a substrate in a given amount of time and space is referred to as its intensity. It is additionally equal to the wave speed times the power density. It is commonly evaluated in Watts per square meter. The intensity of a beam depends on its height and power.
Briefing:Here,
The intensity of unpolarized light , I0 = 28 W/m²
The brightness of the light that comes through I1 = 0.5 * I0
I1 = 14 W/m²
Light output through to the second polarizer, measured in intensity,
I2 = I1 * (cos(∅1 + 90 - ∅2) )²
I2 = 14 * cos²(40 + 90 - 20) W/m²
I2 = 1.64 W/m²
Light output through the third polarizer, in terms of intensity I3 = I2 * (cos(180 - ∅2 - ∅1) )²
I3 = 1.64 * cos²(180 - 20 - 20) W/m²
I3 = 0.962 W/m²
The fourth polarizer's ability to intensify light,
I4 = I3 * (cos(∅3 + 90 + ∅4) )²
I4 = 0.962 * cos²(28 + 90 + 20) W/m²
I4 = 0.53 W/m²
The process delivers sunlight that has a 0.53 W/m² intensity.
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The complete question is-
In the figure, unpolarized light with an intensity of 28.0 W/m2 is sent into a system of four polarizing sheets with polarizing directions at angles θ1 = 40.0˚, θ2 = 20.0˚, θ3 = 20.0˚, and θ4 = 28.0˚, What is the intensity of the light that emerges from the system?
As you watch the video, notice that the size of the tidal bulges varies with the Moon's phase, which depends on its orbital position relative to the Sun. Which of the following statements accurately describes this variation?
Low tides are lowest at both full moon and new moon.
Low tides are highest at both full moon and new moon.
High tides are highest at full moon and lowest at new moon.
Low tides are highest at full moon and lowest at new moon.
High tides are highest at both full moon and new moon.
High tides are highest at first- and third-quarter moon.
The size of the tidal bulges increases as the Moon moves closer to the Earth in its orbit, when it is in the new moon or full moon phase, and decreases as it moves away from the Earth in its orbit, when it is in the first quarter or third quarter phase.
What is tidal bulges?
The fluid and moveable ocean water is drawn towards the moon by the gravitational influence between the moon as well as the Earth. The ocean closest to the moon experiences a "bulge" as a result, as the Earth rotates, the affected waters' locations shift. Imagine the moon as just a magnet drawing the water to it. The force of intertia, which tends to keep an object moving inside a straight line, opposes this motion of the water in the direction of the moon. Our oceans' motion is balanced by this, but since the gravitational pull seems to be stronger, the resulting force also creates our tides.
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if a river has an average width of 15 m, an average depth of 5 m, and is flowing with a velocity of 2 m/s, what is its discharge?
According to the given statement a river has an average 3 * 10⁵ W is its discharge.
What is velocity definition with example?The scalar metric of speed and direction of motion is known as velocity. The speed that an object goes in one side is known as its velocity. Speed may be used to calculate both the vehicle speed traveling north just on main freeway and the velocity of a explosion bursting in space.
Briefing:Water's speed is 2 m/s.
Flow area = 5m x 15m = 75m²
Water has a density of 1000 kg/m³
The volume of water flowing per second in the continuity equation is written as v=Av.
Hence, mass of water m=vρ=Avρ
K.E. = 1/2 mv² = 1/2 Avρ²
K.E. = 1/2 Avρ³
ρ = 1/2 Avρ³
ρ = 1/2 * 75 * (2)³ * 1000
ρ = 3 * 10⁵ W
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four resistors of 3.40 ohms, 6.54 ohms, 8.32 ohms, and 1.34 ohms are connected in parallel with a 12.0 v battery. find the total resistance, in ohms, of the circuit.
The total resistance of the four resistors connected in parallel is 0.762 ohms.
How to calculate the total resistance of resistors connected in parallel?To calculate the total resistance of the four resistors connected in parallel, we use the formula below.
Formula:
1/R' = 1/R₁+1/R₂+1/R₃+1/R₄............ Equation 1Where:
R' = Total resistance of the resistors in parallelR₁, R₂, R₃, R₄ = The resistance of the four resistors in parallel.From the question,
Given:
R₁ = 3.4 ohmsR₂ = 6.54 ohmsR₃ = 8.32 ohmsR₄ = 1.34 ohmsSubstitute these values into equation equation 1
1/R' = 1/3.4+1/6.54+1/8.32+1/1.341/R' = 0.294+0.153+0.12+0.7461/R' = 1.313R' = 1/1.313R' = 0.762 ohmsHence, the total resistance is 0.762 ohms.
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The internal energy within a system associated with the motion of particles and that can be added to a substance is called _____. (1 point).
Answer: The internal energy within a system associated with the motion of particles and that can be added to a substance is called kinetic energy.
Reason:
Internal energy U of a system or a body with well-defined boundaries is the total of the kinetic energy due to the motion of molecules and the potential energy associated with the vibrational motion and electric energy of atoms within molecules.
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a single conducting loop has a radius equal to and carries a current equal to what is the magnitude of the magnetic field on the line through the center of the loop and perpendicular to the plane of the loop
On a current loop, a uniform magnetic field has a net torque but no net force. Let's assume that the magnetic field is parallel to both sides of the loop's two sides and is in its plane. The force on the left and right sides of the loop, if it has width a, height b, and current I, is given by F = IbB. Due to the field's parallel alignment with those other sides, they are not subject to any force.
No net force exists because the two forces are acting in opposite directions, but there is a torque that tends to cause the loop to rotate about an axis that passes through its center. This axis's torque is given by:
τ = F (a/2) + F (a/2) = Fa = IabB.
The area vector is perpendicular to the plane of the loop, so = IAB. Another right-hand rule can be used to determine its direction: curl your right hand's fingers in the direction of the current, and point your thumb outward so that it faces the direction of the area vector.
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an outside loudspeaker (considered a small source) emits sound waves with a power output of 102 w. (a) find the intensity 12.4 m from the source.
The calculated value is 5.6 m. Much more frequently than sound intensities in watts per square meter, sound intensity levels are expressed in decibels (dB).
Both the scientific literature and the public media use decibels as their preferred measurement unit. The rationale behind this decision of units has to do with how we hear. Noise exposure is harmful to the hearing, and it is normal for musicians to suffer from hearing loss that is so severe that it affects their ability to play. Sound intensity, a term that applies to all noises, whether or not they are heard, is the pertinent physical quantity.
We are given Δp, so we can calculate I using the equation I=(Δp)22ρv . Using I , we can calculate β straight from its definition in β (dB)=10 log10(II0) β (dB)=10 log10(II0) .
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if an astronaut knocks a wrench off the outside of the space shuttle (while in space) while she is doing a repair job, the wrench will continue moving in the same direction. which of newton's laws of motion will the wrench demonstrate?
The Newton's first law is demonstrated over here.
If the wrench is thrown then that wrench will keep on moving in the space.
As we all no space has no gravity and since there is no gravity, hence, no force is applied on that body.
The wrench will move freely in the space and will continue to move in same direction until there is some external force is applied to stop or change its direction.
This shows that over here the Newton's first law is applied.
The Newton's first law states that the body will continue to be in the same state or motion and will not change until the external force is applied on it.
This Newton's first law is also known as law of inertia.
Therefore, the wrench will continue to move in the same direction under the influence of Newton's first law.
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There are three forces acting on the foot as shown in the
figure. The foot mass is 450 g.
The foot is in equilibrium, calculate the muscle force on
the calcaneus.
The muscle force on the calcaneus is -14.41 N
What is force?Forces are external factors that change the state of the body at rest or in motion. It has size and direction. The direction in which the force acts is called the direction of the force, and the point at which the force acts is called the point of action of the force. It's SI unit is the Newton (N). A force vector F has magnitude, direction, and orientation.
As the foot is in equilibrium it means that the net force is zero, the equation for this system is as follows:
N + F + W = 0
-N -F = W
Where,
N = Normal (10 N)
F = Muscle force
W = Weight
W = m × g
W = 0.45 × 9.8
W = 4.41 N
Now substitute the values in following equation:
-N -F = W
-10 -F = 4.41
-F = 4.41 + 10
-F = 14.41
F = -14.41 N
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when a submarine dives to a depth of 120 m, to how large a total pressure is its exterior surface subjected? the density of seawater is about 1.03 g/cm3.
Data provided in the question:
Initial depth of the submarine, d = 120 m
Density of water, ρ = 1.03 kg/m³
Now,
Pressure due to water = ρgh
here,
g is the acceleration due to gravity = 10 m/s²
h = height of water above
So,
Increase in pressure = ρgD - ρgd
= ρg(D - d)
= 1.03 × 10 × (120)
= 1236 Pa
Therefore, the total pressure of the submarine is 1236 Pa.
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a parallel-plate air capacitor of capacitance 245 pf has a charge of magnitude 0.148/lc on each plate. the plates are 0.328 mm apart. (a) what is the potential difference between the plates? (
The potential difference between the plates of a parallel-plate air capacitor of capacitance 245 pf has a charge of magnitude 0.148 μC on each plate is 604 V
Q = C V
Q = Charge
C = Capacitance
V = Potential difference
Q = 0.148 μ C
Q = 0.148 * 10⁻⁶ C
C = 245 pF
C = 245 * 10⁻¹² F
V = Q / C
V = ( 0.148 * 10⁻⁶ ) / ( 245 * 10⁻¹² )
V = 604 V
Voltage, also known as electric pressure, electric tension, or potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points.
Therefore, the potential difference is 604 V
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a 10 kg mass slides from an initial velocity of 20 m/s to rest over 30 m. what is the force of friction?
Force of friction is 0.167
What is friction?The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.
What is importance of friction?Things can move more slowly and become immobile when there is friction. In a world without friction, more things would slide around, it would be challenging to keep shoes and clothing on, and it would be extremely challenging for people or cars to move or turn.
According to the given information :
Mass=10 kg
Initial velocity(u)=20m/s
F=−μN
ma=−μmg
a=−μg
Distance travelled force coming to rest=30m
v²−u²=2as
0²−u²=2as
−u²=−2μgs
μ=(10)²/2×10×30=1/6=0.167
μ=0.167
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a boat is traveling at 54 knots in a direction of 48°. it encounters wind moving at 14 knots in a direction of 20°. what is the true velocity and direction of the boat? round to the nearest whole number.
The true velocity and direction of the boat is 67knots, 42degree.
Velocity is the directional pace of an item in motion as an indication of its rate of exchange in the role as determined from a selected frame of reference and as measured by way of a selected standard of time.
Average velocity is calculated by means of dividing your displacement (a vector pointing out of your initial role in your final position) through the entire time; the average pace is calculated by way of dividing the overall distance you traveled by means of the total time.
Calculation:-
velocity of boat = 54 knots
direction = 48°
wind speed = 14 knots
direction = 20°.
The true velocity and direction of the boat is 67knots, 42degree
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Answer:
67 knots; 42°
Explanation:
I took the test and got it right:)
now the switch for coil 1 has been closed for a long time. which direction is the induced current in coil 2 through the current meter while the switch for coil 1 stays closed?.
This causes a force to be exerted on the electrons in coil 2, resulting in induced current flowing in the opposite direction.
What is force?
A force is indeed an influence that can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both direction and magnitude. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.
The induced current in coil 2 will be in the opposite direction as the current in coil 1. This is because when the switch for coil 1 is closed, current will start flowing through coil 1. This will create a magnetic field around coil 1, which intersects with the magnetic field around coil 2. This causes a force to be exerted on the electrons in coil 2, resulting in induced current flowing in the opposite direction.
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an 8.0-newton wooden block slides across a horizontal wooden floor at constant velocity. what is the magnitude of the force of kinetic friction between the block and the floor?
Answer:
2.4 n
Explanation:
The force of kinetic friction between the block and the floor is given by:
where
is the coefficient of kinetic friction
N is the normal reaction of the floor against the block
For a horizontal surface (as in this case), the normal reaction is equal to the weight of the block, so . For wood-wood contact, the coefficient of kinetic friction is approximately . Therefore, the force of kinetic friction between the block and the
A 2.00-kg rock has a horizontal velocity of magnitude 12.0 m/s when it is at point P in the figure (Figure 1). (a) At this instant, what are the magnitude and direction of its angular momentum relative to point O? (b) If the only force acting on the rock is its weight, what is the rate of change (magnitude and direction) of its angular momentum at this instant?
The rate of change (magnitude and direction) of its angular momentum at this instant is 115 kg m/s².
The rate of change of angular momentum is equal to the net torque acting on the rock. The only force acting on the rock is the weight of the rock that is, mg.
As torque is equal to the product of the tangential component of force (
and distance (r) from the axis of rotation to the line of force, the net torque acting on the rock is,
Here, r is the distance from point O to the line of force.
This torque is equal to the rate of change of angular momentum of the rock.
Calculation:-
torque = mgcosθ
τ = mgrcosθ
= 115 kg m/s²
The magnitude of angular momentum is 115 kg m/s².
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If the electron were replaced with a proton moving with the same velocity, how would the resulting acceleration of the particle change?.
The resulting acceleration of proton, compared to the electron's acceleration is in the opposite direction and at a similar rate.
What is resulting acceleration of particle change ?Acceleration is a vector quantity that has elements in both the x- and y-axes. The final acceleration of the item can be calculated by calculating the vector's magnitude and direction.
The proton will accelerate in the opposite direction and at a similar rate because its mass is greater than that of the electron. The acceleration of the proton, however, is less than that of the electron.
In conclusion, the proton's subsequent acceleration would be smaller in amplitude and in the opposite direction from the electron's.
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the 5.2 kg mass and spring are moved to a frictionless 30 degree incline, and positioned so that he psring is parlelle to the incline. determine the spring's new dpslacement at equilibrium
The displacement would be approximately 2.83 meters.
What is displacement?
A displacement is indeed a vector in geometry as well as mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It measures the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the juncture trajectory. The translation that links the starting point and the ending point can be used to spot a displacement. The finishing position xf of the a point relative towards its initial position xi, or a physical location (resulting from of the motion), is another way to describe a displacement. The difference between both the final and initial positions can be used to define the corresponding displacement vector:
The spring's new displacement at equilibrium depends on the angle of the incline. Since the incline is 30 degrees, the displacement of the spring at equilibrium can be found by using the following equation:
Displacement = (mass * gravity * sin(incline angle)) / spring constant
In this case, the displacement would be (5.2 kg * 9.8 m/s2 * sin(30))/ spring constant. Plugging in the values we know, the displacement would be approximately 2.83 meters.
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Two identical blocks are pushed up frictionless inclines as shown. Consider the portion of the motion of block 1 during which it moves a distance L1, and the portion of the motion of block 2 during which it moves a distance L2. Each block is displaced the same vertical distance Z.The hand pushes parallel to the incline with same magnitude of force FBH in both cases. Block 2 moves at a decreasing speed. Is the absolute value of the work done by the gravitational force on block 2 greater than, less than, or equal to the work done by the gravitational force on block 1? Explain.
The answers to these questions are:
The absolute value of the work done by hand on block 1 is less than the absolute value of the work done by the hand on block 2. The force by hand is the same on both blocks but the distance traveled by the block 1 along the incline (L2) is greater than the distance traveled by the block 1 ( L1).The absolute value of the work done by the gravitational force on block 1 is equal to the absolute value of the work done by the gravitational force on block 2. Both blocks travel the same height Z.The speed of block 2 increases. The net work done on block 2 is not zero as in the case of block 1. Hence the speed of the block increases.Therefore, Two identical blocks are pushed up frictionless .
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The materials that made up the solar nebulacan be categorized into the four general types as follows. Rank these meals from left to right based on the dance in the solare forest to lowest ► View Available Hints Reet Help metals rock hydrogen compounds hydrogen and hellum gas Lowest abundance Highest abundance
The materials arranged in order lowest to highest abundance are as follows
Metals> Rocks> Hydrogen compounds >Hydrogen and Helium
The solar nebula begins as a thin gas of hydrogen and helium that is covered in little dust specks. The planets' building blocks are these little grains. Any gas cloud's development depends significantly on the movement of dust particles. These grains serve as the condensation nuclei on which matter accretes.
The solar nebula is composed of 98% light gases, including hydrogen and helium, which were created during the Big Bang. Next, 1.4% of hydrogen compounds, such as water, methane, and ammonia, were found. Finally, 0.4% of rocks, such as silicates, and 0.2% of metals, such as iron, nickel, and aluminum, were found.Due to the intense heat, only metals and rocks could condense in the nebula's interior, while hydrogen compounds, despite being more prevalent, could only do so in the cooler outer regions.
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i have no clue on what to do
Answer:
Explanation:
what are the multiple answers -.-?
you are the science officer on a visit to a distant solar system. prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. you have previously determined that the planet orbits 3.2 × 1011 m from its star with a period of 402 earth days. once on the surface you find that the acceleration due to gravity is 37.8 m/s2. what are the mass of (a) the planet and (b) the star? (g
The mass of the planet and star is [tex]2.4 *10^{25}[/tex] kg and [tex]1.2 * 10^{31}[/tex] kg respectively.
Acceleration due to gravity is the force experienced per unit mass of an object due to gravitational force and it is given by:
[tex]a = \frac{GM_{planet} }{r^{2} }[/tex]
[tex]19.5 =\frac{6.67 * 10^{-11} * M_{planet} }{(0.9 * 10^{7}) ^{2} }[/tex]
[tex]M_{planet} = 2.4 * 10^{25}[/tex] kg
Now this planet orbits a star and so we can use Kepler's Third Law to find the mass of the star.
[tex]T^{2} = \frac{4\pi ^{2} }{GM_{star} } r^{3}[/tex]
T = 402 earth days = 60 x 60 x 24 x 402 = 34732800 seconds
[tex]34732800^{2} = \frac{4\pi ^{2} }{6.67 * 10^{-11} M_{star} } (2.9 * 10^{11}) ^{3}[/tex]
[tex]M_{star} = 1.2 * 10^{31}[/tex] kg
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The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg
g = G M / r
g = Acceleration due to gravity
G = Gravitational constant
M = Mass of star
r = Distance between both bodies
g = 63.6 m / s²
G = 6.67 * 10⁻¹¹ N m² / kg²
r = 8.6 * 10¹¹ m
Ms = 63.6 * 8.6 * 10¹¹ / ( 6.67 * 10⁻¹¹ )
Ms = 82 * 10²² kg
F = G M m / r²
F = m g
Equating,
m g = G M m / r²
Mp = g r² / G
Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹
Mp = 8.58 * 10²⁵ kg
Therefore the mass will be equal to 8.58 * 10²⁵ kg
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A capacitor is charged and then made to discharge through a resistance. The time constant is Ï„. In what time will the potential difference across the capacitor decrease by 10%?
a. t ln 0.1
b. t in 0.9
c. t ln 10/9
d. t in 11/10
Answer:
Q = Q0 e^-t/RC = Q0 e^-t/T
Charge left on capacitor after time t where T is the time constant of the capacitor - R * C
Q / Q0 = .9 charge decreases by 10%
.9 = e^-t/T
ln .9 = -t / T = .10
Or t = -T * ln .9
When elapsed time t = -ln .9 * time constant
Carefully examine a bulb. Two wires extend from the filament of the bulb into the base. You probably cannot see into the base, however, you should be able to make a good guess as to where the wires are attached. Describe where the wires attach. Explain based on your observations in parts A-C. On the basis of the observations that we have made, we will make the following assumptions: 1. A flow exists in a complete circuit from one terminal of the battery, through the rest of the circuit, back to the other terminal of the battery, through the battery and back around the circuit. We will call this flow electric current. 2. For identical bulbs, bulb brightness can be used as an indicator of the amount of current through that bulb: the brighter the bulb, the greater the current. C. We may think of a bulb as presenting an obstacle, or resistance, to the current in the circuit. 1. Thinking of the bulb in this way, would adding more bulbs in series cause the total obstacle to the flow, or total resistance, to increase, decrease, or stay the same as before? 2. Formulate a rule for predicting how the current through the battery would change (i.e., whether it would increase, decrease, or remain the same) if the number of bulbs connected in series were increased or decreased.
1)Now as we increase more bulb in series n increase to (n+1),so the total resistance of the circuit increases.
2)Current increases if number of bulb in series decreases.
Equivalent of the circutes
R=∑P=nn
so resistence increases
i=V/R=V/nn
current i'=V/n'R
i'/i=n/n'
since n'>n
i'<i
so current increases
Resistance is the degree to which a substance obstructs or opposes an electric current. Electron flow is referred to as electric current. To better understand resistance, imagine how difficult it would be for a person to move from one shop to another in a crowded market. The opposition a substance provides to the flow of electrical current is referred to as resistance. The capital letter R is used to symbolize it. The ohm, sometimes written as a word and sometimes represented by the uppercase Greek letter omega, is the commonly used unit of resistance.
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