The larger the velocity changes measured for the planet, the larger will be the mass of the star and smaller will be the orbit's radius.
v = √ ( G M / r )
v = Orbital velocity
G = Gravitational constant
M = Mass of the central body
r = Radius of orbit
v ∝ √ M
v ∝ 1 / √ r
From the above equation is is clear that velocity of the planet increases with the increase of star's mass and increases with the decrease of planet's orbital radius.
Therefore, the larger the velocity changes measured for the star, the larger will be the mass of the star and smaller will be the orbit's radius.
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remember that when dealing with collisions in 2-dimensions, momentum is conserved in each dimension. two pucks are sliding on a frictionless tabletop. block a (mass 3.94 kg) is moving to the east ( x direction) at 2.50 m/s. block b (mass 4.73 kg) is moving to the north ( y direction) at 3.00 m/s. assume the system to be both block a and block b. (note: it could be useful to make a drawing of the situation.) what is the x-component of the total momentum of the system before the collision?
The x-component of the total momentum of the system before the collision is 9.850 kgm/s.
P = MV
3.94 x 2.50 m/s = 9.850kgm/s.
The definition of momentum is "mass in motion." Since every item has mass, if it is moving, it must have momentum because its mass is in motion. The amount of motion and the speed of the motion are the two factors that determine how much momentum an item possesses. An object's linear momentum sometimes referred to as translational momentum or simply momentum is the product of its mass and velocity.
It has both a magnitude and a direction, making it a vector quantity. If an item has mass m and velocity v, then it has momentum p. Momentum can be defined as the amount of motion. Quantity may be quantified in this case since an object has momentum if it is traveling and mass.
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what is the magnitude of the acceleration aaa of the chair? what is the magnitude of the normal force fnfnf n acting on the chair? express your answers, separated by a comma, in meters per second squared and newtons to three significant figures.
535.1 Newton Force is the magnitude of the acceleration of the chair.
Fnet=Fp×cos35-F
=164×cos35-91
=43.34 N
a=Fnet/m
=43.34/45
=0.963 m/s^2
FN = mg + Fp×sin35
=45×9.8+164×sin35
=535.1 N
Newton is the abbreviation for the SI unit of absolute force known as newton (N). It is described as the amount of force required to accelerate a kilogram of mass by one meter per second. In the foot pound second system, one newton is equivalent to around 0.2248 pounds of force or 100,000 dyne in the centimeter gram second (CGS) system. The newton was given its name in of Sir Isaac Newton, whose second rule of motion outlines the modifications that a force may cause in a body motion.
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if this wire is used as a heating element, how much time is required for this wire to raise the temperature of 25.0 g of water from 27.0 o c to 60.0 o c? the wire is completely submerged in the water and all the energy dissipated in the wire is absorbed by the water.
The time required to gain the thermal energy is 3465/P second.
We need to know about thermal energy to solve this problem. The total heat received by the system will equal to total heat released by objects. It should follow
Q released = Q received
The heat can be defined by
Q = m . c . ΔT
where Q is thermal energy, m is mass, c is the specific heat constant and ΔT is the change in temperature.
The given parameters are
m = 25 g = 0.025 kg
c = 4200 J/kgK
ΔT = 60 ⁰C - 27 ⁰C = 33 ⁰C
The thermal energy released by the heating element per second is equal to the power. Let's assume that the heating element has the power of P
Find the thermal energy received by the water
Q = m . c . ΔT
Q = 0.025 . 4200 . 33
Q = 3465 joule
Find the time required to raise the temperature
P = Q / t
P = 3465 / t
t = 3465 / P second
where P is power in the watt unit.
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1. PE = ?
m = 0.6 kg
g= 9.8 m/s²
h = 35 m
WORKS
Answer:
Explanation:
Potential Energy = m * g * h = .6 * 9.8 * 35 = 205.8 J
two blocks are released from the top of a building. one falls straight down while the other slides down a smooth ramp. if all friction is ignored, which one is moving faster when it reaches the bottom?
The first and second blocks move at the same speed.
What is the law of conservation of mechanical energy ?
The law of conservation of mechanical energy states that the total mechanical energy of a system is constant if the only forces acting on the system are conservative.
The total mechanical energy of a system is the sum of kinetic and potential energy.
E = KE + PE
This is the total energy, kinetic energy and potential energy of the system.
The kinetic energy of the
system is:
KE = 1/2 x m x v^{2}
This is the mass and velocity of the object.
The gravitational potential energy is:
PE = mgh
Here is the acceleration of gravity and altitude.
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Mutations can occur randomly during DNA replication. Suppose DNA replication is occurring in a cell. If DNA replication occurs
correctly, the following strand will be produced.
If a point mutation occurs during DNA replication, which of these could represent the mutated strand produced instead?
OA.
ATG GAC CAT TGG C
ATG GAC CAA CTT TCG GC
ATG CGT CAT TTC GGC
ATG GAC CTT TTC GGC
B.
(C.
ATG GAC CAT TTC GGC
OD.
an ice hockey forward with mass 70.0 kg is skating due north with a speed of 5.5 m/s. as the forward approaches the net for a slap shot, a defensive player (mass 110 kg) skates toward him in order to apply a body-check. the defensive player is traveling south at 4.0 m/s just before they collide. if the two players become intertwined and move together after they collide, in what direction and at what speed do they move after the collision? friction between the two players and the ice can be neglected.
The speed of the two players after the collision is 0.31 m/s in a direction of due south.
What is the final speed of the two players?The final speed of the two players after the collision is calculated as follows.
Apply the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
m₁ is the mass of the first playerm₂ is the mass of the second playeru₁ is the initial velocity of the first playeru₂ is the initial velocity of the second playerv is the common speed of both players after the collision.(70 x 5.5) + (-110 x 4) = v(70 + 110)
385 - 440 = 180v
-55 = 180v
v = -55/180
v = -0.31 m/s
Thus, the direction of the speed of the two players after the collision is due south.
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according to modern ideas and observations, what can be said about the location of the center of our expanding universe? according to modern ideas and observations, what can be said about the location of the center of our expanding universe? the milky way galaxy is at the center. the universe does not have a center. earth is at the center. the sun is at the center.
The correct answer is option C:
According to modern ideas and observations, the location of the center of our expanding universe explains that the universe does not have a center.
Our universe is composed of three kinds of substances that are dark matter, normal matter, and dark energy.
Everything in the universe is made of normal matter i.e. planets, stars, human beings, and all other visible objects.
Astronomers have theorized that the universe is expanding at a faster rate. Between any two given points, the distance of the universe is increasing and so we can predict that the universe will be 2x in size after ten billion years.
In general, the universe has no central point and it is expanding continuously because of a dark, mysterious force that is pulling the universe apart.
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In general, how should you shuffle the mass in a rotating object to decrease its overall moment of inertia?.
Bring mass up against the axis of rotation. Consequently, a rotating object's overall moment of inertia will decrease due to its mass. The axis and the mass narrows as the mass moves closer together.
A measure of a body's propensity to resist angular acceleration that is calculated by summing the products of each particle's mass and square of its distance from the axis of rotation moment of inertia
A line along which an item rotates is referred to as its axis of rotation (also known as its axis of revolution). That line is typically fictitious in physics and calculus. The distance from the object's outside border to the axis of rotation is known as the radius of rotation.
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What is the force of gravity pulling on a 12kg block accelerating at 10m/s²?
120N is the force of gravity pulling on a 12kg block accelerating at 10m/s²
F = m × a
F = 10 ×12
F= 120N
How is the potential energy of gravity stored?The mass (m) and height (h) of the item determine how much gravitational potential energy is there. Based on an object's high position relative to a lower location, gravitational energy is potential energy that is stored in the object.
This energy can be utilised later to move an item since it can be stored and utilised at a later time. Three variables—mass, gravity, and height—determine the gravitational potential energy. Energy is directly inversely proportional to all three variables.
Because the highest amount of energy that may be converted into other forms is called potential energy. You need more energy to move the thing at a greater height.
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use as much force as possible to accomplish the task at hand. do not apply pressure between instrumentation strokes. group of answer choices both statements are true. both statements are false. the first statement is true; the second statement is false. the first statement is false; the second statement is true.
Three different activation stroke types are employed during periodontal instrumentation: the assessment stroke (exploratory stroke), the calculus removal stroke (scaling stroke), and the root planing stroke.
What strokes are used during instrumentation?
It is advised to maintain cerebral perfusion pressure between 61 and 80 mmHg if the systolic blood pressure is greater than 180 mmHg and there is proof or reason to suspect that intracranial pressure is raised. Because a standard curet blade positioned for a vertical or oblique stroke is frequently too large to adapt to root curvatures or for deep insertion in the pocket, especially in narrow pockets or regions with tight tissue tone, horizontal strokes are essential for successfully removing calculus in deep pockets. On the mesial, facial, distal, and lingual surfaces of the front teeth as well as the mesial and distal surfaces of the posterior teeth, vertical strokes are utilized.To clear the periodontal pocket and remove dental calculus, there are three main categories of electronic devices. Head is essentially upright.Head in the least strenuous vertical and horizontal posture.In order to avoid neck and head pain, the eyes are pointed downward. The thumb is positioned on the opposite side of the instrument from the four fingers.Dental instruments are handled using the standard pen grip, which involves holding a pen between the tips of the thumb and forefinger and the lateral side of the distal (final) phalanx of the middle finger. No matter where we position our fulcrum, we should always apply lateral pressure, or pressure to the side of the instrument.With this technique, you may make sufficient strokes without slipping off the tooth and damaging delicate tissue. The blade's shape is the primary distinction between a scaler and a curette in terms of design.A curette's blade is semicircular in cross section, whereas a scaler's blade is triangular.To learn more about instrumentation stroke refer
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What stage ends when the piglets
are weaned at about 2-4 weeks?
A. Farrowing
B. Loading
C. Breeding
D. Finishing
the answer to this is finishing
True or false. Objects tend to stay moving because of a force called inertia
Answer:
true
Explanation:
a rocket started at rest.after initiating the launch,it had an acceleration of 90m/s2.how long did it take to reach a speed of 2430 m/s2
The time taken for the rocket to reach a speed of 2430m/s from rest is 27.0 seconds.
What is the time taken for the rocket to reach a speed of 2430m/s?Motion is simply the change in position of an object over time.
From the First Equation of Motion;
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration and t is time elapsed.
Given the data in the question;
Since it starts from rest, Initial velocity u = 0m/sFinal velocity v = 2430m/sAcceleration a = 90m/s²Elapsed time t = ?To determine the time, substitute the given values into the formula above and solve for t.
v = u + at
2430m/s = 0 + ( 90m/s² × t )
2430m/s = 90m/s² × t
t = 2430m/s / 90m/s²
t = 27.0s
Therefore, the elapsed time is 27.0 seconds.
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A rocket launched with an acceleration of 90 m/s², and a final speed of 2430 m/s. So the time required to reach the final speed is 27 seconds.
What is acceleration?The ratio of change in velocity to time is referred to as acceleration. It has a SI unit m/s² with dimension formula MLT⁻².
According to the question, the given values are,
Final velocity, v = 2430 m/s
Initial velocity, u = 0 m/s
The acceleration is given as, a = 90 m/s².
Use the equation of motion to find the time required to reach the final speed,
v = u + at
2430 = 0 + ( 90 × t )
2430 = 90 × t
t = 2430 / 90
t = 27.0 seconds.
Hence, the time taken to reach the final speed is 27 seconds.
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rocky the flying squirrel is carrying a nut of mass 0.5 kg while flying horizontally at a height of 15 m above the ground at a speed of 12 m/s. bullwinkle is eagerly awaiting the delivery of the nut on the ground. rocky releases the nut as he is directly above bullwinkle. how far from bullwinkle will the nut land if bullwinkle does not move
The nut distance from the Bullwinkle after uniform motion is 21 m.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, the parameters given are
m = 0.5 kg
s = 15 m
vx = 12 m/s
vo = 0 m/s
a = g = 9.8 m/s²
Find the time taken of the nut for landing
s = vo . t + 1/2 . a . t²
15 = 0 + 1/2 . 9.8 . t²
t² = 3.06
t = 1.75 s
Find the distance of nut in horizontal direction
vx = x / t
12 = x / 1.75
x = 12 . 1.75
x = 21 m
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a cubical box of mass 2kg with each side 2 cm is lying on the ground. Calculate the pressure exerted by the block on the ground
Answer:
25000Nm⁻² using rounded g figure
Explanation:
The box is in cm. It needs to be converted into SI metres.
1m = 100cm
1cm = ( 1 / 100 )m
2cm = ( 1 / 50 )m
A = ( 1 / 2500 )m²
Assume that g = 10ms⁻¹. Use your own definition.
F = 10N
P = F / A
P = 10N( 2500 )m⁻²
25000Nm⁻²
Answer:
Explanation:
Given:
m = 2 kg
a = 2 cm = 0.02 m
g =9.8 m/s²
_______________
P - ?
Area of the cube:
S = a² = 0.02² = 0,0004 m²
Gravity:
F = m·g = 2·9.8 = 19.6 N
Pressure:
p = F / S = 19.6 / 0,0004 = 49 000 N/m²
HELP!
Noble gases are the ____________________.
A. most reactive of all elements
B. least consistent of all elements
C. most consistent of all elements
D. least reactive of all elements
Answer: Most consistent of all elements (if consistency here denotes stability)
if not, then the answer will be (D)
Explanation:
Nobel gasses have full outermost electron shells which means that they are very stable and do not need to lose, gain, or share electrons to gain stability. So they do not react with other elements to form ionic or covalent bonds
an interference pattern is produced by four parallel and equally spaced narrow slits. by drawing appropriate phasor diagrams, explain why there is an interference minimum when the phase difference from adjacent slits is:
The minimum interference when the phase difference from adjacent slits is ( A1 -A2)².
The amplitude of a periodic variable is the degree of its change in a single duration. The amplitude of a non-periodic signal is its important as compared with a reference cost. there are various definitions of amplitude, which are all features of the magnitude of the variations between the variable's excessive values.
Let A1 be the amplitude of the 1st wave and A2 be the amplitude of the 2nd wave.
Let the resultant amplitude be A.
the formula of interference, we get,
A= (A1)²+(A2)²+ 2×A₁× A₂ (cos theta)
When theta = 180 degrees = π radian, cos π= -1
Putting the value of cos theta in the equation we get,
A= (A1)² +(A2)² - 2×A1×A2
A= ( A1 -A2)²
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A car is traveling on a highway. the distance (in miles) from its destination and the time (in hours) is given by the equation d = 420 minus 65 t. what is the slope of the line represented by the equation? what is the practical meaning of the slope? a. m = 420; the total distance is 420 miles. b. m = 65; the car is traveling 65 miles per hour. c. m = negative 65; the car is traveling 65 miles per hour. d. m = negative 420; the total distance is 355 miles.
Two people are playing soccer. The kinetic energy of each soccer player depends on the soccer players mass and speed. Compare the two soccer players
The two soccer players kinetic energy are 1 / 2 m1 v1² and 1/ 2 m2 v2² for soccer player 1 and 2 respectively
KE = 1 / 2 m v²
KE = Kinetic energy
m = Mass
v = Velocity
Let the mass and velocity be m1 and v1 respectively for soccer player 1. Let the mass and velocity be m2 and v2 respectively for soccer player 2.
For soccer player 1,
m = m1
v = v1
KE1 = 1 / 2 m1 v1²
For soccer player 2,
m = m2
v = v2
KE2 = 1 / 2 m2 v2²
KE ∝ m
KE ∝ v²
The kinetic energy is directly proportional to mass and velocity squared. So increase in any of these factors will increase the kinetic energy and similarly decrease in any of these factors will result in decrease of kinetic energy.
Therefore, the two soccer players kinetic energy are 1 / 2 m1 v1² and 1 / 2 m2 v2² for soccer player 1 and 2 respectively
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Answer:
Cristiano Ronaldo SUII
Explanation:
Physics Question A ball of Mass 4. 0kg Moving at 6m5' collided with a vertical wall, and retraces its path in the opposite direction at 3 ms: If the time of impact is 0. 20g, Calculate:
1. Magnitude of the change in the linear momentum of the bofy.
ii magnitude of the loss in the Kinetic energy. Iii magnitude of the force experienced by the body due to collision with the ball.
The ball experiences an equal and opposing force from the wall as a result of Newton's third law .Therefore, in a perfect world, the ball would return at the same speed it originally did, preserving momentum.
explain magnitude of the loss in the Kinetic energy?
An object's mass times its velocity change equals the change in momentum of that object.Δp=m⋅(Δv)=m⋅(vf−vi) Pi=m1v1 will be the system's initial momentum.Therefore, the difference between the initial and final kinetic energies is non-zero, demonstrating that kinetic energy is always lost in inelastic collisions. The magnitude of this loss is Loss=12m1v12[m2m1+m2]. The ball is severely deformed as it is struck due to the bat's tremendous force.The average force acting during the bat-ball collision is therefore about two tons, with a peak force of nearly four tons, during the 0.7 millisecond contact time. By multiplying the magnitudes of two forces acting in the same direction along a straight line, you can quickly calculate the combined force.To learn more about magnitude refer
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while riding a roller coaster, a girl drops an object. the roller coaster was rising vertically at a velocity of 11.0m/s and was 5.00m above the ground when the object was dropped. how long does it take to reach the ground
Answer:
Approximately [tex]0.388\; {\rm s}[/tex], assuming that air resistance is negligible and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Initial vertical velocity of the object: [tex]u = 11.0\; {\rm m\cdot s^{-1}}[/tex], upwards (same as that of the rollercoaster.)
Initial height of the object: [tex]h_{0} = 5.00\; {\rm m}[/tex].
If air resistance is negligible, this object will accelerate downwards at a constant [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex]. Note that [tex]a[/tex] is negative since the object is accelerating downwards.
The SUVAT equation [tex]h = (1/2)\, a\, t^{2} + u\, t + h_{0}[/tex] gives the height [tex]h[/tex] of this object at time [tex]t[/tex]. Note that while the initial height is [tex]5.00\; {\rm m}[/tex], [tex]h = 0[/tex] when the object reaches the ground.
Since acceleration [tex]a[/tex], initial velocity [tex]u[/tex], and initial height [tex]h_{0}[/tex] are all given, setting [tex]h\![/tex] to [tex]0[/tex] and solving for [tex]t[/tex] will give the time it takes for this object to reach the ground:
[tex](1/2)\, a\, t^{2} + u\, t + h_{0} = 0[/tex].
[tex](1/2)\, (-9.81) \, t^{2} + 11.0\, t + 5.00 = 0[/tex].
[tex](-4.905)\, t^{2} + 11.0\, t + 5.00 = 0[/tex].
Solve this equation for [tex]t\![/tex] using the quadratic formula. Note that [tex]t > 0[/tex] since [tex]t[/tex] denotes the amount of time required for the object to reach the ground.
[tex]\begin{aligned} t &= \frac{-11.0 + \sqrt{11.0^{2} - 4 \times (-4.905) \times 5.00}}{2\times (-4.905)} \\ &\approx 0.388\; {\rm s}\end{aligned}[/tex].
The other root of this quadratic equation is negative and isn't a valid solution to the question.
In other words, it will take approximately [tex]0.388\; {\rm s}[/tex] for this object to reach the ground.
is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) is it possible for the electric force on a charge moving in an electric field to be zero? (c) is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?
a) Yes, provided that the speed is parallel to the magnetic field.
b) No, it is not possible electric field to be zero.
c) No. the magnetic force can be zero.
How do magnetic forces work?Magnets, which can be used to repel or attract other things, exert a force known as magnetism. One of the fundamental forces of nature, electromagnetic, is one of the components of this potent physical phenomenon. A magnetic field is produced when electrically charged particles, which are present in all matter, move.
Briefing:a)Yes, provided that the speed is parallel to the magnetic field.
b) No, the electric force acting on a charge travelling in an electric field cannot be zero since the electric field's amplitude and direction are independent of the motion or velocity of the charged particles.
c) No, the electric force cannot be zero because it is unaffected by the motion of the particles, but the magnetic force can be zero.
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. gun sights are adjusted to aim high to compensate for the effect of gravity, effectively making the gun accurate only for a specific range. (a) if a gun is sighted to hit targets that are at the same height as the gun and 100.0 m away, how low will the bullet hit if aimed directly at a target 150.0 m away?
The problem describes a situation where a bullet is launched at a certain angle respect to the horizontal to hit in the target, given the launching conditions and the distance to the target. The formulas to compute the magnitudes involved in the projectile motion are
x=[tex]v0[/tex] cos0 t
Y=[tex]V0[/tex] sin0 t
xm=[tex]v0[/tex]² sin 20/g
[tex]Xm[/tex] is the maximum horizontal distance the object can reach when it returns to the ground (or launching height).
let's check if X is computed correctly .
The set of data is correct. We can now proceed to the required distance. We know the bullet is shot directly to the target, so the angle is 0, keeping the same speed. The new maximum distance is 150 m, so we can compute the time needed to complete the flight
since
Let's find the time from the formula
X=[tex]V0[/tex] cos0 t
t=[tex]Xm[/tex]/[tex]V0[/tex] cos0
t=150/100=1.5
Y=(9.8)(0.66)²÷2
Y=-2.134
The bullet will hit 2.134 meters below the target
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If a magnifying glass uses a convex lens of focus length 6.25 cm when it is held 5.20 cm in front of an object what is the image distanceMind your minus signs Unit cm
Answer:
30.95 cm
Explanation:
The focal length f, the object distance do, and the image distance di are related with the following equation:
[tex]\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_i}[/tex]So, replacing the values, we get:
[tex]\frac{1}{6.25}=\frac{1}{5.20}+\frac{1}{d_i}[/tex]Then, solving for di, we get:
[tex]\begin{gathered} \frac{1}{6.25}-\frac{1}{5.2}=\frac{1}{d_i} \\ -\frac{21}{650}=\frac{1}{d_i}_{} \\ -\frac{650}{21}=d_i \\ -30.95\operatorname{cm}=d_i \end{gathered}[/tex]Therefore, the image distance is 30.95 cm
2200 J of work was done in 10 s. What is the amount of power?
We will have that the power will be:
[tex]\begin{gathered} P=\frac{W}{\Delta t}\Rightarrow P=\frac{2200J}{10s} \\ \\ \Rightarrow P=220J/s\Rightarrow P=220W \end{gathered}[/tex]So, the power was 220 Watts.
If an object is thrown horizontally, travels with an average x-component of its velocity equal to 5m/s, and does not hit the ground, what will be the x-component of the displacement after 20s?
Answer:
100 m
Explanation:
5 m/s * 20 s = 100 m
How do these forces affect the car's
movement?
Thrust, Lift, Drag, and Weight are four opposing forces that affect every vehicle, whether it's a car, truck, boat, airplane, helicopter, or rocket.
What is force?A force is an influence that can cause an object's motion to change. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force exist as a vector quantity because it has both magnitude and direction. A mass object's velocity changes when it is pushed or pulled. Force is an external agent that can change the state of rest or motion of a body. It has a magnitude as well as a direction. The term "force" has a specific meaning. At this level, it is perfectly acceptable to refer to a force as a push or a pull.To learn more about force, refer to:
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Two uniform cylinders are machined out of solid aluminum. One has twice the radius of the other. If both are placed at the top of the same ramp and released, which is moving faster at the bottom?.
Both cylinders will reach the same speed since speed is independent of mass and radius.
Radius of smaller cylinder = R1
Radius of bigger cylinder = R2
their masses = m1/m2 = [tex]\frac{R1}{2R1} ^{2}[/tex]
From law of conservation of energy we have
[tex]mv^{2} /2 + Iw^{2}[/tex] = mgh
[tex]1/2 mv^{2}[/tex] + [tex]m\frac{R}{L}[/tex] × [tex]\frac{x}{y}[/tex] = mgh
3/4 v2 = gh
v= [tex]\sqrt{4/3gh}[/tex]
Since from the above relation, speed is independent of mass and radius, so both cylinders have same speed.
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Neither of the two cylinders moves faster at the bottom. Both cylinders move with the same velocity at the bottom.
By the formula for conservation of energy, for a solid cylinder placed at the top of a ramp and rolling down to the bottom, we have
The kinetic energy of linear motion + rotational kinetic energy = potential energy (1)
Kinetic energy due to linear motion (of the center of mass of cylinder)= [tex]\frac{1}{2} mv^{2}[/tex]
Rotational kinetic energy = [tex]\frac{1}{2}Iw^{2}[/tex]
m = mass of cylinder, v = velocity of the center of mass of the cylinder
I = moment of inertia of solid cylinder = [tex]\frac{1}{2}mR^{2}[/tex] (R = radius of cylinder)
angular velocity w = v/R
g = acceleration due to gravity, h= height of the ramp
From equation (1)
[tex]\frac{1}{2}mv^{2}+ \frac{1}{2}Iw^{2} = mgh[/tex]
⇒[tex]\frac{1}{2}mv^{2}+\frac{1}{2}(\frac{1}{2}mR^{2}* \frac{v^{2} }{R^{2} } ) = mgh[/tex]
⇒[tex]\frac{1}{2}mv^{2}+\frac{1}{4}mv^{2}=mgh[/tex]
⇒[tex]\frac{3}{4}[/tex][tex]mv^{2} =mgh[/tex]
⇒v=√(4gh/3) (cancel m on both sides)
Thus we see the velocity at the bottom of the sloping ramp that is v is independent of the mass or radius of the solid cylinders and only depends on the height of the ramp and acceleration due to gravity.
Thus both cylinders reach the bottom with the same velocity.
What is the moment of inertia of a body:
brainly.com/question/15246709
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To find the density of an object you would use a graduated cylinder to find what characteristic of the obiect? A)mass b)length c)volume d)weight
Answer:
C Volume
Explanation:
You would use a graduated cylinder with liquid in it to see how much is displaced when the object is placed in it to determine the volume of the object