n = 7.5 times/minute does a boat bob up and down on ocean waves that have a wavelength of 29.6 m and a propagation speed of 7.08 m/s.
How do you find time with wavelength and speed?The wave moves one wavelength in one period. Speed is calculated using the formula v = / T. Wave speed, frequency, and wavelength are related by the equation v = f because the frequency, f, is 1/T.As a result, the equation becomes v = f * or = v / f when solving for. Wave speed is measured in terms of distance travelled in a unit of time, such as metres per second or m/s. Frequency is measured in Hz. Wavelength is a distance parameter, often measured in metres (m).The wave's velocity and wavelength first, it is simple to calculate the frequency using the formulas f = v. Using T = 2 = 1 f, we can calculate the time period after calculating the frequency.Given data :
Wavelength of the ocean wave, λ = 29.6 mThe speed of the ocean wave, v = 7.08 m/sThe relation between the speed of wave, wavelength and frequency is given by :
v = f x λ
f = v / λ = 7.08 / 29.6 = 0.239 Hz
The number of times per minute the bob moves up and down is given by :
n = f x t = 0.239 x 60 = 14.35 times / minute.
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visible light having a wavelength of 6 × 10−7 m appears orange. compute the frequency and energy of a photon of this light.
Energy of the photon is 3.315×1[tex]0^-^1^9[/tex] J
The frequency of a medium is the number of full vibration cycles that occur in one second.
It travels a distance equal to the length of its wave in one cycle.
Given,
Let's use the following formula
c=λν
λ=6×1[tex]0^-^7[/tex] m, h=6.63×1[tex]0^-^3^4[/tex] J
c=3×1[tex]0^8[/tex] m/s
C represents the speed of light, which has a value of approximately
λ represents the wavelength and the units should be in meters.
v represents the frequency, which should have units of Hz or [tex]s^-^1[/tex]. Hz is hertz or reciprocal seconds.
Now let's rearrange the equation to solve for v:
c=λν
3×1[tex]0^8[/tex] =6×1[tex]0^-^7[/tex]×ν
ν=5×1[tex]0^1^4[/tex]Hz
E=hν
=6.63×1[tex]0^-^3^4[/tex]×5×1[tex]0^1^4[/tex]
=3.315×1[tex]0^-^1^9[/tex] J
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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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a generator is connected to a resistor and a 0.027-h inductor in series. the rms voltage across the generator is 9.2 v. when the generator frequency is set to 180 hz, the rms voltage across the inductor is 3.2 v. determine the resistance of the resistor in this circuit.
The resistance of the resistor in this circuit is 82.31 Ohms
How to solve for the resistanceWe would first have to solve for the angular frequency
ω = 2π* f
f = 180 hz
= 2* 3.14 * 180
= 1130.4
Next we would have to solve for the Inductive reactance XL = ω* L
= 1130.4 * 0.027
= 30.52
The current is
3.2 v / 30.52
= 0.1048
Impedance Z = V/ I
9.2 v / 0.1048
= 87.79
To get the resistance we would have to use
Z² = (R² + XL²)
87.79² = R² + 30.52²
R² = 87.79² - 30.52²
= 7707.08 - 931.47
= 6775.6
R = √6775.6
= 82.31 ohms
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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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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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i have no clue on what to do
Answer:
Explanation:
what are the multiple answers -.-?
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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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
7. An engineer is investigating potential energy with two identical magnetic roller coaster cars on different sides of a center magnet that cannot move. To test her ideas, the engineer will move one car one space. Which movement will result in the largest increase in potential energy?.
The same change in potential energy will be produced by each of these actions because they all move a roller coaster car by the same amount of space.
What is potential energy, exactly?
Due to its position, an object has the ability to store energy. The bow has no energy stored when it assumes its normal position. The bow can yet store energy when its position is changed from its normal equilibrium position because of its position. Potential energy is the energy of position that a thing has stored inside it.
Because the train is moving against the magnetic pull, the potential energy is increased. However, because the magnets in the system are unchanged, the potential energy is unaffected. Engineer is testing two identical magnetic roller coaster vehicles on either side of a stationary center magnet.
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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:)
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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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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170 students sit in an auditorium listening to a physics lecture. Because they are thinking hard, each is using 125 W of metabolic power, slightly more than they would use at rest. An air conditioner with a COPof 5.0 is being used to keep the room at a constant temperature. What minimum electric power must be used to operate the air conditioner?
The calculated power is P = 3500 W. Power can be defined as the amount of work completed in a given amount of time.
Watt (W), which is derived from joules per second (J/s), is the SI unit of power. Horsepower (hp), which is roughly equivalent to 745.7 watts, is a unit of measurement sometimes used to describe the power of motor vehicles and other devices.
There are n = 140 students in the auditorium overall.
Each pupil is using a metabolic power of p = 125 W.
To keep the temperature in the auditorium consistent, the air conditioner's coefficient of performance (COP) is listed as 5.
Let P represent the required minimum amount of electric power to operate the air conditioner.The fact that
np = P in COP
P = np/COP
= ( 140 x 125 ) / 5
= 3500 W
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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
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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how much work w is done by a pump in raising 5 m3 of water 20 m and forcing it into a main at a gauge pressure of 150 kpa?
The amount of labor required by a pump to raise 5 m3 of water 20 meters and force it into the main at such a pressure head of 150 kpa is 1.73×10⁶ J.
What is the straightforward meaning of work?Force applied across a distance is called work. Example of effort include dragging down a trapped helium balloon, driving down a hill, and lifting an item against the gravitational attraction of the Earth. Energy manifests mechanically as work. The joule (J), and coulomb (N m), is the accepted work unit.
Briefing:W= (Effort to raise water) + ( Work to push it in )
= mgh+PΔV
W = (5.00 m³)(1000 kg/m³)(9.81 m/s²)(20.0 m)+(1.50×10⁵ N/m²)(5.00 m³)
=1.73×10⁶ J.
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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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What are the total force and aboute preure on the bottom of a wimming pool 22m by 8. 5cm whoe uniform depth i 2m? what will be the preure againt the ide of the pool near the bottom?
19600N[tex]m^{2}[/tex] is the total pressure near the bottom of the pool as per the given data in the statement.
What is pressure?Pressure: The perpendicular force applied to surface of any object tending to be distributed per unit area is known as pressure.
According to the given data :
length of the pool = 22m
breadth of the pool =8.5 cm=0.085 m
depth =2 m
To find the pressure near the bottom of the pool we use the following formula
P=hpg, where h=height or depth, p= density of liquid and g= 9.8m/s
P=2*1000*9.8
P=19600N[tex]m^{2}[/tex]
Hence, 19600N[tex]m^{2}[/tex] is the total pressure near the bottom of the pool as per the given data in the statement.
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19600N[tex]m^{2}[/tex] is the total pressure near the bottom of the pool as per the given data in the statement.
What is pressure?Pressure: The perpendicular force applied to surface of any object tending to be distributed per unit area is known as pressure.
According to the given data :
length of the pool = 22m
breadth of the pool =8.5 cm=0.085 m
depth =2 m
To find the pressure near the bottom of the pool we use the following formula
P=hpg, where h=height or depth, p= density of liquid and g= 9.8m/s
P=2*1000*9.8
P=19600N[tex]m^{2}[/tex]
Hence, 19600N[tex]m^{2}[/tex] is the total pressure near the bottom of the pool as per the given data in the statement.
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an iron bar magnet having a coercivity of 4000 a/m is to be demagnetized. if the bar is inserted within a cylindrical wire coil 0.15 m long and having 100 turns, what electric current is required to generate the necessary magnetic field?
The electric current necessary for generate the magnetic field by a cylindrical coil of 100 turns is 6 A.
Coercivity of magnet = H = 4000 a/m
Length of cylindrical coil = L = 0.15 m
Number of turns in the coil = N = 100 N
Electric current of the coil required to generate magnetic field= I =
= I = (HX L) / N
= I = ( 4000 x 0.15 ) / 100
= I = 600 / 100
= I = 6 A
The current required for the coil of length 0.15 m with 100 turns and coercivity of 4000 a/m to generate magnetic field is 6 amperes.
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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?.
The square of the distance between the two charges has an inverse relationship with the force's size. As a result, when the gap between two charges is doubled, the attraction or repulsion weakens and drops to one-fourth of its initial strength.
What is force?An object's push or pull is seen as exerting a force. The interaction of the objects produces push and pull.
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. The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.
A spring balance can be used to calculate the Force. Newton is the SI unit of force (N).
What are repulsion force?The interaction between two or more comparable or similar charges to produce force. Repulsion between similar charges occurs. Charges that resemble one another separate from one another. Chemical bonding involves repulsive forces.
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Oil is spilled from an oil rig in the Gulf of Mexico andspreads in a circle with the circumference changing at a rate of 40m/sec. How fast is the area of the spill increasing when thecircumference of the circle is 100Ï€ meters?
The area of the spill increasing when the circumference of the circle is 100π meters at a rate of 2000 sq. m/sec.
What is circumference ?In geometry, the perimeter of a circle or ellipse is its circumference. In other words, the circumference would equal the length of the arc if the circle were expanded up and straightened out to a line segment.
The term "perimeter" is most frequently used to describe the radius of any closed shape. The exact location of the circle, which corresponds to the edge of a disc, is also referred to as its circumference.
Given parameters:
circumference changing at a rate = 2π dr = 40m/sec.
the circumference of the circle is = 2πr = 100π meters
Hence, the rate of area of the spill increasing = 2πrdr
= 100π meters × 40m/sec/2π
= 2000 sq. m/sec.
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an evil doer has stolen the unstable atomic nuclear mass (17.0 x 10 -27 kg) from the unstable nuclear mass facility. while waiting at a stop light the unthinkable happens (actually quite expected and predictable up to a probability) and the mass disintegrates into three particles. one of the particles, of mass 5.00 x 10 -27 kg, moves in the y-direction with a speed of 6.00 x 10 6 m/s. another particle, of mass 8.40 x 10 -27 kg, moves in the x-direction with a speed of 4.00 x 10 6 m/s.
(a) Find the magnitude and direction of the velocity of the third particle.
(b) If the evil doer had been driving with a speed of 30 m/s when the disintegration occurred, how would this have changed your answer to part (a)? Use an Order of Magnitude sense-making argument to help with this analysis.
Momentum's conservation:
m1 v1 + m2 v2 + m3 v3 = 0 (vectors)
X axis : m2 v2 + m3 v3x = 0
v3x = - m2 v2/m3
Y axis : m1 v1 + m3 v3y = 0
v3y = - m1 v1/m3
m3 = m - (m1 + m2) = 1.92*10^-26 - (5.02 + 8.5)*10^-27 = 5.68*10^-27 kg
So :
v3x = - 5.98*10^6 m/s ;
v3y = - 5.30*10^6 m/s
(a) The vector v3 = - (5.98 i + 5.30 j)*10^6 m/s
(b) The total kinetic energy is:
Ek = (1/2)(m1 v1^2 + m2 v2^ + m3 v3^2)
Ek = 3.40 * 10^13 J
Velocity can be notion of as the rate at which an object covers distance. A quick-moving object has a high speed and covers a notably big distance in a given amount of time, whilst a sluggish-shifting item covers a relatively small amount of distance in the same amount of time.
The primary unit or the S.I. unit of velocity is m/s or ms?¹.
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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
if it takes a bike wheel 6 seconds to complete one revolution, what is the wheel's angular velocity? answer: degree/s.
The angular velocity of the wheel when the bike takes 6 s to complete one revolution is 0.33π
Time taken by the wheel = t = 6 s
Angle of the wheel = θ
= θ = 2π
Angular Velocity = ω =
= ω = angle / time taken
= ω = θ / t
= ω = 2π / 6
= ω = π/3
= ω = 0.33π
Angular velocity is how fast the rigid body rotates with respect to its centre of rotation and is independent to the choice of origin. It is the displacement of the object revolving with respect to the time taken by the object.
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A 1270 kg sedan has the same amount of momentum as a 3600 kg truck moving with a speed of 14 m/s what is the speed of the sedan
The speed of sedan is 39.68m/s.
What is momentum?By dividing a particle's mass by its speed, momentum is produced. Momentum is a vector quantity because it has both a direction and a magnitude. Isaac Newton's second law of motion states that the time rate of change of momentum is equal to the force acting on the particle. the laws of motion established by Newton.
Momentum = mass × velocity
Momentum of the truck = 3600 × 14
Momentum of the truck = momentum of sedan
3600 × 14 = 1270 × speed
Speed of sedan = 3600 × 14/1270
Speed of sedan = 39.68m/s.
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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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Which state of equilibrium is a person in while running on a treadmill?
Answer: Dynamic equilibrium.
Explanation: When a person is running on a treadmill, they are in a state of dynamic equilibrium. Dynamic equilibrium occurs when a system is in constant motion and the forces acting on the system are balanced. In this case, the person is in motion (running on the treadmill) and the forces acting on them (gravity and the force of the treadmill belt) are balanced, allowing them to maintain their motion at a constant speed.
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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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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a bicycle wheel with radius 0.3 m rotates from rest to 3.1 rev/s in 5.7 s. what is the magnitude (in m/s2) of the total acceleration vector at the edge of the wheel at 1.2 s?
The magnitude of the total acceleration vector at the edge of the wheel at 1.2 s is 5.22 m/s².
Given that,
Radius of the wheel = 0.3 m
Initial angular velocity ω₀ = 0
It rotates 3.1 rev/s in 5.7s. Therefore, ω = 2*π*r = 2*π* 3.1 = 19.47 rad/s
We know that, ω = ω₀ + αt
where, α = angular acceleration
ω = Final angular velocity
t = time
α = 19.47/5.7 = 3.42 rad/s²
Total acceleration at any point will be a vector sum of tangential acceleration and centripetal acceleration
ω = ω₀ + αt
ω = 0 + 3.42* 1.2 = 4.11 rad/s
αc = ω² * r = 4.11² * 0.3 = 5.07 m/s²
Tangential acceleration αt = α * r
αt = 4.11 * 0.3 = 1.23 m/s²
α net = √(5.07² + 1.23²) = √(25.7049 + 1.5129) = 5.22 m/s²
Thus, the magnitude of total acceleration vector at the edge of the wheel is 5.22 m/s².
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