The distance of do is 83.34 cm for the magnification -0.40.
Magnification is the process of increasing apparent size.
It is usually done to see the object in an enlarged view by increasing its resolutions so that a more clear view of the object can be visualized.Microscopes like light, electron and compound microscopes are used to see a high resolution image of the object.Magnification can be calculated by the formula M = -(l/f₀)(25/f₁)M = magnification = - 0.40
l = distance between the eyepiece and the objective lens
f₀ = focal length of the objective
f₁ = focal length of the eyepiece
the focal length of David's lens is: f = 50 cm.
Distance 'u' between the object is to be calculated
According to the formula;
u =f( 1/m -1)
⇒ u = 50(-1/0.40-1) = 83.34 cm.
Hence, distance do is 83.34 cm.
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what is a condition in which there is a progressive thickening of the lens causing vision to become cloudy, opaque, and distorted?
Cataract is a condition in which there is a progressive thickening of the lens causing vision to become cloudy, opaque, and distorted.
What are the signs and symptoms of cataracts?vision that is cloudy, blurry, or dim.Nighttime eyesight is becoming more challenging.a sensitivity to glare and brightness.Brighter lighting is required for activities like reading."Halos" around lights being perceived.prescription for glasses or contacts changing frequently.colour fading or yellowing.Having double vision in just one eye.The majority of cataracts occur when the tissue that makes up the eye's lens changes due to age or trauma.
The risk of cataracts may be increased by some hereditary genetic abnormalities that can result in other health issues. Other eye diseases, previous eye surgery, or other disorders like diabetes might also lead to cataracts. Cataracts can also form as a result of prolonged steroid drug usage.
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When a 0.650-kg mass oscillates on an ideal spring, the frequency is 1.95 Hz. What will the frequency be if 0.160 kg are added to the original mass? Try to solve this problem without finding the force constant of the spring.
The frequency will be 1.74 Hz if 0.160 kg are added to the original mass.
What is frequency?
In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.
After moving through a sequence of situations or locations and then returning to its initial position, a body in periodic motion is said to have experienced one cycle or one vibration. See also basic harmonic motion and angular velocity.
Frequency (f) of a spring is inversely proportional to square root of its mass. So,
f₁√m₁ = f₂√m₂
⇒ f₂ = f₁√m₁ /√m₂
= 1.95√(0.650/0.810) Hz = 1.74 Hz.
Hence, the frequency will be 1.74 Hz if 0.160 kg are added to the original mass.
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f. What happens if the Physics student is standing on ice?
g. What is the force between the student and the ground called?
Answer:
Explanation:
f. Student slips on ice
g. The force is called sliding friction force
light traveling in water strikes a water-air interface such that the light is incident directly along the normal to the interface. what happens to the light?
When light travels from air into water, it slows down, causing it to change direction slightly.
What is light travels?
Light moves in waves. It does not, however, require any substance or material to transport its energy forward, unlike sound waves or water waves. This implies that light may pass through a vacuum, or an area that is entirely devoid of air. (In contrast, sound must pass through a solid, liquid, or gas.)
Light slows down and somewhat changes direction as it passes through water from air. Refraction is the name for this shift in direction. Light "bends" more in the direction of the normal line when it enters a denser material (one with a higher refractive index).
Light bends in the direction of the normal as it passes through an interface into a material having a greater index of refraction. On the other hand, light bending over a higher n to lower n contact will deviate from the usual.
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a coin is placed on a flat, horizontal turntable which makes 3 revolutions in 3.14s. a. what is the speed of the coin when it rides without slipping at a distance of 5.0cm from the center of the turntable?
The speed of the coin when it rides without slipping at a distance of 5.0cm from the center of the turntable is 0.49 m/s.
No of revolutions made in 3.14s = 3rev
No of revolutions made in 1s = 3/3.14 = 0.96rev
Frequency = 0.96Hz
Time period T = 1/f = 1/0.96 = 1.05s
Angular velocity ω = 2π / T = 2π / 1.05 = 5.98 rad/s
Speed v = rω = 0.05 * 5.98 = 0.49m/s
The distance traveled rel.ative to the time it took to travel that distance is how fast s0mething is moving. As it just has a direction and no magnitude, speed is a scalar quantity. When an object travels an identical distance in an identical amount of time, it is said to be moving at uniform speed.
If an object travels a varied distance at regular intervals while maintaining the same speed, the speed is said to be variable.
Average speed is the average speed that is determined by the ratio of an object's total distance traveled to its total time traveled.
Instantaneous speed is the speed of an object while it is travelling at any given moment at a changeable pace.
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At what rate will a pendulum clock run on uranus, where the acceleration due to gravity is 9. 01 m/s2, if it keeps time accurately on earth? that is, find the time (in hours) it takes the clock's minute hand to make one revolution on uranus.
The time taken in hours for the clock's minute hand to make one revolution on Uranus is 0.0174 hours.
It is given to us that -
Acceleration due to gravity in Uranus = [tex]9.01 m/s^{2}[/tex]
Time on Earth = 1 minute = 0.0167 hours
We have to find out time taken in hours for the clock's minute hand to make one revolution on Uranus.
We know that period of oscillation observed in Earth can be given as -
[tex]T_{E}=2\pi \sqrt{\frac{l}{g_{E} } }[/tex] ----- (1)
where,
[tex]T_{E}[/tex] = 0.0167 hours (given)
[tex]l[/tex] = length of the pendulum
[tex]g_{E}[/tex] = acceleration due to gravity of Earth
According to the given information, the length of the pendulum will be equivalent on Uranus. This implies that the period of oscillation observed in Uranus can be given as -
[tex]T_{U}=2\pi \sqrt{\frac{l}{g_{U} } }[/tex] ----- (2)
where,
[tex]l[/tex] = length of the pendulum
[tex]g_{U}[/tex] = acceleration due to gravity of Uranus = [tex]9.01 m/s^{2}[/tex] (given)
Now, from equations (1) and (2),
[tex]\frac{T_{U} }{T_{E} }= \frac{ 2\pi \sqrt{\frac{l}{g_{U} } }}{2\pi \sqrt{\frac{l}{g_{E} } }} \\= > \frac{T_{U} }{T_{E} }=\sqrt{\frac{g_{E}}{g_{U} } } \\= > \frac{T_{U} }{0.0167 }=\sqrt{\frac{9.81}{9.01 } } \\= > T_{U} = 0.0167 * 1.0434\\ = > T_{U} =0.0174 hours[/tex]
Thus, the time taken in hours for the clock's minute hand to make one revolution on Uranus is 0.0174 hours.
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A hockey puck has a coefficient of kinetic friction of = .20. If the puck feels a normal force of 5 N, what is the frictional force that acts on the puck?
Answer: 5 N
Explanation:
Friction is a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, like the traction required to walk without slipping, may be advantageous, they also pose a significant amount of resistance to motion.
The given parameters;
coefficient of kinetic friction, μk = 0.1normal force of the puck, Fₙ = 5 NBy multiplying the normal force and the coefficient of kinetic friction, the frictional force acting on the puck is calculated.
The frictional force that acts on the puck is calculated as follows;
F= u*f
Substitute the given parameters in the above equation and solve the frictional force.
F=0.2*5
F= 1 N
Thus, the frictional force that acts on the puck is 1 N.
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Choose a device or machine that you use regularly. What do you do to make sure it works efficiently?
laptop is a device which is used regularly andto make it work properly we should follow some precautions.
what is the efficiency of a device?
The efficiency of a device is the proportion of the energy supplied that is transferred in useful ways. The work out of a device divided by the work into the device is defined as efficiency.
precautions to make laptop work efficiently
Always shut down your laptop when you are done with your work instead of in sleep mode.Always clean temp files from your laptop to make them more efficient.Keep up to date you have recommendedDon’t use unsecured websites it may risk your laptopPlace the laptop on some wooden or another material platform for better heat exchangeClean the screen and laptop so dust will not enter the processorRemove the battery plug when it is fully chargedUse the license version software instead of crack versionreduce heat lossTo know more about efficiency of the device, check out:
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a noisy machine in a factory produces a decibel rating of 77 db. how many identical machines could you add to the factory without exceeding the 85 db limit?
A noisy machine in a factory produces a decibel rating of 77 dB. The Number of 10 machines add to the factory without exceeding the 85 db limit.
sound level in decibels is
β dB = 10 log ( I / I₀ )
where I is the intensity of sound
I₀ is the relative intensity
80 = 10 log ( I ÷ 10⁻¹² )
8 = log ( I ÷ 10⁻¹² )
10⁸ = I ÷ 10⁻¹²
I = 10⁸ × 10⁻¹² = 10⁻⁴ W /m2
if the sound level is 90 dB, the number of identical machines is n.
90 = 10 log ( n × I / I₀)
90 = 10 log ( n × 10⁻⁴ / 10⁻¹²)
9 = log ( n × 10⁸)
10⁹ = n × 10⁸
n = 10
Therefore, a number of 10 machines add to the factory without exceeding the 85 db limit.
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a diffraction grating has 2,070 lines per centimeter. at what angle in degrees will the first-order maximum be for 550 nm wavelength green light?
7.87° is the first-order maximum for 550 nm.
What is diffraction?Diffraction is the spreading of waves in the presence of obstacles. Diffraction occurs with sound, electromagnetic radiation such as light, X-rays, and gamma rays, and very small moving particles with wavelike properties such as atoms, neutrons, and electrons.The locations of the interference fringes are given by the equation d sin θ = m λ d sin θ = m λ.Using diffraction equations,
d = 0.01/Number of lines, where 0.01 m = 1 cm and d = line spacing
Therefore,
d = 0.01/2070 = 4*10^-6 m
Similarly,
d x Sin X = m x Y;
When X = Angle
m = order = 1
Y = wavelength = 550 nm =550*10^-9 m
By substituting;
Sin X = mY / d = (1*550*10^-9)/(4*10^-6) = 0.1375
X = Sin⁻¹(0.1375) = 5.97°
As a result, the first-order maximum for 550 nm will be 7.87°.
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if the charge on q1 is doubled, assuming that charge of q2 and the distance of r stay the same, what will happen to the force between the two charges? (3 points)
Electromagnetic Force causes electric and magnetic effects such as the repulsion between like electrical charges or the interaction of bar magnets in a similar fashion of attraction & repulsion. It is long-ranged, but much weaker than the strong force. It can be attractive or repulsive and acts only between pieces of matter carrying electrical charge. Electricity, magnetism, and light are all produced by this force.
If the charge on q1 is doubled the force becomes 4 times its initial value.
Since, we know
F = (k×q1×q2)/r²
When the charges are doubled, we have :
F' = (k × 2q1 × 2q2)/r²
F' = 4 (k×q1×q2)/r²
Thus,
F' = 4F
Therefore, the force becomes 4 times its initial value.
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By how much does the gravitational potential energy of a 50- kg pole vaulter change if her center of mass rises about 4. 0 m during the jump?.
Consequently, the acceleration due to gravity of the pole voulter is 2000J. any object at ground surface has a potential energy = zero newtons.
What is meant when we talk about gravitational potential energy?Gravitational potential energy is the energy that an object has due to its location within a gravitational field. The most usual use of gravitational potential energy is for a body at the surface of the Earth, where it is reasonable to assume that the gravitational pull is constant at about 9.8 m/s. 2.Any object at ground level has a potential energy of zero newtons becuase anything multiplied by zero is zero. An object with mass of 54 kg, 4 meters above the ground has a gravitatinal potential energy of 2116.8 Joules.
What is the source of gravitational potential energy?If an object is located at a height that is higher (or lower) than the zero height, it has gravitational potential energy. If an object is situated on an elastic media in a position besides the equilibrium position, it has elastic potential energy.
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as an ideal fluid flows vertically upward through a uniform (constant radius) pipe, what happens to the fluid speed and fluid pressure?
A pipe's pressure is essentially comprised of two pressures: a kinetic pressure that is measured in the flow's center and a static pressure that is determined precisely at the pipe wall's interior.
What means fluid pressure?the force a fluid applies to any point inside of it. The sum of the difference in height, their density, and the rate of free fall determines the difference in pressure between two levels.
Why does fluid pressure exist?Similar to the air from the inside of a tire, all liquids exert pressure. Fluid particles constantly and randomly move in all directions. The particles constantly collide with one another and anything else that crosses their path as they advance. Pressure is produced by these impacts, and it is applied uniformly in all directions.
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4. what happens to the orbital period as the star-planet distance increases? why do you think there is a relationship?
If Moto moved farther from the star, its orbital speed would slow down and it would have a wider orbit to travel, increasing the orbital period.
Why does orbital period lengthen as we travel farther?Since the Sun's gravitational pull on a planet farther away is weaker, it not only travels a greater distance than a planet closest to it, but it also moves more slowly. Therefore, a planet takes longer to complete its orbit the larger it is.
What is orbital period of earth?As seen from above the Northern Hemisphere, the Earth circles the Sun at an average distance of 149.60 million kilometers (92.96 million miles), counterclockwise. In 365.256 days (1 sidereal year), the Earth completes one orbit, covering 940 million kilometers (584 million mi).
What is gravitational pull?The force that attracts all masses in the universe, particularly theat attracts all masses in the universe, particularly the earth's mass's attraction to anything close to its surface. Gravitation, gravitational force, and similar terms.
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the image shows a pendulum that is released from rest at point a. an illustration of a pendulum at 5 different positions. the central position, the equilibrium position is labeled c. the two positions on the left are labeled a and b respectively. the two positions on the right are labeled d and e respectively. all positions are equally spaced. which pair of labels is correct? a: maximum kinetic energy c: maximum gravitational potential energy b: maximum kinetic energy d: maximum gravitational potential energy a: maximum gravitational potential energy c: maximum kinetic energy b: maximum gravitational potential energy d: maximum kinetic energy
The appropriate energy transformations are:
Kinetic energy changes into center of gravity from A to C.
Gravitational acceleration energy is converted into kinetic energy from C to E.
What is Kinetic energy?
Kinetic energy is a type of power that a moving object or particle possesses. An object gains kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object as well as particle has kinetic energy, which depends on both its mass and its rate of motion. Any combination of motions, including translation, rotation about in an axis, and vibration, may be the type of motion.
A body's translational kinetic energy, or 1/2mv2, is determined by multiplying its mass, m, by the square of it's own velocity, v.
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a substance absorbs wavelengths of light in the range of 550 - 750 nm. a) approximately what wavelength range in the visible region is being transmitted?
The wavelengths of visible light are really not interfere constructively affected with by reflected waves.
What does constructive interference entail?When the maximum of two waves are combined together in a way that makes the amplitude of the resulting constructive wave equal to the sum of the separate waves, this is known as constructive interference, or doppler effect is the interference.
Briefing :
The constructive interference for two waves, in same phase can be find out as,
λ = [tex]\frac{2'nd}{m}[/tex]
Here, m=1,2,3,....
The range of wavelengths of visible light given from 550 nm to 750 nm. It has to be found out that, for which visible wavelengths of light, do the reflected waves interfere constructively,
Visible wavelength of light is a range of electromagnetic spectrum, which can be visible by human eyes. This ranges from 550 nm to 700 nm (approx). In the problem given, the range of wavelengths of visible light is from 550 nm to 750 nm.
Put the value of the 2nd wavelength (750 nm) in the above formula for m equal to 1 as,
λ = [tex]\frac{750}{1}[/tex]
λ = 750nm
For m equal to 2,
λ =[tex]\frac{750}{2}[/tex]
λ = 375nm
Both the values does not fall under the range of visible light. Hence, The visible wavelengths of light do not reflected waves interfere constructively.
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who is responsible for testing electrical conductor insulation and keeping the test records?
The resistance to insulation is measured using an IR tester. This is a portable device that resembles an ohmmeter in many ways and has a built-in generator for creating a high DC voltage.
How do you test a conductor for insulation?An IR tester is used to assess insulation resistance. This is a portable device that resembles an ohmmeter in many ways and has a built-in generator for creating a high DC voltage. A current moves across the surface of the insulation as a result of the voltage, which is normally at least 500V.
Insulation testers evaluate the resistance in wires and motor windings using a high voltage, low current DC charge to find current leakage and defective or damaged insulation, which can result in arc faults, blown circuits, and the possibility of electrical shock or fire.
To help prevent risks like electric shock and short circuits created when the insulation in electrical devices, parts, and equipment is compromised, portable insulation resistance testers and megohmmeters are available.
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what is the allowable ampacity for each of the following conductors, if all conductors are to be installed in the same raceway? (assume all conductors to be current carrying thwn copper) qty: (2)
Ampacity can be calculated by dividing the Wattage by the rated voltage.
What is the ampacity of each conductor?
The highest continuous current that a conductor may carry under normal use settings without going above its temperature rating is known as ampacity. The unit of measurement for current is one amp. To avoid the wire overheating, you must choose the proper size wire for the circuit's current (load) requirements.
Divide the Wattage by the rated voltage to get the ampacity. The predicted Amperage of the circuit is the quotient. Many times, a circuit's particular application correction factors (as mentioned above) will make ampacity necessary.
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When wind speeds up as it blows over the top of a hill, atmospheric pressure there.
When wind speeds up as it blows over the top of a hill, decreases atmospheric pressure there.
What is Atmospheric pressure ?As the ratio of the force the atmosphere exerts per unit area, atmospheric pressure can be defined. Pascal can be used to both calculate and measure atmospheric pressure. 101325 pascals is what the normal atmospheric pressure is.
Your immediate environment is pressed against by the weighty air that surrounds you. It is known as air pressure or atmospheric pressure. It is the pressure from the air above a surface that pulls it toward Earth. Typically, a barometer is used to measure atmospheric pressure.
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two horizontal forces act on a wagon, 150 n forward and 700 n backward. what force is needed to produce a net force of zero?
Answer: When two horizontal forces act on a wagon, 150 n forward and 700 n backward. 550 n force is needed to produce a net force of zero
Explanation:
According to Newton's first law of motion, unless pushed to alter its condition by the operation of an external force, every object will continue to be at rest or in uniform motion along a straight line.Net force is the sum of all the forces from all the direction which are applied on the object.For the net force to be zero two force from opposite direction should be equal so that they will cancel out each other.
150 N→ Wagon ←700
← 550
Net force in current state is 550 in backward direction.
So to cancel out the additional force, same amount of force has to be applied from the backward direction.
150 N+ 550 N → Wagon ←700 N ⇒ Net force = 0
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c) calculate the magnitude f of the force due to the water on a viewing port of the submarine at this depth if the viewing port has a surface area of 0.0100 m2.
If a submarine's viewing port has a surface area of 0.0100 m2, the force exerted by the water on it at this depth will be 416,000 N in magnitude.
Pgauge is equal to F/A 412(1.01 x 105) = F/0.01 F = 416,000 N.
The two fluid pressures that are in play are the internal atmospheric air pressure and the external water pressure, which includes the atmosphere operating on it at the surface. The net force due to fluid pressure can be calculated by using the gauge pressure of the water since the atmospheric pressure acts both internally and is also included in the water pressure and the air pressures virtually cancel each other out.
A force is an influence that has the power to alter how an object moves. A force can cause an object with mass to accelerate and change its velocity (for example, moving from a state of rest). Force can also be conce.ptualized as a push or a pull. A force is a vector quantity since it has b0th magnitude and direction. It is calculated using newtons as the SI unit of mea.sure (N). F stands for force (formerly P).
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what is the velocity of the falre when it is moving toward the ground and its position is equal to 131 feet
The velocity of the flare is -92 feet per second while it is going toward the earth, in accordance with the question.
What does physics define as velocity?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, the velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
Briefing:We determine the speed at this time after first determining t.
131 = -3t^2 + 100t + 3
-3t^2 + 100t - 128 = 0
-(3t - 4)(t - 32) = 0
t = 4/3, 32
At 32, the flare will be released.
s'(t) = -6t + 100
s'(32) = -6(32) +100 = -92
The velocity is 92 ft/sec down.
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The complete question is-
In a scene from the Martin Matt Damon shoots a flare straight up into the sky. The height( in feet) of the flare after t seconds is given by
s(t)= -3t squared + 100t + 3
What is the velocity of the flare when it is moving toward the ground and its position is equal to 131 feet?
with what tension must a rope with length 2.10 mm and mass 0.120 kgkg be stretched for transverse waves of frequency 45.0 hzhz to have a wavelength of 0.790 mm ?
The tension of a rope of length 2.10 mm and mass 0.120 kg which is stretched for transverse waves of frequency 45.0 hzhz to have a wavelength of 0.790 mm is 51.4 N
What is frequency ?
The quantity of waves that pass a set location in a predetermined period of time is known as frequency.
From the given information -
length =2.10 mm
mass = 0.120 kg
frequency = 45.0 Hz
wavelength = 0.790 mm
V = sqrt (T/u)
V = 40 *0.79 = 31.6 m/s
T/u = 900
Tension = 900* 0.12/2.1
Tension = 51.4 N
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a particular am radio station broadcasts at a frequency of 1040 kilohertz. what is the wavelength of this electromagnetic radiation?
Answer:
1040 Kilohertz = 1.04E6 /sec
Speed of electromagnetic waves = 3.00E8 m/s
3.00E8 / 1.04E6 = 288 m (a λ/4 antenna still requires 72 m)
an object of mass m is launched at speed at angle with respect to the horizontal from a height h. find the horizontal velocity component when the object is at its maximum height g
The horizontal velocity component when the object is at its maximum height Hmax = [tex]u^{2} sin^{2}[/tex]θ /2g
The vertical and horizontal components of motion are separated into two parts for solving velocity problems in physics. When solving problems involving a trajectory's angle, vertical velocity is used. When an object moves horizontally, its horizontal velocity becomes crucial. Any mathematical solution will consider the horizontal and vertical elements independently because they are not reliant on one another. Horizontal velocity, which can be expressed in terms of meters per second or miles per hour, is typically defined as horizontal displacement divided by time. The distance that an object has traveled since leaving a starting position is known as displacement.
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for a current ratio with a value greater than or equal to 1.0, the current ratio will increase if:
If a company's current ratio is larger than 1, it implies that its current liabilities exceed its current assets; conversely, if it is or less 1, it means that its current assets exceed its current liabilities.
What does an current ratio less than 1 indicate?If the ratio is less than 1, it means that the firm has more obligations due in the next year or less than it does in cash or other brief assets that are anticipated to be converted into money in the next year or less.
What ratio results from a reduction in current obligations and assets?Now The ratio would rise to 2.25:1 if current obligations and assets were both decreased by $1,000.
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an automobile sounds its horn while passing an observer at 25.5 m/s. the actual horn frequency is 405 hz. assume the speed of sound is 345 m/s. find its frequency heard by the observer while the car is approaching.
The frequency heard by the observer is 437.3 Hz.
What is doppler effect?
The Doppler effect or Doppler shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. Doppler shift is frequently demonstrated by the change in pitch that occurs as a car approaches and moves away from a viewer while sounding its horn.
It is estimated by the formula:
[tex]f_o = \frac{v +v_o}{v + v_s} f_s[/tex]
where,
[tex]f_o[/tex] = observer frequency of sound
[tex]v[/tex] = speed of sound waves
[tex]v_o\\[/tex] = observer velocity
[tex]v_s[/tex] = source velocity
[tex]f_s[/tex] = actual frequency of sound waves
Given,
[tex]f_s[/tex] = 405Hz
[tex]v_s[/tex] = 25.5 m/s
[tex]v[/tex] = 345 m/s
[tex]v_o\\[/tex] = 0 m/s
[tex]f_o = \frac{v +v_o}{v + v_s} f_s[/tex]
Observer to source = Positive
Source to observer = Negative
[tex]f_o = \frac{v}{v + v_s} f_s[/tex]
[tex]f_o = \frac{345}{345 - 25.5}[/tex] × 405
[tex]f_o[/tex] = 437.3 Hz
The frequency heard by the observer is 437.3 Hz.
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Assume you have a sealed jug that contains only air. If you heat the air in the jug, it will have a higher temperature. What other property of the air will also change?.
Assume you have a sealed jug that only contains air. If you heat the air in the jug it will have a higher temperature. Air Pressure properties of air will change.
What is Pressure?
The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units.
The number of atoms of air in the sealed container cannot change. Assuming that the container does not expand when heated, the volume of the container cannot change when it is heated. If neither the mass nor the volume change as the can is heated, neither can the density change.
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A bowling ball with a circumference of 27 in. weighs 14lb and has a radius of gyration of 3.28 in. If the ball is released with a velocity of 20ft/sec but with no angular velocity as it touches the alley floor, compute the distance traveled by the ball before it begins to roll without slipping. The coefficient of friction between the ball and the floor is 0.20.This is a question I would really liked answered. Thanks!!
The distance travelled by the bowling ball is 18.6566 ft
Circumference = 2πr = 27
Weight of the ball = 14 lb
Radius of gyration = 3.28
Velocity = rω = 20 ft/s
Coefficient of friction = 0.20
Total force on y axis= 0, therefore N = W
= F = μN = μW
and, ∑M = Iα
Hence,
= Fr = Iα
Total force on x axis = 0,
= F = ma = μW
= a = μg
Combining all the equations,
= Fr = Iα
= μWr = mk²α
= α = (μgr) / k²
If initial velocity = 0 then, ω = αt
= ω = αt = [ (μgr) / k² ] t
= t = (vk²) / (μgr²)
Now, v = u + αt
= v - u = (μg) + (vk²) / (μgr²)
= u = v [ 1 +(k²/r²) ]
Distance travelled by the ball = s =
= v² = u² - 2αs
= ( u² ) / [ 1 +(k²/r²) ] ² = u² - 2μgs
= s = (u²/2μg) [1 - (1/(1 + (k²/r²))²)]
= s = 18.6566 ft
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a 40 kg stone tied to a string is whirled horizontally at a speed of 2.2 m/s what is the tension in the string
The tension in the string when a 40 kg stone tied to a string is whirled horizontally at a speed of 2.2 m/s will be 488 N/m.
When two solid things come into touch with one another, tension is the force that is generated. A force of tension is the force generated by a rope, string, or chain.
When one mass is drawn vertically and another is being pulled horizontally, there is tension force acting on the string. In the absence of gravity, this gives the tension force pulling on a string.
We are aware that T = mg + ma is the formula used to compute the force of tension.
T = 40(10) + 40(2.2)
T = 488 N/m.
Given that tension is a form of force, it shares the same measurement and unit as force. The CGS unit for tension is dyne whereas the SI unit is newton (N).
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The centripetal acceleration of the stone is:
ac = v2 / r
Let us assume the radius of the string is 1m.
ac = (2.2 m/s)2 / 1
The tension in the string is:
T = m a = (40)*(2.2*2.2)
T = 40 * 2.2 * 2.2
T = 193.6 N
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