Answer:
Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²
Explanation:
Time period of simple pendulum is given by
[tex]T=2\pi\sqrt{\frac{l}{g}}[/tex], l is the length of pendulum, g is acceleration due to gravity value.
We can solve acceleration due to gravity as
[tex]g=\frac{4\pi^2l}{T^2}[/tex]
Here
Length of pendulum = 1.20 m
Pendulum executes simple harmonic motion and makes 100 complete oscillations in 450 s.
Period, [tex]T=\frac{450}{100}=4.5s[/tex]
Substituting
[tex]g=\frac{4\pi^2\times 1.2}{4.5^2}=2.34m/s^2[/tex]
Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²
How many centimeters are there in meter? b. 10 c. d 1000 e. 10000 100 2. A centimeter is equal to 1 inch b.½inch C 1/2.54 inch d. 2.54 inches e. 37.39 inches
Answer:
a) There are 100 centimeters in 1 meter.
b) [tex]\texttt{A cm is equal to }\frac{1}{2.54}\texttt{ inch}[/tex]
Explanation:
a) We have the conversion
1 m = 100 cm
So there are 100 centimeters in 1 meter.
b) 1 inch = 2.54 cm
[tex]1cm=\frac{1}{2.54}inch[/tex]
[tex]\texttt{A cm is equal to }\frac{1}{2.54}\texttt{ inch}[/tex]
A 62.0-kg woman runs up a flight of stairs having a rise of 4.28 m in a time of 4.20 s. What average power did she supply? a) 63.2 W b) 619 W c) 596 W d) 629 W e) 609 W
Answer:
The average power is 619 W.
(B) is correct option
Explanation:
Given that,
Weight = 62.0 kg
Height = 4.28 m
Time t = 4.20 s
We need to calculate the work done
Work done by woman
[tex]W=mgh[/tex]
Where,
m = mass
g = acceleration due to gravity
t = time
Put the value into the formula
[tex]W=62\times9.8\times 4.28[/tex]
[tex]W=2600.528 J[/tex]
We need to calculate the power
Using formula of power
[tex]P=\dfrac{W}{t}[/tex]
Where,
W = work done
t = time
Put the value in to the formula
[tex]P=\dfrac{2600.528}{4.20}[/tex]
[tex]P=619\ W[/tex]
Hence, The average power is 619 W.
The average power supplied by the woman is calculated by first determining the work done against gravity to move up the stairs, and then dividing this by the time taken. After performing these calculations, the most accurate answer is approximately 629 W.
Explanation:The question is asking to calculate the average power supplied by a woman while running up the stairs. Power is defined as the rate at which work is done. In this scenario, the work is the woman's movement against the gravitational force, which is calculated using the formula W = mgh, where m is mass, g is the acceleration due to gravity and h is the height of the stairs. Substituting the given values, we get W = 62.0 Kg * 9.8 m/s² * 4.28 m = 2650.368 Joules. Power is calculated by dividing the work done by the time taken, so P = W/t = 2650.368 J / 4.20 s = 630.8 Watts, which is closest to option (d) 629 W.
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A proton moves perpendicularly to a uniform magnetic field B with a speed of 1.5 × 107 m/s and experiences an acceleration of 0.66 × 1013 m/s 2 in the positive x direction when its velocity is in the positive z direction d the magnitude of the field. The elemental charge is 1.60 × 10−19 C . Answer in units of T.
Answer:
Magnetic field, B = 0.0045 T
Explanation:
It is given that,
Speed of the proton, [tex]v=1.5\times 10^7\ m/s[/tex]
Acceleration of the proton, [tex]a=0.66\times 10^{13}\ m/s^2[/tex]
Charge on proton, [tex]q=1.6\times 10^{-19}\ C[/tex]
The magnetic force is balanced by the force due to the acceleration of the proton as :
[tex]qvB=ma[/tex]
[tex]B=\dfrac{ma}{qv}[/tex]
[tex]B=\dfrac{1.67\times 10^{-27}\ kg\times 0.66\times 10^{13}\ m/s^2}{1.6\times 10^{-19}\ C\times 1.5\times 10^7\ m/s}[/tex]
B = 0.0045 T
So, the magnitude of magnetic field on the proton is 0.0045 T. Hence, this is the required solution.
slope of stress-strain curve in elastic deformation region is a. Plastic modulus b. Poisson's ratio c. Elastic modulus d. None the these a) all of these
Answer:
c) Elastic Modulus
Explanation
As we know that when deformation is under elastic limit then stress applied to the given material is proportional to the strain developed in it
So here we can say that since they both are directly proportional to each other so the proportionality constant here is known as Modulus of elasticity.
So we can say it is given as
[tex]stress = E (strain)[/tex]
so now if we draw a graph between between stress and strain then it must be a straight line and the the slope of this straight line is given as
[tex]Slope = \frac{Stress}{Strain}[/tex]
So here correct answer will be
c) Elastic Modulus
Final answer:
The slope of the stress-strain curve in the elastic deformation region is known as the Elastic Modulus or Young's Modulus, which measures the stiffness of the material. The correct answer to the given question is 'c. Elastic Modulus'.
Explanation:
The slope of the stress-strain curve in the elastic deformation region represents the relationship between stress and strain under elastic conditions. This slope is in fact the Elastic Modulus, which is also known as Young's Modulus when it's in tension or compression. It serves as a measure of the stiffness or rigidity of the material, indicating how much stress is required to achieve a certain amount of strain.
In the context of a stress-strain curve, the plastic modulus is associated with plastic deformation, not the elastic region. Poisson's ratio is another material property that describes the ratio of transverse strain to axial strain, and is not the slope of the curve. Hence, the correct answer to the question is 'c. Elastic Modulus'.
A man, a distance d=3~\text{m}d=3 m from a target, throws a ball at an angle \theta= 70^\circθ=70 ∘ above the horizontal. If the initial speed of the ball is v=5~\text{m/s}v=5 m/s, what height hh does the ball strike the building?
Answer:
The ball doesn't strike the building because it strikes the ground at d=1.62 meters.
Explanation:
V= 5 m/s < 70º
Vx= 1.71 m/s
Vy= 4.69 m/s
h= Vy * t - g * t²/2
clearing t for the flying time of the ball:
t= 0.95 s
d= Vx * t
d= 1.62 m
A meteoroid is traveling east through the atmosphere at 18. 3 km/s while descending at a rate of 11.5 km/s. What is its speed, in km/s?
Answer:
The speed of meteoroid is 21.61 km/s in south-east.
Explanation:
Given that,
A meteoroid is traveling through the atmosphere at 18.3 km/s. while descending at a rate of 11.5 km/s it means 11.5 km/s in south.
We need to draw a diagram
Using Pythagorean theorem
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC^2=(18.3)^3+(11.5)^2[/tex]
[tex]AC=\sqrt{(18.3)^2+(11.5)^2}[/tex]
[tex]AC=21.61\ km/s[/tex]
Hence, The speed of meteoroid is 21.61 km/s in south-east.
The speed of the meteoroid is calculated using the Pythagorean theorem and is approximately 21.62 km/s.
To calculate the speed (magnitude of the velocity), the equation is: speed = √(horizontal velocity)² + (vertical velocity)².
Thus, the speed = √(18.3 km/s)² + (11.5 km/s)² = √(335.29 + 132.25) km²/s² = √467.54 km²/s² = 21.62 km/s.
The meteoroid's speed through the atmosphere is approximately 21.62 km/s.
The earth orbits the sun once per year at the distance of 1.50 x 1011 m. Venus orbits the sun at a distance of 1.08 x 1011 m. These distances are between the centers of the planets and the sun. How long (in earth days) does it take for Venus to make one orbit around the sun
It takes 225 Earth days for Venus to orbit the Sun. Interestingly, Venus spins on its axis so slowly that its day (243 Earth days) is longer than its year. The Sun takes 117 Earth days to return to the same place in Venus' sky.
Explanation:The time it takes for Venus to make one orbit around the sun, also known as its orbital period, is actually 225 Earth days. This is quite different compared to Earth which takes 365.25 days to orbit the Sun. Additionally, Venus spins on its axis very slowly, with its rotational period being 243 Earth days. As a result, a day on Venus - considering its rotation - is longer than its year! Also, this leads to an unusual phenomenon where the sun takes 117 Earth days to return to the same place in the Venusian sky. This suggests that Venus' rotation and orbit display unique characteristics compared to other planets in our solar system, likely due to factors from its formation.
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Venus completes one orbit around the Sun in approximately 225 Earth days. This is shorter than Earth's orbital period due to Venus's closer distance to the Sun.
Orbit of Venus Around the Sun-
The distance between the Earth and the Sun is approximately 1.50 x 1011 meters, while Venus is closer, at 1.08 x 1011 meters. This difference in distance influences the orbital period of each planet. Venus takes about 225 Earth days to complete one full orbit around the Sun.
Venus has a nearly circular orbit and, being closer to the Sun than Earth, receives almost twice as much light and heat. The elliptical orbits mean that different planets have different orbital periods, with those closer to the Sun having shorter years.
An alpha particle travels at a velocity of magnitude 760 m/s through a uniform magnetic field of magnitude 0.034 T. (An alpha particle has a charge of charge of 3.2 × 10-19 C and a mass 6.6 × 10-27 kg) The angle between the particle's direction of motion and the magnetic field is 51°. What is the magnitude of (a) the force acting on the particle due to the field, and (b) the acceleration of the particle due to this force
Answer:
(a) 6.42 x 10^-18 N
(b) 9.73 x 10^8 m/s^2
Explanation:
v = 760 m/s, B = 0.034 T, m = 6.6 x 10^-27 kg, q = 3.2 x 10^-19 C, theta = 51 degree
(a) F = q v B Sin theta
F = 3.2 x 10^-19 x 760 x 0.034 x Sin 51
F = 6.42 x 10^-18 N
(b) Acceleration, a = Force / mass
a = (6.42 x 10^-18) / (6.6 x 10^-27)
a = 0.973 x 10^9
a = 9.73 x 10^8 m/s^2
A satellite orbits the earth in a circle with constant speed. Which of the following is true? The net force on the satellite is zero because the satellite is not accelerating. The net force on the satellite is directed forward, in the direction of travel. The net force on the satellite is directed straight down, toward the Earth. The net force on the satellite is directed outward, away from the Earth.
Explanation:
A satellite orbiting the Earth is a characteristic example of the uniform circular motion, where the direction of the velocity vector [tex]\vec{V}[/tex] is perpendicular to the radius [tex]r[/tex] of the trajectory. Hence, the velocity is changing although the speed is constant.
On the other hand, acceleration [tex]\vec{a}[/tex] is directed toward the center of the circumference (that is why it is called centripetal acceleration).
Now, according to Newton's 2nd law, the force [tex]\vec{F}[/tex] is directly proportional and in the same direction as the acceleration:
[tex]\vec{F}=m.\vec{a}[/tex]
Therefore, the net force on the satellite resulting from its circular motion points towards the center of the circle (where the Earth is in the Earth-satellite system).
A propeller is modeled as five identical uniform rods extending radially from its axis. The length and mass of each rod are 0.715 m0.715 m and 2.51 kg2.51 kg , respectively. When the propellor rotates at 527 rpm527 rpm (revolutions per minute), what is its rotational kinetic energy?
Answer:
3260.33 J
Explanation:
[tex]n [/tex] = number of rods = 5
[tex]L [/tex] = length of each rod = 0.715 m
[tex]m [/tex] = mass of rod = 2.51 kg
[tex]I [/tex] = total moment of inertia
Total moment of inertia is given as
[tex]I = \frac{nmL^{2}}{3}[/tex]
[tex]I = \frac{(5)(2.51)(0.715)^{2}}{3}[/tex]
[tex]I [/tex] = 2.14 kgm²
[tex]w [/tex] = angular speed = 527 rpm = 55.2 rad/s
Rotational kinetic energy is given as
E = (0.5) [tex]I [/tex] ([tex]w [/tex] )²
E = (0.5) (2.14) (55.2)²
E = 3260.33 J
Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always twotwo times its height. Suppose the height of the pile increases at a rate of 33 cm divided by scm/s when the pile is 1010 cm high. At what rate is the sand leaving the bin at that instant?
Answer:
-423 m³/s
Explanation:
Volume of a cone is:
V = ⅓ π r² h
Given r = 2h:
V = ⅓ π (2h)² h
V = ⁴/₃ π h³
Taking derivative with respect to time:
dV/dt = 4π h² dh/dt
Given h = 1010 cm and dh/dt = 33 cm/s:
dV/dt = 4π (1010 cm)² (33 cm/s)
dV/dt ≈ 4.23×10⁸ cm³/s
dV/dt ≈ 423 m³/s
The pile is growing at 423 m³/s, so the bin is draining at -423 m³/s.
The rate at which the sand is leaving the bin at that instant is [tex]423\times 10^{6} cm^{3}/s[/tex].
GivenIt is given that the radius of a conical bin is two times its height and at the instant when the height of the bin is [tex]1010cm[/tex], the height of the pile increases at a rate of [tex]33 cm/s[/tex].
Volume of the binThe formula for the volume of a cone is given as,
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
Substitute [tex]r=2h[/tex] as per the question
[tex]V=\frac{4}{3}\pi h^{3}[/tex]
This is the volume of the conical bin.
Rate of change in the volume of the binTo find the rate of change in the volume of the bin, differentiate the expression for volume w.r.t. time using the chain rule as follows,
[tex]\frac{dV}{dt}=\frac{dV}{dh}\times \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt}=\frac{4}{3}\pi (3h^{2}) \times \frac{dh}{dt}\\\\\frac{dV}{dt}=4\pi h^{2} \times \frac{dh}{dt}\\[/tex]
Now, according to the question, at [tex]h=1010cm[/tex], [tex]\frac{dh}{dt}=33[/tex].
Substituting these values, the rate at which the sand is leaving the bin is,
[tex]\frac{dV}{dt}=4\pi (1010)^{2} \times 33\\\frac{dV}{dt}=423,025,503.90235\\\frac{dV}{dt}=423\times10^{6}cm^{3}/s[/tex]
So, the rate at which the sand leaves the conical bin at the given instant is [tex]423\times10^{6}cm^{3}/s[/tex]
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A 2.0 kg ball and a 3.5 kg ball, each moving at 0.90 m/s, undergo a head-on collision. The lighter ball rebounds opposite its initial direction, with speed 0.90 m/s.Find the post-collision velocity of the heavier ball. Assume the initial direction of the lighter ball as positive.How much mechanical energy was lost in this collision? Express your answer in J.How much mechanical energy was lost in this collision? Express your answer as a fraction of the system's initial mechanical energy.
Explanation:
It is given that,
Mass of first ball, m₁ = 2 kg
Mass of other ball, m₂ = 3.5 kg
Velocities of both balls, u = 0.9 m/s
(1) The lighter ball rebounds opposite its initial direction, with speed 0.90 m/s. We need to find the final velocity of second ball. Applying the conservation of momentum as :
[tex]2\ kg\times 0.9-3.5\ kg\times 0.9\ m/s=-2\ kg\times 0.9\ m/s+3.5v[/tex]
v is the final velocity of heavier ball.
v = 0.128 m/s
or
v = 0.13 m/s
Initial kinetic energy, [tex]E_i=\dfrac{1}{2}\times (2\ kg+3.5\ kg)\times (0.9\ m/s)^2=2.23\ J[/tex]
Final kinetic energy, [tex]E_f=\dfrac{1}{2}\times 2\ kg\times (0.9\ m/s)^2+\dfrac{1}{2}\times 3.5\ kg\times (0.13\ m/s)^2=0.84\ J[/tex]
Lost in kinetic energy, [tex]\Delta KE=0.84-2.23=-1.39\ J[/tex]
Hence, this is the required solution.
An ambulance with a siren emitting a whine at 1570 Hz overtakes and passes a cyclist pedaling a bike at 2.45 m/s. After being passed, the cyclist hears a frequency of 1560 Hz. How fast is the ambulance moving? (Take the speed of sound in air to be 343 m/s.)
Answer:
The speed of the ambulance is 4.66 m/s.
Explanation:
Given that,
The siren emitting a whine at 1570 Hz
The cyclist pedaling a bike at 2.45 m/s
The cyclist hears a frequency of 1560 Hz
We know that,
Speed of sound wave
[tex]v = 343\ m/s[/tex]
We calculate the speed of the ambulance
Using Doppler effect,
[tex]f'=f\times\dfrac{v+v_{o}}{v+v_{s}}[/tex]
Where,
[tex]f' [/tex]= frequency of ambulance siren
[tex]f [/tex]= cyclist hears the frequency
[tex]v_{s}[/tex]=speed of source
[tex]v_{v}[/tex]= speed of observer
Put the value in to the formula
[tex]v_{s}=f\times\dfrac{v+v_{o}}{f'}-v[/tex]
[tex]v_{s}=1570\times\dfrac{343-2.45}{1560}-343[/tex]
[tex]v_{s}=4.66\ m/s[/tex]
Hence, The speed of the ambulance is 4.66 m/s.
Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 4.00. What should be the length of B⃗ so that the magnitude of their vector sum is 9.00?
Answer:
B= [tex]\sqrt{65}[/tex] ≅8.06
Explanation:
Using the Pythagorean theorem:
[tex]C^{2}[/tex]= [tex]A^{2}[/tex] + [tex]B^{2}[/tex]
where C represents the length of the hypotenuse and A and B the lengths of the triangle's other two sides, we can find out the lenght of B assuming the value of the hypotenuse being 9 and A being 4.
[tex]9^{2}[/tex]=[tex]4^{2}[/tex] + [tex]B^{2}[/tex]
81= 16+ [tex]B^{2}[/tex]
81-16= [tex]B^{2}[/tex]
B= [tex]\sqrt{65}[/tex] ≅8.06
The length of B is equal to 8.06 units
Data given;
A = 4.0B = ?C = 9.0Resolution of VectorsTo solve this question, we have to use the formula of finding resultant vectors
Since it's a right-angle triangle, let's use Pythagoras' theorem
[tex]C^2=A^2 + B^2\\9^2 = 4^2 + B^2\\b^2 = 9^2 - 4^2\\b^2 = 65\\b = \sqrt{65}\\b = 8.06[/tex]
From the calculation above, the length of B is equal to 8.06.
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Consider a simple tension member that carries an axial load of P=22.44N. Find the total elongation in the member due to the load. Assume that the member is made of steel, which has a modulus of elasticity of E=204.00 N/mm2. Also assume that the member is 3048 mm long and has a cross-sectional area of 1290 mm2
Answer:
The total elongation for the tension member is of 0.25mm
Explanation:
Assuming that material is under a linear deformation then the relation between the stress and the specific elongation is given as:
[tex]\sigma=E*\epsilon[/tex] (1)
Where E is the modulus of elasticity, σ the stress and ε the specific deformation. Also, the total longitudinal elongation can be expressed as:
[tex]\delta L=L*\epsilon[/tex] (2)
Here L is the member extension and δL the change total longitudinal elongation.
Now if the stress is found then the deformation can be calculated by solving the stress-deformation equation (1). The stress applied sigama is computed dividing the axial load P by the cross-sectional area A:
[tex]\sigma=P/A[/tex]
[tex]\sigma=22.44N / 1290 mm^2[/tex]
[tex]\sigma=0.0174 N/mm^2[/tex]
Solving for epsilon and replacing the calculated value for the stress and the value for the modulus of elasticity:
[tex]=\sigma=E*\epsilon[/tex]
[tex]\epsilon=\sigma/E[/tex]
[tex]\epsilon=0.0174 \frac{N}{mm^2}/\ 204 \frac{N}{mm^2} [/tex]
[tex]\epsilon=8.53*10^-{5}[/tex]
Finally introducing the specific deformation and the longitudinal extension in the equation of total elongation (2):
[tex]\delta L=3048 mm * 8.53*10^{-5} [/tex]
[tex]\delta L= 0.25 mm [/tex]
The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s. A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion. How far away is the explosion?
Answer:
21828 m
Explanation:
[tex]v_{ground}[/tex] = speed of sound through ground = 6 km/s = 6000 m/s
[tex]v_{air}[/tex] = speed of sound through air = 343 m/s
t = time taken for the vibrations to arrive
t' = time taken for sound to arrive = t + 60
d = distance of the point of explosion
time taken for the vibrations to arrive is given as
[tex]t = \frac{d}{v_{ground}}[/tex] eq-1
time taken for the sound to arrive is given as
[tex]t' = \frac{d}{v_{air}}[/tex]
[tex]t + 60 = \frac{d}{v_{air}}[/tex]
using eq-1
[tex]\frac{d}{v_{ground}} + 60 = \frac{d}{v_{air}}[/tex]
[tex]\frac{d}{6000} + 60 = \frac{d}{343}[/tex]
d = 21828 m
An arrangement of source charges produces the electric potential V=5000x2V=5000x2 along the x-axis, where V is in volts and x is in meters. What is the maximum speed of a 1.0 g, 10 nC charged particle that moves in this potential with turning points at ± 8.0 cm?
Answer:
v = 0.025 m/s
Explanation:
Given that the voltage is
[tex]V = 5000 x^2[/tex]
now at x = 0
[tex]V_1 = 0 Volts[/tex]
also we have at x = 8 cm
[tex]V_2 = 5000(0.08)^2 = 32 Volts[/tex]
now change in potential energy of the charge is given as
[tex]\Delta U = q\Delta V[/tex]
[tex]\Delta U = (10 \times 10^{-9})(32 - 0)[/tex]
now by mechanical energy conservation law
[tex]\frac{1}{2}mv^2 - 0 = 3.2 \times 10^{-7}[/tex]
[tex]\frac{1}{2}(1 \times 10^{-3})v^2 = 3.2 \times 10^{-7}[/tex]
[tex]v = 0.025 m/s[/tex]
The maximum speed of the particle in arrangement of source charges produces 32 volts electric potential is 0.025 meter per second.
What is electric potential energy?Electric potential energy is the energy which is required to move a unit charge from a point to another point in the electric field.
It can be given as,
[tex]U=qV[/tex]
Here, (q) is the charge and (V) is the electric potential difference.
Given infroamtion-
The electric potential producers by the arrangement of source charges is given by,
[tex]V=5000x^2[/tex]
The mass of the particle is 1.0 gram.
The charge of the particles 10 nC.
As, the electric potential producers by the arrangement of source charges is given by,
[tex]V=5000x^2[/tex]
At the x equal to 8 cm or 0.08 m, the equation become,
[tex]V=5000(0.08)^2\\V=32\rm V[/tex]
Thus the potential difference at the is 32 volts.
The electric potential energy of the particle is,
[tex]U=10\times10^{-9}\times32\\U=3.2\times10^{-7}\rm j[/tex]
Now the electric potential energy is equal to the kinetic energy of the particle. Thus,
[tex]\dfrac{1}{2}\times0.001\times v^2=3.2\times10^{-7}\\v=0.025\rm m/s[/tex]
Thus the maximum speed of particle is 0.025 meter per second.
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An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was 7000 N {\rm N}. When the craft was lowered or raised at a steady rate, the motion through the water added an 1800 N {\rm N} drag force.
Part A
What was the tension in the cable when the craft was being lowered to the seafloor?
Express your answer to two significant figures and include the appropriate units.
Part B
What was the tension in the cable when the craft was being raised from the seafloor?
Express your answer to two significant figures and include the appropriate units.
Answer:
A) 5.2 x 10³ N
B) 8.8 x 10³ N
Explanation:
Part A)
[tex]F_{g}[/tex] = weight of the craft in downward direction = tension force in the cable when stationary = 7000 N
[tex]T[/tex] = Tension force in upward direction
[tex]F_{d}[/tex] = Drag force in upward direction = 1800 N
Force equation for the motion of craft is given as
[tex]F_{g}[/tex] - [tex]F_{d}[/tex] - [tex]T[/tex] = 0
7000 - 1800 - [tex]T[/tex] = 0
[tex]T[/tex] = 5200 N
[tex]T[/tex] = 5.2 x 10³ N
Part B)
[tex]F_{g}[/tex] = weight of the craft in downward direction = tension force in the cable when stationary = 7000 N
[tex]T[/tex] = Tension force in upward direction
[tex]F_{d}[/tex] = Drag force in downward direction = 1800 N
Force equation for the motion of craft is given as
[tex]T[/tex] - [tex]F_{g}[/tex] - [tex]F_{d}[/tex] = 0
[tex]T[/tex] - 7000 - 1800 = 0
[tex]T[/tex] = 8800 N
[tex]T[/tex] = 8.8 x 10³ N
A 2010 kg space station orbits Earth at an altitude of 5.35×105 m. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98×1024 kg and 6.37×106 m, respectively.
Answer:
Force, F = 16814.95 N
Explanation:
It is given that,
Mass of space station, m = 2010 kg
Altitude, [tex]d=5.35\times 10^5\ m[/tex]
Mass of earth, [tex]m=5.98\times 10^{24} kg[/tex]
Mean radius of earth, [tex]r=6.37\times 10^6\ m[/tex]
Magnitude of force is given by :
[tex]F=G\dfrac{Mm}{R^2}[/tex]
R = r + d
[tex]R=6.37\times 10^6\ m+5.35\times 10^5\ m=6905000\ m[/tex]
[tex]F=6.67\times 10^{-11}\times \dfrac{2010\ kg\times 5.98\times 10^{24} kg}{(6905000\ m)^2}[/tex]
F = 16814.95 N
So, the force between the space station and the Earth is 16814.95 N. Hence, this is the required solution.
A motoris st enters a freeway at a speed of 35 mi/h and accelerates uniformly to a speed of 55 mi h. The motorist travels 500 ft while accelerating. I Determine: ) The acceleration of the car 2) The time required to reach 55 mi/h.
Answer:
1) The acceleration of the car = 1.17 m/s²
2) The time required to reach 55 mi/h = 7.59 seconds.
Explanation:
1) Initial speed of motorist, u = 35 mph = 15.56 m/s
Final speed of motorist, v = 55 mph = 24.44 m/s
Distance traveled, s = 500ft = 152.4 m
We have v² = u² + 2as
24.44² = 15.56² + 2 x a x 152.4
a = 1.17 m/s²
The acceleration of the car = 1.17 m/s²
2) We have v = u + at
24.44 = 15.56 + 1.17 x t
t = 7.59 s
The time required to reach 55 mi/h = 7.59 seconds.
A mass of 0.14 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.28 m)cos[(8 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass .
Answer:
The amplitude of oscillation for the oscillating mass is 0.28 m.
Explanation:
Given that,
Mass = 0.14 kg
Equation of simple harmonic motion
[tex]x(t)=(0.28\ m)\cos[(8\ rad/s)t][/tex]....(I)
We need to calculate the amplitude
Using general equation of simple harmonic equation
[tex]y=A\omega \cos\omega t[/tex]
Compare the equation (I) from general equation
The amplitude is 0.28 m.
Hence, The amplitude of oscillation for the oscillating mass is 0.28 m.
A proton is placed in a uniform electric field and then released. Then an electron is placed at this same point and released. Which of the following is correct?
The 2 particles experience the same magnitude of force, experience the same magnitude of acceleration, and move in different directions.
The 2 particles experience the same magnitude of force, experience different magnitudes of acceleration, and move in different directions.
The 2 particles experience different magnitudes of force, experience different magnitudes of acceleration, and move in different directions.
The 2 particles experience the same magnitude of force, experience different magnitudes of acceleration, and move in the same direction.
None of the above.
Answer:
option (b)
Explanation:
Let the electric field is given by E.
mass of proton = mp
mass of electron = me
acceleration of proton = ap
acceleration of electron = ae
Charge on both the particle is same but opposite in nature.
The force on proton = q E
The force on electron = - q E
acceleration of proton, ap = q E / mp
acceleration of electron, ae = - q E / me
We observe that the force is same in magnitude but opposite in direction, acceleration is also different and opposite in direction.
Final answer:
The electron and proton experience the same magnitude of force but different accelerations due to their mass difference, and move in opposite directions because of their opposite charges.
Explanation:
When a proton and an electron are placed in a uniform electric field and released, they both experience the same magnitude of force, because they have equal and opposite charges of the same magnitude. However, their accelerations differ due to their masses. The electron has a much smaller mass compared to the proton, and according to Newton's second law (F = ma), a given force will produce a larger acceleration on an object with a smaller mass.
Therefore, while the magnitudes of the forces are the same, the electron will experience a greater magnitude of acceleration than the proton. Finally, they move in opposite directions because the electric field exerts a force in the direction of the field on positive charges and in the opposite direction on negative charges. Therefore, the electron moves in the opposite direction to the proton when released in the same electric field.
A marble rolls off the edge of a table top with a speed of 2.00 m/s. a.) What is the magnitude of its velocity 0.100 s later? b.) How far from the table does it land? The height of the table is 1.00m.
Answer:
(a) 2.23 m/s
(b) 0.9 m
Explanation:
h = 1 m, t = 0.1 second
horizontal component of initial velocity, ux = 2 m/s
vertical component of initial velocity, uy = 0
(a) Let v be the velocity after 0.1 seconds. Its vertical component is vy and horizontal component is vx.
The horizontal component of velocity remains constant as in this direction, acceleration is zero.
vx = ux = 2 m/s
Use first equation of motion in Y axis direction.
vy = uy + g t
vy = 0 + 9.8 x 0.1 = 0.98 m/s
Resultant velocity after 0.1 second
v^2 = vx^2 + vy^2
v^2 = 2^2 + 0.98^2
v = 2.23 m/s
(b) Let it takes time t to land.
Use second equation of motion along Y axis
h = uy t + 1/2 g t^2
1 = 0 + 1/2 x 9.8 x t^2
t = 0.45 second
Let it lan at a distance x.
so, x = ux x t
x = 2 x 0.45 = 0.9 m
For an RLC series circuit, R = 100Ω, L = 150mH, and C = 0.25μF. (a) If an ac source of variable frequency is connected to the circuit, at what frequency is maximum power dissipated in the resistor? (b) What is the quality factor of the circuit?
Answer:
[tex]\omega_O = 0.16 rad /sec[/tex]
Q = 0.24
Explanation:
given data:
resonant angular frequency is given as \omega_O = \frac{1}{\sqrt{LC}}
where L is inductor = 150 mH
C is capacitor = 0.25\mu F
[tex]\omega = \frac{1}{\sqrt{150*10^{6}*0.25*10^{-6}}}}[/tex]
[tex]\omega_O = 0.16 rad /sec[/tex]
QUALITY FACTOR is given as
[tex]Q = \frac{1}{R}{\sqrt\frac{L}{C}}[/tex]
Putting all value to get quality factor value
Q =[tex] \frac{1}{1000}{\sqrt\frac{150*10^{6}}{0.25*10^{-6}}}[/tex]
Q = 0.24
Final answer:
The maximum power dissipation in the resistor occurs at a frequency of approximately 1175.5 Hz in an RLC series circuit with the given values of R, L, and C. The quality factor of the circuit is approximately 57.74.
Explanation:
In an RLC series circuit, the maximum power dissipation in the resistor is achieved at the resonant frequency, which is given by the formula:
fr = 1 / (2π √LC)
Substituting the given values:
R = 100Ω, L = 150mH (or 0.15H), and C = 0.25μF (or 0.00000025F), we can calculate the resonant frequency:
fr = 1 / (2π √(0.15 x 0.00000025))
fr ≈ 1175.5 Hz
Therefore, the maximum power dissipation in the resistor occurs at a frequency of approximately 1175.5 Hz.
The quality factor (Q) of the circuit is a measure of its damping ability. It is given by the formula:
Q = R √C / L
Substituting the given values:
R = 100Ω, L = 150mH (or 0.15H), and C = 0.25μF (or 0.00000025F), we can calculate the quality factor:
Q = 100 √(0.00000025) / 0.15
Q ≈ 57.74
Therefore, the quality factor of the circuit is approximately 57.74.
A 34.34 g sample of a substance is initially at 26.7 °C. After absorbing 2205 J of heat, the temperature of the substance is 152.1 °C. What is the specific heat (c) of the substance?
Answer:
The specific heat of the substance is c= 512.04 J/kg K
Explanation:
ΔQ= 2205 J
m= 0.03434 kg
ΔT= 125.4 ºC
ΔQ= m * c * ΔT
c= ΔQ / (m * ΔT)
c= 512.04 J/Kg K
A stone with a mass of 10 kg is sitting on the ground, not moving. a) What is the weight of the stone? b) What is the normal force acting on the stone?
Answer:
A) weight=mass X gravitational force
10Kg X 10 M/S 2
100 KgM/S2
100Newton
B) Force =Mass X gravitational force
10Kg X 10 M/S2
100 Newton
The weight of a 10kg stone sitting at rest on the ground is 98 Newtons, and the normal force acting on it is also 98 Newtons.
Explanation:The weight of an object is calculated by multiplying its mass by the acceleration due to gravity. In this case, the mass of the stone is 10kg and The standard acceleration due to gravity on Earth is approximately 9.8 m/s2. Therefore, the weight of the stone would be 10 kg x 9.8 m/s^2 = 98 Newtons.
b) The normal force acting on the stone is the force exerted by the surface of the ground on the stone in the upward direction. When the stone is sitting on the ground, the normal force is equal in magnitude and opposite in direction to the weight of the stone. Therefore, the normal force is also 98 N.
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A 78 kg skydiver can be modeled as a rectangular "box" with dimensions 24 cm × 35 cm × 170 cm . If he falls feet first, his drag coefficient is 0.80.What is his terminal speed if he falls feet first? Use ? = 1.2 kg/^m3 for the density of air at room temperature.
Answer:
The terminal speed of his is 137.68 m/s.
Explanation:
Given that,
Mass of skydiver = 78 kg
Area of box[tex]A =24\times35=840\ cm[/tex]
Drag coefficient = 0.80
Density of air [tex]\rho= 1.2\times kg/m^3[/tex]
We need to calculate the terminal velocity
Using formula of drag force
[tex]F_{d} = \dfrac{1}{2}\rho v^2Ac[/tex]
Where,
[tex]\rho[/tex] = density of air
A = area
C= coefficient of drag
Put the value into the formula
[tex]78\times9.8=\dfrac{1}{2}\times1.2\times v^2\times24\times10^{-2}\times35\times10^{-2}\times0.80[/tex]
[tex]v^2=\dfrac{2\times78\times9.8}{1.2\times24\times10^{-2}\times35\times10^{-2}\times0.80}[/tex]
[tex]v=\sqrt{\dfrac{2\times78\times9.8}{1.2\times24\times10^{-2}\times35\times10^{-2}\times0.80}}[/tex]
[tex]v=137.68\ m/s[/tex]
Hence, The terminal speed of his is 137.68 m/s.
The terminal speed of the skydiver with dimensions as a rectangular box as he falls feet first is 137.68 m/s.
What is the terminal speed?Terminal speed of a body is the maximum speed, which is achieved by the object when it fall through a fluid.
In the case of terminal velocity, the force of gravity becomes equal to the sum of the drag force and buoyancy force due to fluid on body.
Terminal velocity can be find out as,
[tex]v=\sqrt{\dfrac{2mg}{\rho AC_d}}[/tex]
Here, (m) is the mass, (g) is gravitational force, ([tex]\rho[/tex]) is the density of fluid, (A) is the project area and ([tex]C_d[/tex]) is the drag coefficients.
It is given that, the mass of the skydiver is 78 kg The dimensions of the skydiver is s 24 cm × 35 cm × 170 cm.
The coefficient of drag is 0.80 and the density of air is 1.2 kg/m³.
Put the values in the above formula as,
[tex]v=\sqrt{\dfrac{2\times78\times9.8}{1.2\times0.24\times0.35\times 0.8}}\\v=137.68\rm m/s[/tex]
Thus the terminal speed of the skydiver as he falls feet first is 137.68 m/s.
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When two or more resistors are connected in parallel to a battery A) the voltage across each resistor is the same. B) the total current flowing from the battery equals the sum of the currents flowing through each resistor. C) the equivalent resistance of the combination is less than the resistance of any one of the resistors D) all of the other choices are true
Answer:
Here, for parallel resisitors
Option D) all of the other choices are are true
is correct.
Explanation:
In parallel connection:
1) Voltage across each element connected in parallel remain same.
2) Kirchhoff's Current Law (KCL), sum of the current entering and leaving the junction will be zero
3) The equivalent resistance of the elements connected in parallel is always less than the individual resistance of any resistor in the circuit.
The equivalent resistance in a parallel circuit is given by:
[tex]\frac{1}{R_{eq}} = \frac{1}{R_1} +\frac{1}{R_2} +......+ \frac{1}{R_n}[/tex]
Final answer:
When resistors are connected in parallel, the voltage across each resistor is the same, the total current flowing from the battery equals the sum of the currents flowing through each resistor, and the equivalent resistance of the combination is less than the resistance of any one of the resistors.
Explanation:
When two or more resistors are connected in parallel to a battery:
The voltage across each resistor is the same. This is because in a parallel circuit, all the resistors have the same potential difference across them.
The total current flowing from the battery equals the sum of the currents flowing through each resistor. In a parallel circuit, the total current is divided among the different resistors.
The equivalent resistance of the combination is less than the resistance of any one of the resistors. This is because adding resistors in parallel decreases the overall resistance of the circuit.
You are trying to take an image of a particular star with apparent magnitude m=10, and need to figure out how long you will need to expose for with your telescope. Your friend tells you that her telescope of diameter 0.05 metres can detect the star in 119.5 minutes.
a) If your telescope has diameter 0.18 metres, how long do you need to expose for? Answer in minutes.
You haven't told us anything about the detectors being used. We don't know how the sensitivity of the detector is related to the total number of photons absorbed, and we don't even know whether you and your friend are both using the same type of detector.
All we can do, in desperation, is ASSUME that the minimum time required to just detect a star is inversely proportional to the total number of its photons that strike the detector. That is, assume . . .
(double the number of photons) ===> (detect the source in half the time) .
-- The intensity of light delivered to the prime focus of a telescope is directly proportional to the AREA of its objective lens or mirror, which in turn is proportional to the square of its radius or diameter.
So your telescope gathers (0.18/0.05)² = 12.96 times as much light as your friends telescope does.
-- So we'd expect your instrument to detect the same star in
(119.5 min) / (12.96) = 9.22 minutes .
We're simply comparing the performance of two different telescopes as they observe the same object, so the star's magnitude doesn't matter.
If your telescope has diameter 0.18 metres, for 9.22 minutes, you need to expose for.
What is telescope ?An optical telescope is one that collects and sharply concentrates light. Mostly from the visible parts of the spectrum. That is to make a magnified image for close inspection, to take a picture, or you might say to get information from an electronic sensor image.
A reflecting telescope, sometimes called a reflector, is one that creates images by reflecting light off either a single curved mirror or a group of mirrors. Sir Isaac Newton created the reflecting telescope inside the 17th century as a replacement for the refracting one.
your telescope gathers (0.18/0.05)² = 12.96 times as much light as your friends telescope does.
(119.5 min) / (12.96) = 9.22 minutes
Therefore, for 9.22 minutes, you need to expose for.
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A Ferris wheel has radius 4.0 m and makes one revolution every 30 s with uniform rotation. A woman who normally weighs 600 N is sitting on one of the benches attached at the rim of the wheel. What is her apparent weight (the normal force exerted on her by the bench) as she passes over the top of the Ferris wheel? A. 590 N
B. 600 N
C. 520 N
D. 0 N
Answer:
A) Apparent Weight = 590 N
Explanation:
As we know that frequency is given as
[tex]f = \frac{1}{30}[/tex]
[tex]f = 0.033 Hz[/tex]
now the angular speed is given as
[tex]\omega = 2\pi f[/tex]
[tex]\omega = 2\pi(0.033) = 0.21 rad/s[/tex]
now at the top position we will have
[tex]mg - N = m\omega^2 R[/tex]
[tex]N = mg - m\omega^2 R[/tex]
[tex]N = 600 - \frac{600}{9.8}(0.21)^2(4.0)[/tex]
[tex]N = 590 N[/tex]
The woman's apparent weight at the top of the Ferris wheel is less than her actual weight due to the centripetal force experienced during the uniform circular motion. This apparent weight can be calculated by subtracting the centripetal force from the gravitational force, yielding an answer of 590 N.
Explanation:This problem revolves around the concepts of centripetal force and apparent weight in the context of uniform circular motion. The woman's apparent weight at the top of the Ferris wheel is less than her actual weight because of the centripetal force directed towards the center of the Ferris wheel.
To calculate the apparent weight, we should subtract the centripetal force from the gravitational force. The gravitational force is her actual weight, and since weight = mass * gravity, her mass equals 600N/9.8 m/s2 ~= 61.2 kg. The angular velocity of the Ferris wheel (ω) is 2π rad/30s since it makes one revolution every 30s. Using the formula centripetal force = m*ω2*r, we find that the centripetal force equals 61.2 kg * (2π rad/30s)2 * 4m = 10 N approximately.
Finally, the woman's apparent weight at the top is the gravitational force minus the centripetal force, or 600 N - 10 N, which equals 590 N. Therefore, the correct answer is A) 590 N.
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