Answer:
20 N
Explanation:
Vertical component will be 44 sin 63
HORIZONTAL component is 44 cos 63 N = 19.97 =~ 20 N
a square loop of wire with initial side length 20 cm is placed in a magnetic field of strength 0.5 t. the field is parallel to the axis of the loop. somebody carefully grabs the edges of the loop and begins pulling them apart such that the area of the loop increases at a rate of 20 cm2/s. what is the magnitude of the induced emf in the loop?
The magnitude of the induced emf in the loop is 1mV.
The formula to be used is:
E = B (dA/dt)
B = magnetic of magnetic field parallel to the axis of loop = 0.5 T
dA/dt = rate of change of area of the loop = 20 cm²/s = 20 x 10⁻⁴ m²
θ = Angle of the magnetic field with the area vector = 0
E = emf induced in the loop
Now, plugging in the values we get:
E = B (dA/dt)
E = (0.5) (20 x 10⁻⁴ )
E = 10 x [tex]10^{-4}[/tex] volts
E = 1 mV
Therefore, the magnitude of the induced emf in the loop is 1mV.
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you have two solid metal sphere that are identical except thatr one has a radius exactly twice the other(with the same density). what is the ratio of their moment of inertia?
The elasticity and Poisson's ratio for this metal is 0.232.
What is ratio?
The realation between two numbers which shows how much bigger one quantity is than another.
Sol-
As per the given question
P=190KN
d=16 mm
Lo=50mm
X=50.1349-50=0.1349mm
Y=15.99-16=-0.01mm
The formula-
E=ó/€
Ó=P/A
A=r/4 d^2 =π/4(16)^2=201.062 mm
ó={190(1000)}201.062=944.982 Mpa
E=944.982/0.002698=350.253 GPa
€y=-0.000625
v=0.232(answer)
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tell the answer please
r - Radius
h - Height
1. Area of a circle = π×r²
2. Circumference of a circle = 2×π×r
3. Volume of a cylinder = π×r²×h
A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been a solid in three dimensions. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
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suppose we want to place a weather satellite into a circular orbit 300 kmkm above the earth's surface. what speed, period, and radial acceleration must it have? the earth's radius is 6380km
a. The speed of the satellite is 244 m/s
b. The period of the satellite is 1.72 × 10⁷ s
c. The radial acceleration of the satellite is 8913 rad/s
What is the speed of the satellite?The speed of the satellite is given by v = √(GM/R) where
G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.972 × 10²⁴ kg and R = radius of orbit = r + r' where r = radius of earth = 6380 km and r' = radius of orbit = 300 kmSo, substituting the values of the variables into the equation, we have that
v = √(GM/R)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6380 km + 300 km)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6680 km)
v = √(39.83324 × 10¹³ Nm²/kg ÷ 6.680 × 10⁶ m)
v = √(5.963 × 10⁻³ × 10⁷ Nm²/kg)
v = √(5.963 × 10⁴ Nm/kg)
v = 2.44 × 10² m/s
V = 244 m/s
So, the speed of the satellite is 244 m/s
b. What is the period of the orbit?The period of the orbit is given by T = 2πR/v where
R = radius of orbit = 6680 km and v = speed of orbit = 244 m/sSo, substituting the values of the variables into the equation, we have
T = 2πR/v
T = 2π × 6680 km/244 m/s
T = 2π × 6680 × 10³ m/244 × 10⁵ m/s
T = 13660π × 10³ m/244 × 10⁵ m/s
T = 41971.68 × 10³ m/244 × 10⁵ m/s
T = 17201.5 × 10³ s
T = 1.72015 × 10⁷ s
T ≅ 1.72 × 10⁷ s
So, the period of the satellite is 1.72 × 10⁷ s
What is the radial acceleration of the satellite?The radial acceleration of the satellite is given by a = v²/R where
v = speed of satellite = 244 m/s and R = radius of orbit = 6680 kmSubstituting the values of the variables into the equation, we have
a = v²/R
a = (244 m/s)²/6680 km
a = 59536 m²/s²/6680 × 10³ m
a = 8.913 × 10³ rad/s
a = 8913 rad/s
So, the radial acceleration of the satellite is 8913 rad/s
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an electron moves from one point a to point b. while moving, the electron remains on an equipotential surface created by nearby charges. what can you say about the speed of the electron as it moved?
At initial speed must the quarter back through the ball for it to reach the reciver.
What is initial speed
The initial speed is the velocity at which motion start.
Sol-
The horizontal velocity is Vi*cos38.6and the vertical velocity is Vi*sin38.6
horizontal
28.4=Vi*cos38.6 time find time in terms of Vi.
Vertical
hf=hi+Vi*sin38.6*t -1/2 g t^2
now hf=hi=0
so
0=Vi*sin 38.6-1/2 g t and put the expression you got for t, then solve for Vi. You will encounter the need for one trig identity.
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Given a block which is at rest on a perfectly flat smooth surface with no friction. You push with your hand horizontally on the block with some force. If the force on the block= 4.00 N and the block moves a distance of 2.00 m on the table, then what is the work done on the block? A) 1.29 JB) 8.00 JC) 9.31 JD) 3.65 JE) 4.57 J
ANSWER
B) 8.00 J
EXPLANATION
Given:
• The force applied to move the block, F = 4.00N
,• The distance the block is moved, d = 2.00 m
Unknown:
• The work done on the block, W
If there is no friction between the block and the table, the only force acting upon the block in the direction of movement is the applied force F. Since the force is applied in the direction of movement, then the angle between the force and the displacement is 0, so the work done on the block is,
[tex]W=F\times d=4.00N\times2.00m=8.00J[/tex]Hence, the work done on the block is 8.00 J.
A force of 30 N to the right is applied to an object. An opposite force of 20 N to the left is applied to the same object. What is the net force applied to the object?
A. 10 N to the left
B. 50 N to the right
C. 50 N to the left
D. 10 N to the right
The net force on an object if a force of 30 N to the right is applied to an object. An opposite force of 20 N to the left is applied to the same object is 10 N to the right. And the right option is D.
What is net force?The net force is the vector sum of all the forces that act upon an object.
To calculate the net force applied to the object, we use the formula below.
Formula:
F = Fa-Fb................. Equation 1Where:
F = Net force applied to the object.Fa = Force applied to the rightFb = Force applied to the leftFrom the question,
Given:
Fa = 30 N to the rightFb = 20 N to the leftSubstitute these values into equation 1
F = 30-20F = 10 N to the right.Hence the right option is D. 10 N to the right.
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A horizontal rope is attached from a truck to a 1475-kg car. As the truck tows the car on a horizontal straight road, the rope will break if the tension is greater than 2551 N. Ignoring friction, what is the maximum possible acceleration of the truck if the rope does not break?
Given data
*The given mass of the car is m = 1475 kg
*The maximum tension is T = 2551 N
The formula for the maximum possible acceleration of the truck is given by Newton's second law as
[tex]\begin{gathered} T=ma_{\max } \\ a_{\max }=\frac{T}{m} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} a_{\max }=\frac{2551}{1475} \\ =1.72m/s^2 \end{gathered}[/tex]Hence, the maximum possible acceleration of the truck is a_max = 1.72 m/s^2
What type of energy is the sum of kinetic and potential energy in an object that is used to do work?.
Mechanical energy type of energy is the sum of kinetic and potential energy in an object that is used to do work.
What is an example mechanical energy?Potential energy plus kinetic energy are combined to form mechanical energy. It refers to the power underlying an object's location and motion. A compressed spring, for instance, has mechanical energy in the form of potential energy, while a moving vehicle has mechanical energy in the form of kinetic energy.
How does mechanical energy become electrical energy?A sequence of blades installed on a rotor shaft in a turbine generator are pushed by a flowing fluid, including such air, water, steam, combustion gases, or water. A generator's rotor shaft rotates or spins due to the fluid's force on the blades. In turn, the generator converts the rotor's physical (kinetic) energy into electricity.
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a cliff diver steps off a cliff and hits the water 2.2 seconds later. How high was the cliff?
The height of the cliff is 24.2 m.
Let:
'h' be the height of the cliff'u' be the initial velocity of diver; u = 0m/s'+'ve been the annotation for the Downward directiona = 10m/s^2 be the approximation of acceleration due to gravityUsing the Second Equation of Motion:
[tex]h = ut + 1/2 at^{2} \\h = 0 + 1/2 (10)(2.2)^{2} \\h = 0 + 5(2.2)^{2} \\h = 5(4.84)\\h = 24.2m[/tex]
The Second Equation of Motion establishes a relationship between displacement and time. It can be used to calculate the displacement and time, in different conditions.
The cliff was 24.2m high above the water surface, into which the cliff diver dived.
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a person throws a ball at an angle of 30 o with the horizontal with a velocity of 32 m/s. as the ball is thrown, a second person is running past the thrower at a constant velocity. at what velocity must this second person run so that she may catch the ball as it hits the ground?
If the second player moved horizontally, the speed he must maintain to catch the ball is 27.67 m/s.
What is the range of the projectile (ball)?
The range of the projectile is the maximum horizontal distance travelled by the ball.
R = (u²sin(2θ)) / (g)
where;
u is the initial velocityθ is the angle of projectiong is acceleration due to gravityR = (32² x sin(2 x 30) ) / (9.8)
R = 90.49 m
The time of motion of the ball is calculated as follows;
R = uₓt
where;
uₓ is the horizontal component of the velocityR = ucosθ(t)
t = R/ucosθ
t = (90.49) / (32 cos30)
t = 3.27 seconds
If the second player moved horizontally, the speed he must maintain to catch the ball is calculated as;
R = Ut
U = R/t
U = (90.49) / (3.27)
U = 27.67 m/s
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A car is driving with a constant velocity around a circular track. The track’s radius is 156.1 m, and the car returns to its starting position in 49.3 s. What is the car’s centripetal acceleration?
A car is driving with a constant velocity around a circular track. The track’s radius is 156.1 m, and the car returns to its starting position in
49.3 s the car’s centripetal acceleration is 0.327 m/sec².
What is acceleration?Rate of change of velocity with respect to time is called acceleration.
when the magnitude of velocity is constant and direction is changing
than the acceleration is centripetal acceleration.
Given that is question radius of track is 156.1 m and car returns to its starting position in 49.3 s.
Velocity of car = Circumference of Circle / total time
= 352.308/ 49.30
v = 7.14 m/sec
Centripetal acceleration = v²/r
= 51.06/156.1
= 0.327 m/sec²
The car’s centripetal acceleration is 0.327 m/sec².
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Air pressure increases as you travel higher above sea level. This is the reason that cabins in commercial airliners require pressurization.
True
False
The answer is true about the cabins in commercial airliners that require pressurization.
Why are the cabins of commercial airplanes pressurized?Airplanes are pressurized because the air is very thin at the high altitude where they fly. The passenger jet has a cruising altitude of about 30,000 - 40,000 feet. At this altitude or height, humans can't breathe very well and our body gets less amount of oxygen. Most aircraft cabins are pressurized to an altitude about 8,000 feet. This is called cabin altitude. Aircraft pilots have access to the control's mode of a cabin pressure control system and if needed it can command the cabin to depressurize.
So we can conclude that cabins in commercial airliners require pressurization because of the greater pressure of the surrounding environment.
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A meteorite is found to contain two isotopes of element x, x-12, and x-14. Experimental analysis determined 95% of the element is isotope x-12, whereas 5% of the element is isotope x-14. What is the average atomic mass of element x?.
Considering the definition isotopes and atomic mass of an element, the average atomic mass of element x is 12.1
Definition of isotopeThe same chemical element can have the same atomic numbers, but the number of neutrons is different. These atoms are called isotopes of the element.
Definition of atomic massThe atomic masses of chemical elements are calculated as the weighted average of the masses of the different isotopes of each element, taking into account the relative abundance of each of them.
Atomic mass of the element in this caseIn this case, you know:
Isotope x-12 is 95% abundant (the atomic mass is 12).Isotope x-14 is 5% abundant (the atomic mass is 14).The average mass of the element x can be calculated as:
average mass of element x=12 amu×0.95 + 14 amu×0.05
average mass of element x= 12.1 amu
Finally, the atomic mass of the element x is 12.1.
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a cubical box of mass 2kg with each side 2 cm is lying on the ground. Calculate the pressure exerted by the block on the ground
Answer:
25000Nm⁻² using rounded g figure
Explanation:
The box is in cm. It needs to be converted into SI metres.
1m = 100cm
1cm = ( 1 / 100 )m
2cm = ( 1 / 50 )m
A = ( 1 / 2500 )m²
Assume that g = 10ms⁻¹. Use your own definition.
F = 10N
P = F / A
P = 10N( 2500 )m⁻²
25000Nm⁻²
Answer:
Explanation:
Given:
m = 2 kg
a = 2 cm = 0.02 m
g =9.8 m/s²
_______________
P - ?
Area of the cube:
S = a² = 0.02² = 0,0004 m²
Gravity:
F = m·g = 2·9.8 = 19.6 N
Pressure:
p = F / S = 19.6 / 0,0004 = 49 000 N/m²
6. What is the acceleration of a 15 kg object being pushed with 200 N of force?
The acceleration of the object will be 13.33 m/s^2.
According to Newton's second law of motion,
The magnitude of Force is equal to the product of the mass of the body and the acceleration it is given ( or achieves ).
The units of force, mass and acceleration are Newton, kg and m/s^2 respectively.
In numerical terms,
Force = mass × acceleration
i.e. F = m × a
Given,
mass of the body = 15 kg
Force applied to the body = 200 N.
Putting these values in the equation,
200 = 15 × a
=> a = 200/15
=> a = 13.33 m/s^2.
Therefore, the acceleration of the given body will be 13.33 m/s^2.
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the radius of the planet mercury is 2.43*10^6m and its mass is 3.2*10^23 kg. find the period of a satellite orbiting mercury 265,000 m above its surface?
The period of a satellite orbiting mercury 265,000 m above its surface is 100 minutes if the radius of the planet mercury is 2.43*10^6m and its mass is 3.2*10^23 kg.
v = √ G M / r
r = R + d
v = Orbital velocity
G = Gravitational constant
M = Mass of planet
r = Radius of the orbit
R = Radius of planet ( mercury )
d = Distance from surface to satellite
m = 3.2 * [tex]10^{23}[/tex] kg
R = 2.43 * [tex]10^{6}[/tex] m
d = 265000 m
G = 6.67 * [tex]10^{-11}[/tex] N m² / kg²
r = R + d
r = 2.43 * [tex]10^{6}[/tex] + 265000
r = 2.695 * [tex]10^{6}[/tex] m
v = √ ( 6.67 * [tex]10^{-11}[/tex] * 3.2 * [tex]10^{23}[/tex] ) / 2.695 * [tex]10^{6}[/tex]
v = √ 7.92 * [tex]10^{6}[/tex]
v = 2.81 * 10³ m / s
v = 2.81 km / s
v = 2 π r / T
T = Time period
T = 2 * 3.14 * 2.695 * [tex]10^{6}[/tex] / 2.81 * 10³
T = 6.02 * 10³ s
T = 100 minutes
Therefore, the period of a satellite orbiting mercury is 100 minutes
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a long ladder 20 feet long is leaning against a wall with one end on the floor. the bottom end of the the ladder is being pulled along the floor away from the wall at a constant rate of 1 2 feet/sec. assume that the top of the ladder is always in contact with the wall. what are the velocity and acceleration of the top of the ladder when the bottom of the ladder is 12 feet from the wall?
When a ladder with 20 ft. long is pulled along the floor away with a constant rate 1.2 ft/s, then the top of the ladder is moving toward the floor with velocity - 0.9 ft/s and there is no acceleration.
Let:
x = the distance between the bottom of the ladder from the wall
y = the distance between the top of the ladder from the floor
When x = 12 ft, then using the Pythagorean Theorem:
x² + y² = 20² (Equation 1)
12² + y² = 20²
y² = 20² - 12² = 16²
y = 16 ft.
Take the derivative of equation 1 with respect to t
2x . dx/dt + 2y. dy/dt = 0
Substitute x = 12, y = 16, dx/dt = 1.2 ft/s
2 . 12 . (1.2) + 2 . 16 . dy/dt = 0
dy/dt = - 0.9 ft/s
Hence, the velocity is - 0.9 ft/s
Since the floor is moving with a constant rate, the acceleration is zero.
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how would an increase in force affect the mechanical advantage of a simple machine
Mechanical advantage is a measure of the ratio of the output force produced to the input force applied in a system, mainly in the case of simple machines, such as levers and pulleys. It is a dimensionless quantity.
From the definition, the mechanical advantage of a simple machine is inversely proportional to the input force applied on the system. So, an increase in this force decreases the mechanical advantage of a simple machine.
For example, the mechanical advantage of a lever can be decreased by increasing the force on load arm or by reducing the force on the effort arm.
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The of earth’s orbit is among the planet’s unique characteristics. this characteristic allows water to exist in solid, liquid, and gas forms on earth. earth’s distance from the as well as the near- nature of its orbit, allow this phenomenon to take place.
It is distinguished from the other planets by the presence of liquid water on its surface, the presence of life, and active plate movement. It rotates on its axis once every 24 hours (a day) and orbits the Sun once every 365 days (a year). The Earth has a single moon.
What are the unique characteristics of Earth that allows the existence of life? It is the proper distance from the Sun, its magnetic field protects it from harmful solar radiation, an insulating atmosphere keeps it warm, and it contains the necessary chemical ingredients for life, including water and carbon.The Earth's orbit around the Sun is an ellipse, and the eccentricity measures how far the orbit deviates from a circle . The point on the orbit closest to the Sun is known as the perihelion, and the point farthest from the Sun is known as the aphelion.To learn more about : Earth's orbit
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The longest shish kebab ever made was 881.0m long. Suppose the meat and veggies need to be delivered in a cart from one end of this shish kebab skewer to the other end. A cook pulls the cart by applying a force of friction acting on the cart is 28.00N, what is the net work done on the cart and it’s content during the delivery.
Answer:
Explanation:
Given:
L = 881.0 m
F = 28.0 N
___________
A - ?
The work :
A = L*F = 881.0 * 28.0 ≈ 24 670 J
How could these electronegativity values benefit you in analyzing data from the Curiosity rover?
It is to be noted that electronegativity will assist the analyst in the determination of the nature of the interactions between the elements discovered by the Curiosity Rover.
What is Electronegativity?The electronegativity values of two bound atoms indicate whether a bond is nonpolar or polar covalent, as determined by the bonding atoms' properties.
Electronegativity is a measurement of an atom's proclivity to attract electrons (or electron density) toward itself.
Electrons in a polar covalent bond are moved toward the more electronegative atom; consequently, the atom with the partial negative charge is the more electronegative atom. The bigger the electronegativity difference, the more polarized the electron arrangement and the larger the atoms' partial charges.
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a 68.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. he then drops through a height of 1.56 m, and ends with a speed of 8.51 m/s. how much nonconservative work (in kj) was done on the boy?
The non-conservative work done on the boy is 1.337 kJ
Given that,
Mass of boy, m = 68.1 kg
Initial speed of boy, u = 1,60 m/s
The boy then drops through a height of 1.56 m
Final speed of boy, v = 8.51 m/s
Now, we have to find the non-conservative work was done on the boy.
The Work done by the non-conservative forces is equal to the sum of total change in kinetic energy and total change in potential energy.
[tex]W=\frac{1}{2}m (v^{2}-u^{2})+(0-mgh)[/tex]
[tex]W=\frac{1}{2}m (v^{2}-u^{2})-mgh[/tex]
[tex]W=\frac{1}{2}(68.1) ((8.51)^{2}-(1.60)^{2})-68.1*9.8*1.56[/tex]
W = 1337.62 Joules
or
W = 1.337 kJ
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. gun sights are adjusted to aim high to compensate for the effect of gravity, effectively making the gun accurate only for a specific range. (a) if a gun is sighted to hit targets that are at the same height as the gun and 100.0 m away, how low will the bullet hit if aimed directly at a target 150.0 m away?
The problem describes a situation where a bullet is launched at a certain angle respect to the horizontal to hit in the target, given the launching conditions and the distance to the target. The formulas to compute the magnitudes involved in the projectile motion are
x=[tex]v0[/tex] cos0 t
Y=[tex]V0[/tex] sin0 t
xm=[tex]v0[/tex]² sin 20/g
[tex]Xm[/tex] is the maximum horizontal distance the object can reach when it returns to the ground (or launching height).
let's check if X is computed correctly .
The set of data is correct. We can now proceed to the required distance. We know the bullet is shot directly to the target, so the angle is 0, keeping the same speed. The new maximum distance is 150 m, so we can compute the time needed to complete the flight
since
Let's find the time from the formula
X=[tex]V0[/tex] cos0 t
t=[tex]Xm[/tex]/[tex]V0[/tex] cos0
t=150/100=1.5
Y=(9.8)(0.66)²÷2
Y=-2.134
The bullet will hit 2.134 meters below the target
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assume that you weight yourself on a bathroom scale. would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward?
The springs inside a bathroom scale will be more compressed.
What is acceleration due to gravity?
In physics, gravitational acceleration is the acceleration of an object in free fall in a vacuum (hence no resistance). This is a steady increase in velocity caused solely by the gravitational pull. All objects accelerate at the same speed in a vacuum, regardless of their mass or composition . The measurement and analysis of these velocities is known as gravimetry.
At a fixed point on the surface, the magnitude of the Earth's gravity is the combined effect of gravity and the centrifugal force due to the rotation of the Earth. Free-fall acceleration at various points on the Earth's surface ranges from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft /s2) depending on altitude, latitude and longitude . The old standard is precisely defined as 9.80665 m/s2 (32.1740 ft/s2). Locations that deviate significantly from this value are called gravity anomalies. Other effects such as lift and air resistance are not taken into account.
When the elevator accelerates and shows a higher weight reading. As the lift accelerates and descends, the springs in the bathroom scale are compressed less and the displayed weight value is reduced.
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What is the weight of a boy with a mass of 50 kg on Earth?
Use g= 9.81 m/s² and do not include units in your answer.
Answer:
490.5
Explanation:
Force = Mass × Acceleration
Since, Weight is a force and 'g' is the acceleration due to the earth's gravity,
Weight = Mass × g
Weight = 50 kg × 9.81 m/s² = 490.5 kg-m/s² or 490.5 N
A freight train moves due north with a speed of 8 m/s. The mass of the train is 6 x 106 kg. How fast would a 1500 kg automobile have to be moving due north to have the same momentum as the train
The freight train has a momentum of mv = (4.5 × 105 kg)(1.4 m/s) = 6.3 ×105 kg-m/s.
An automobile with a mass of 1800 kg would need to go at a speed of 6.3 × 105 kg-m/s ÷ 1800 kg = 350 m/s in order to have a momentum of the same magnitude. (Roughly 800 mph)
A moving body's amount of motion is referred to as momentum. It has units of kg m/s and is theoretically represented as p = m * v.
The momentum equation connects the total force exerted on a fluid element to its acceleration or rate of change of momentum and is a formulation of Newton's Second Law. You're certainly familiar with the formula F = ma, which links applied force and acceleration in solid mechanics analysis.
Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum.
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this si a 2 part question84) A shock absorber is designed to quickly damp out the oscillations that a car would otherwise make because it is suspended on springs. (a) Find the period of oscillation of a 1610-kg car that is suspended by springs that make an effective force constant of 5.75×104 N/m. (b) Find the damping constant b that will reduce the amplitude of oscillations of this car by a factor of 5.00 within a time equal to half the period of oscillation.
Given data
*The given mass of the car is m = 1610 kg
*The given effective force constant is k = 5.75 × 10^4 N/m
(a)
The formula for the period of oscillation of a 1610 kg car is given as
[tex]T=2\pi\sqrt[]{\frac{m}{k}}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} T=2\times3.14\times\sqrt[]{\frac{1610}{5.75\times10^4}} \\ =1.05\text{ s} \end{gathered}[/tex]Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s
(b)
As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as
[tex]A=A_0e^{-\frac{bt}{2m}}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} \frac{A_0}{5.0}=A_0e^{-\frac{bt}{2m}} \\ bt=2m\ln (5.0)_{} \\ b(\frac{T}{2})=2m\ln (5.0) \\ b=\frac{4m\ln (5.0)}{T} \\ =\frac{4\times1610\times\ln (5.0)}{1.05} \\ =9871.2\text{ kg/s} \end{gathered}[/tex]Hence, the damping constant is b = 9871.2 kg/s
Jose applies a force of 20 N North, Johnny applies a force of 10 N West and Janie applies a force of 25 N south on a heavy dresser. Find the resultant force on the dresser.
Answer:
Resultant force of the given forces: approximately [tex]11.2\; {\rm N}[/tex] at approximately [tex]53^{\circ}[/tex] west of south.
Explanation:
The resultant force of these forces will be:
[tex]25\; {\rm N} - 20\; {\rm N} = 5\; {\rm N}[/tex] to the south (the [tex]20\; {\rm N}[/tex] force to the north partially balances the [tex]25\; {\rm N}[/tex] force to the south), and[tex]10\; {\rm N}[/tex] to the west.Refer to the diagram attached. The resultant [tex]5\; {\rm N}[/tex] force to the south and the [tex]10\; {\rm N}[/tex] force to the west are perpendicular to each other, forming the two legs of a right triangle. The hypotenuse of this right triangle will be the net effect of these two forces.
Apply Pythagorean's Theorem on this triangle to find the magnitude of this net effect:
[tex]\begin{aligned}(\text{length of hypotenuse}) &= \sqrt{10^{2} + 5^{2}} \approx 11.2\end{aligned}[/tex].
Hence, the magnitude of this net effect will be approximately [tex]11.2\; {\rm N}[/tex].
Let [tex]\theta[/tex] denote the angle between this resultant force and west. In this right triangle:
[tex]\begin{aligned} \tan(\theta) &= \frac{(\text{opposite})}{(\text{adjacent})} \\ &= \frac{5\; {\rm N}}{10\; {\rm N}} \\ &= \frac{1}{2}\end{aligned}[/tex].
[tex]\begin{aligned} \theta &= \arctan\left(\frac{1}{2}\right) \approx 27^{\circ}\end{aligned}[/tex].
Hence, the angle between this resultant force and south will be approximately [tex](90^{\circ} - 27^{\circ}) = 63^{\circ}[/tex]. This resultant force will be at approximately [tex]63^{\circ}[/tex] west of south.
Suppose you were a farmer trying to grow plants in a greenhouse. Why would it be important to know what the limiting factor is ?
Limiting factors are those factors which limits the growth in the ecosystem. Examples of limiting factors include temperature, sunlight, soil configuration, precipitation and nutrients. It is important to know what the limiting factor is for the limiting factors greatly affects the growth of the plants. Not considering these limiting factors would result in the failure of growing the plants in a greenhouse.
What is Limiting factors ?
Any element (variable) in the environment that has the potential to restrict a process, such as the expansion, abundance, or distribution of a population of species in an ecosystem, is referred to as a limiting factor. Both density-dependent and density-independent limiting variables are possible. Those that depend on population density have a tendency to restrict population increase, abundance, or dispersal. On the other hand, a limiting factor that is independent of population density can restrict population expansion, abundance, or dispersal.
Limiting factors are those factors which limits the growth in the ecosystem. Examples of limiting factors include temperature, sunlight, soil configuration, precipitation and nutrients. It is important to know what the limiting factor is for the limiting factors greatly affects the growth of the plants. Not considering these limiting factors would result in the failure of growing the plants in a greenhouse.
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