Answer:
The correct choice is 8o.
Explanation:
The given weight is hanging at the mid point of the rope and the buildings are at the same level, Obtain the given equation by equating the vertical components of force,
2Tsin(φ)=W
where φ is the angle made by rope with the horizontal.
Given T=1800 N and W=500 N, the value of φ is calculated as follows,
2*1800*sin(φ)=500
sin(φ)=0.1388
φ=7.90
φ≈8o
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Satellite C revolves around Earth 10 times a day. What is the radius of its orbit, measured from Earth's center? Assume that Earth generates the only significant gravitation attraction on the satellite. Note: The mass of Earth is 5.98 × 1024 kg, and the constant of universal gravity (G) equals 6.674 × 10-11 N m2/kg2.
The radius of its orbit, measured from Earth's center, will be 1.44 × 10⁷ mm.
What is Newton's law of gravitation?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data in problem is;
The mass of Earth is, [tex]\rm m_E = 5.98 \times 10^{24} \ kg[/tex]
Gravitational constant, G =6.674 × 10⁻¹¹ N m₂/kg²
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
[tex]\rm F_g = \frac{Gm_sm_e}{r^2}[/tex]
The centripetal force due to rotation of the satellite;
[tex]\rm F_c = \frac{m_s v^2}{r}[/tex]
The centripetal and the gravitational force are equal;
[tex]\rm F_g = F_c \\\\ \frac{Gm_sm_e}{r^2} = \frac{m_s v^2}{r} \\\\ r = G \frac{m_E }{v^2 } \\\\ r = G \frac{m_E }{(r \omega )^2 } \\\\ r = \sqrt[3]{\frac{Gm_E}{\omega^2}} \\\\ r = \sqrt[3]{\frac{6.67 \times 10^{-11}(5.98 \times 10^{24})}{(3.63 \times 10^{-4})^2}} \\\\ r = 1.44 \times 10^7 \ mm[/tex]
Hence, the radius of its orbit measured from Earth's center will be 1.44 × 10⁷ mm.
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it is observed that in water the meniscus in the capillary tube is higher than the meniscus in the beaker,while in mercury the meniscus in the capillary tube is lower tha the meniscus in the beaker.Explain these observations
The adhesion forces between mercury and glass are far weaker than the cohesive forces between mercury atoms causing the meniscus in the capillary tube to be lower than the meniscus in the beaker.
What is surface tension?
The force operating at a border between two phases is measured as surface tension.
Surface tension at liquid-air interfaces is caused by the higher attraction of liquid molecules to each other than air molecules.
Due to the relatively strong attraction of water. Hence molecules of water have high surface tension.
Because the water wets the glass and seeps up the tube's side when it is contained in a glass tube, the meniscus of the water has a concave form.
The cohesive forces between mercury atoms, on the other hand, are far stronger than the adhesion forces between mercury and glass.
The meniscus in the capillary tube is, therefore, higher than the meniscus in the beaker, but with mercury, the meniscus in the capillary tube is lower than the meniscus in the beaker.
Hence, the meniscus in the capillary tube is lower than the meniscus in the beaker
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Voltage is defined as the. Select one: a. force that causes electrons to flow b. opposition to current flow c. basic unit in which current is measured d. current flowing through a conductor
Voltage is defined as the force that causes electrons to flow. That is option A.
What is a voltage?A Voltage is defined as an electromotive force and the potential difference in charge between two points in an electrical field.
It is equally known as the force that causes electrons of a current to flow.
Mathematically, it's = V = current × resistance.
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At what speed must a 150-kg football player be moving to have the same momentum as a 15.0-g bullet traveling at 300 m/s
The football must have the speed of 0.03 m/s to have the same momentum.
What is momentum conservation:
It states that, the total amount of momentum remains constant; momentum is neither created nor destroyed, but only changed through the action of forces as described by Newton's laws of motion.Momentum defines by formula: P = m*vhere,
mass of football, m1 = 150 kg
mass of bullet, m2 = 15 g = 0.015 kg
speed of bullet, v2 = 300 m/s
According to conservation of momentum:
m1*v1 = m2*v2substituting the values in equation,
150* v1 = ( 0.015 )* (300)
v1 = 0.03 m/s
Hence,
The football must have the speed of 0.03 m/s to have the same momentum.
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A brine solution of salt flows at a constant rate of l/min into a large tank that initially held l of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of l/min. If the concentration of salt in the brine entering the tank is kg/l, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach kg/l?.
To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.
What is concentration in a solution?The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.
A concentrated solution is one that has a relatively large amount of dissolved solute. A dilute solution is one that has a relatively small amount of dissolved solute.
The concentration ,C(t) of salt at time t is given by the mass x(t) at time t divided by the volume t + 100 at time t.
That is C(t) = x(t)/ (t+100)
So that,
C(t) = 0.2 - [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]
The concentration of salt is 0.1 kg/L ,
we solve C(t) =0.1 ,
Giving the equation,
0.10.2 - [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]
t = [tex]100\sqrt[4]{2} -100[/tex]
≈ 18.9 minutes
Therefore,
To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.
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Gauss's Law states that the net electric flux, , through any closed surface is proportional to the charge enclosed: . The analogous formula for magnetic fields is:
The analogous formula for magnetic fields is the Ampere's law.
To find the answer, we need to know about the Ampere's law of magnetism.
What's Ampere's law of magnetism?Ampere's law states that the close line integral of magnetic field around a current carrying loop is directly proportional to the current enclosed within it.
What's is the mathematical expression of Ampere's law?Mathematically, Ampere's law is
B•dl= μ₀I
Thus, we can conclude that the analogous formula for gauss law is the Ampere's law in magnetism.
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Suppose a large star explodes in a supernova, leaving a core that is 10 times the mass of the Sun. What would happen to the core of the star
If a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse.
What is a star?A star can be defined as a giant astronomical object that contains a luminous sphere of plasma, and it is bounded together by its own gravitational force.
Based on astronomical information, if a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse due to its own gravity which creates a violent explosion known as a supernova.
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What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter70 cm when the bike is moving 8.0 m/s?
Answer:
The acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
Explanation:
The centripetal acceleration acts on a body when it is performing a circular motion.
Here, a point on the bicycle is performing circular motion as the rotation of the wheel produces a circular motion.
The centripetal acceleration of a point moving with a velocity and at a distance of from the axis of rotation is given as:
a = v2/r
Here, V = 8m/ s,r = 0.70 m
∴ a = 8/0.70 = 11.43m/ s2
Therefore, the acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
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why are gases poor conductors of sound?
Answer:
Their atoms are spread farther apart
Answer: because gaseous molecules are farther apart
A jogger runs 6.0 km [E], then 4.0 km [N], and finally 2.0 km [W]. The entire trip takes 2.0 h to complete. Calculate the jogger's
(a) average speed
(b) average velocity
(a) The trip covers a total distance of 6.0 + 4.0 + 2.0 = 12.0 km, so the jogger's average speed is (12.0 km)/(2.0 h) = 6.0 km/h.
(b) The jogger undergoes a total displacement given by the vector
(6.0 km) i + (4.0 km) j + (-2.0 km) i = (4.0 km) (i + j)
where i is the unit vector pointing due East and j is the unit vector pointing due North. This vector has magnitude
||(4.0 km) (i + j)|| = (4.0 km) √(1² + 1²) ≈ 5.7 km
so the jogger's average velocity is approximately (5.7 km)/(2.0 h) ≈ 2.8 km/h.
A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear velocity? Group of answer choices
The boy has the greater linear velocity.
The linear velocity in a rotatory system is defined as:
v = ω×r
where,
v is the linear velocity
ω is the angular velocity
r is the radius.
As mentioned in the question, they are turning out at a constant rate, so the angular velocities of both the boy and the girl are the same.
The linear velocity now only depends on the radius of the disc, according to the aforementioned inference. The distance from the center has a directly proportional relationship with the linear velocity.
As a result, linear velocity increases as the distance from the center increases.
From the question, it is clear that the boy is farther away from the center than the girl is. The boy has a higher linear velocity as a result.
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A special purpose nozzles that are often lowered through holes or other openings to the cellar of an occupancy are called
A special purpose nozzles that are often lowered through holes or other openings to the cellar of an occupancy are called cellar nozzles.
What is a nozzle:
A nozzle is a device in which steadily flowing fluid can be made to accelerate by a pressure drop along the duct in a cross-sectional area.
So when a fluid flows through a nozzle, its velocity increases continuously and pressure decreases continuously.
There are different types of tips like hollow cone, solid cone or flat fan.
The cellar nozzle (also called a Bresnan nozzle) is designed to be used under the surface the operator is standing on.
Hence,
The cellar nozzles are often lowered through holes or other opening to the cellar of an occupancy.
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25. A cup contains 177.44 ml. of chocolate milk. How many gallons of chocolate milk does it hold?
(Given: 1 ml. 0.001 L; 1 gal = 3.78 L.)
Answer:
0.0469 gal
Explanation:
177.49 ml is 0.17749 L.
So, 0.17749/3.78 gives the answer
The answer is 0.0469 gallons of chocolate milk a cup can hold which contains 177.44 ml of chocolate milk.
A liquid volume measurement that is equivalent to 231 cubic inches or four quarts is known as Gallon.
To calculate gallons of chocolate milk a cup can hold:
Given,
1 ml = 0.001 L
1 gal = 3.78 L
Convert 177.44 ml to liters:
1 Liter = 1000 ml
177.44 ml * 0.001 L/ml = 0.17744 L
Convert liters (L) to gallons (gal):
= 0.17744 L / 3.78 L/gal
= 0.0469 gal
Thus, a cup that contains 177.44 ml. of chocolate milk holds 0.0469 gal.
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A person who normally weighs 580 N is riding in an elevator that is moving upward, but slowing down at a steady rate. If this person is standing on a bathroom scale inside the elevator, what would the scale read
Answer:
M au = Fs - M g au = upwards acceleration; Fs = scale reading
Fs = M (au + g) scalar quantities where g is positive downwards and au is positive upwards - Fs is the net force acting on the person
If the acceleration is zero Fs = M g and the scale reads the persons weight
If the elevator is decelerating then au is negative and the scale reading Fs = (g - au) M and the scale reading is less than the weight of the person
The voltage supplied by the common household outlet has a frequency of 60 hz. What is the period of the voltage?.
The period of the voltage that has a frequency of 60Hz is 0.0166s. Details about period can be found below.
How to calculate period?Period in physics refers to the length of time during which the same characteristics of a periodic phenomenon recur.
The period is measured in seconds and is denoted by T. It can be calculated by dividing 1 by the frequency of an oscillation because it is inverse of the frequency.
T = 1/60 = 0.0166s
Therefore, the period of the voltage that has a frequency of 60Hz is 0.0166s.
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I want to examine the surface of a planet that is covered by a thick atmosphere (which includes oxygen and contains a very thick layer of water clouds that never clears). What wavelength of electromagnetic radiation would I be smartest to use:
I want to examine the surface of a planet that is covered by a thick atmosphere (which includes oxygen and contains a very thick layer of water clouds that never clears). What wavelength of electromagnetic radiation would I be smartest to use: radar waves.
Radars send out electromagnetic waves much like wireless computer networks and cell phones. The signals are despatched out as short pulses which can be reflected by objects of their route, in part reflecting returned to the radar.
The radio waves travel outward from the antenna at the velocity of light (186,000 miles or three hundred,000 km in keeping with the second) and keep going until they hit something.
Then some of them bounce back in the direction of the antenna in a beam of contemplated radio waves also visiting at the speed of light. the speed of the waves is crucially vital.
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A block is attached to one end of a spring, while the other end of the spring is attached to a fixed axis. The block is moving in a horizontal circle centered at the axis at a constant speed, held in the circular path only by the spring. The system has a total energy of 2 Joules, the spring has a stiffness of 200 Newton/meter, and the unstretched spring has a length of 50 centimeters. Find how much the spring is stretched from its natural length as the block moves in this circle.
The spring is stretched about 3.5cm from its natural length as the block moves in this circle.
Acceleration is given by formula = [tex]\frac{v^{2} }{r}[/tex] where,..... (1)
v= velocity and r = total distance
In this case r = L+Δx where,
L is the length of unstretched spring
Δx = Change in Spring length
According to Hooke's law
F=kΔx …..(2) where,
F= force , k is constant and Δx= change in spring length
Also,
F=ma …..(3) where,
F= force , m= mass of body and a = acceleration
From equation (2) and (3)
ma = kΔx
Now, from equation (1)
mv²/L+Δx = kΔx
mv² = kΔx(L+Δx)…. (4)
Total energy(E) = 1/2mv² + 1/2kx²
From equation (4)
E = 1/2kΔx(L+Δx) + 1/2kΔx²
By solving this equation, this becomes
kΔx² + 1/2kΔxL - E = 0
Given,
k=200N/m L=50cm=0.5m E=2J
Δx = 0.035 m = 3.5cm
Hence, the spring is stretched about 3.5cm from its natural length as the block moves in this circle.
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how is this true?.........
Answer:
because the a and the b both have ones next to them so a is 1 and b is 1 so the sum is 2 and the minus changes because it is within the two lines
Explanation:
Two microwave frequencies are authorized for use in microwave ovens, 910 and 2555 MHz. Calculate the wavelength (in cm) of each.
The wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.
What is frequency:
Frequency describes the number of waves that pass a fixed place in a given amount of time.
What is wavelength:
It is defined as the distance in meter required to complete one circle.
here, two microwave frequencies are given
f1 = 910 MHz = 910* 10^6 Hz
f2 = 2555 MHz = 2555* 10^6 Hz
According to formula of frequency:
λ = v / fwhere
v is speed of wave.
f is frequency of wave.
All electromagnetic wave moves with same speed v = 3×10⁸ m/s.
for f1:
substituting the values in equation,
λ1 = v / f1
λ1 = 3×10⁸ / 910* 10^6
λ1 = 0.329 m
λ1 = 32.9 cm
for f2:
λ2 = v / f2
λ2 = 3×10⁸ / 2555* 10^6
λ2 = 0.117 m
λ2 = 11.7 cm
Hence,
the wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.
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4 (JAMB) The diagram below shows a light see-saw, which is balanced horizontally by the weights W₁, W2, W3, W4 in the positions shown: d a W₁ Fig. 4.44 W₂ b W3 WA Which of the following equations correctly represents the principle of the lever balance? A W₁ + W₂ = W3 + W4 B W₁-W₁ = W4 - W3 C W₁a+W₂b = W3c+Wad D (W₂-W₁)a= (W4 - W3)c E (W₁ + W₂ )ab = (W3+ W4)cd (SCIGCE) 4 ( JAMB ) The diagram below shows a light see - saw , which is balanced horizontally by the weights W₁ , W2 , W3 , W4 in the positions shown : d a W₁ Fig . 4.44 W₂ b W3 WA Which of the following equations correctly represents the principle of the lever balance ? A W₁ + W₂ = W3 + W4 B W₁ - W₁ = W4 - W3 C W₁a + W₂b = W3c + Wad D ( W₂ - W₁ ) a = ( W4 - W3 ) c E ( W₁ + W₂ ) ab = ( W3 + W4 ) cd ( SCIGCE )
The equation that represents the principle of the lever balance is:
W₁ + W₂ = W3 + W4; option A.What is the principle of moments?The principle of moments states when a body is in equilibrium, the sum of the clockwise moment about a point equals the sum of anticlockwise moment about that point.
A see-saw represents a balanced system of moments.
The sum of clockwise moment = The sum of anticlockwise moments.
Assuming W1 and W2 are clockwise moments and W3 and W4 are anticlockwise moments.
The equation will b: W₁ + W₂ = W3 + W4
In conclusion, a balanced see-saw illustrates the principle of the lever balance.
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Which of the diagrams below show forces that would result in a movement of the block to the left?
Diagram A will result in the movement of the block to the left as a result of the forces.
What is Force?This is referred to an influence which is capable of changing the motion of an object.
Diagram A has equal upward and downward force and left side which is 60N is higher than the right side which has 20N. The block will therefore move to the left.
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A stone is thrown upwards into the air. Describe what is the magnitude and direction of its acceleration.
Answer:
Every object on the surface of the earth is pulled towards its surface because of a force known as the gravitational force. It is a force of attraction that exists between any two objects with mass.
The gravitational force of the earth pulls every object towards the surface of the earth. Because of this, an object free in the air is accelerated. The acceleration caused by the gravitational force is known as the acceleration due to gravity.
The magnitude of the acceleration is constant in a downward direction.
What is acceleration?Acceleration is the rate of change in velocity.
price at which speed adjustments with time, in phrases of each pace and direction. A factor or an object shifting in a direct line is extended if it hastens or slows down.Earth's acceleration is always in the downward direction.so when an object is thrown upward its acceleration is directed downward.if the object is downward then also the acceleration is downward.Learn more about acceleration here:-https://brainly.com/question/460763
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wishing to collect weather data on a remote island, you come up with an idea for sending a weather balloon to the location. You attach a +1 C charged object to the balloon and plan to propel the balloon to the island using an electrostatic force. Given the balloon's size and standard wind patterns en route, you realize you will need to be able to overcome an opposing air resistance of up to 100N at any point on the balloon's 750km journey to the island. How big oof a charge will you need at your location to propel the +1C balloon, even in the face if the opposing wind, up to a distance of 750 km away?
The magnitude of the second charge needed to propel the first charge is 6,250 C.
Magnitude of the second charge to propel the first charge
The magnitude of the second charge is calculated by applying Coulomb's law as follows;
F = kq₁q₂/r²
where;
k is Coulomb's constantq₁ is magnitude of first chargeq₂ is magnitude of second charger is the distance between the chargesFr² = kq₁q₂
q₂ = Fr²/kq₁
q₂ = (100 x 750,000²)/(9 x 10⁹ x 1)
q₂ = 6,250 C
Thus, the magnitude of the second charge needed to propel the first charge is 6,250 C.
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Adjusting your speed to address one hazard at a time is called multiple risks. a) Compromising b) Deconflicting c) Separating d) Clear path of travel
The act of Adjusting your speed to address one hazard at a time when faced with multiple risks is: (c) Separating
Meaning of separating Hazards
A hazard can be defined primarily as an occurrence that can lead to damage of properties and destruction of live.
separating Hazards can be defined as an act of adjusting one's speed in other to attend to one hazard before another.
In conclusion, The act of Adjusting your speed to address one hazard at a time when faced with multiple risks is: (c) Separating
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does a turtle have a incomplete metamorphosis? its for my little brother
Answer:
No. They do not undergo any stage of metamorphosis at all. Once they hatch from their eggs, they remain as the same form for the rest of their life. They grow quite a bit, but they do not "morph", or transform, the way caterpillars turn into butterflies.
A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag, and assuming that the average mass of each loaded chair is 250 kg, determine the power required to operate this ski lift. Also, estimate the power required to accelerate this ski lift in 14 s to its operating speed when it is first turned on.
The power required to accelerate this ski life in 14 s to its operating speed is ______ kW.
Power is needed for (1) acceleration and (2) lifting the loaded chairs. These two parts can be calculated separately and then added together.
(1) Power for acceleration:
The final speed of the lift is
V=(10 km/h)(1 h×1000 m60 sec×1 km)=2.887 m/s.
Then the power needed is
Pa=12m(V2−V20)/Δt=12(50×250 kg)(2.778 m/s)2=9.6 kW.
(2) Power for lift
Assume that the acceleration is constant (i.e. power supply is constant), its value will be
a=ΔVΔt=2.778 m/s5 s=0.556 m/s2.
Then the vertical lift during acceleration will be
(12at2)×(2001000)=1.36 m.
Hence, the power needed to increase the potential energy of the lift is
Pg=mgΔhΔt=(50×250 kg) (9.89 m/s2)(1.36 m)/(5 s)=3.41 kW.
Then the total Power required is
Ptotal=Pa+Pg=9.6+34.1=43.7 kW.
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I need help asap it’s due today
For this experiment on a solar collector, the variables include the following:
Time TemperaturePlastic wrapBlack plasticWhat are the variables?In Science, a variable can be defined as a measurable attribute or physical quantity that changes or varies across an experiment and as such can take on different numerical values.
For this experiment on a solar collector, there are different variables and these include the following:
Time TemperaturePlastic wrapBlack plasticFurthermore, you should determine both the greatest and smallest rate of temperature change for each of the trials by subtracting the initial temperature from the final temperature based on the numerical values obtained from this experiment.
In conclusion, the trial with the greatest numerical value has the greatest rate of temperature change while the trial with the smallest numerical value has the smallest rate of temperature change
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Complete Question:
1. What are the variables in this investigation?
2. Which trial had the greatest rate of temperature change?
3. Which trial had the smallest rate of temperature change?
Students are asked to conduct an investigation on the mixing of color. They have three flashlights, each covered with a piece of colored acetate (a transparent plastic). One flashlight is red, one is green, and one is blue. They shine the lights against a white background and observe that when the colors are mixed together, they see a white light. The students then hold a hand in front of the white background and switch on the lights one at a time. They record their observations for the color of the object and its shadow. They repeat this experiment with all three lights on and record the shadows they observe. Which best explains the difference in the results obtained for the shadow colors with all three lights on?
Block the red and green lights and you get a blue shadow. Block all three lights, you get a black shadow.Block one of the three lights, you get a shadow whose colour is a mixture of the two other colours.
What is colour spectrum?The distribution of colors produced when light is dispersed by a prism.
In this demonstration,
Students experiment with red, green, and blue light to get different shadow colours.
Primary colors are not a fundamental property of light but are related to the physiological response of the eye to light. Light is a continuous spectrum of all of the wavelengths that can be detected by the human eye.
The human eye normally contains only three types of colour ranges of the colour spectrum.
Humans and other species with three such types of color receptors are known as trichromats.
The R, G, B cones are most sensitive to the red, green, and blue wavelengths.
The colours each receptor is the most sensitive to. The blue cone will also pick up purple, blue, and green hues.
Green cones will pick up purple, blue, green, yellow, and orange hues. Red cones will pick up purple, blue, green, yellow, orange, and red hues. The sensitivities of the three cones overlap to let us perceive all visible colours.
Hence,
When red light, blue light, and green light stimulate the three colour receptors on our retinas equally, the signal gets blended in our brain and we see "white" light.
This is why we see sunlight as white light, not as its individual colours.
Slight changes in the relative signals of the cones enable us to see a myriad of different colour combinations, which is why we "see" more than just three colours.
In this demonstration, coloured filters are affixed to flashlights.
The coloured filters block some wavelengths and let others through. The red-filtered flashlight puts out wavelengths from red through to orange and yellow. The green-filtered flashlight puts out yellow, green and blue wavelengths. The blue-filtered flashlight puts out green, blue, and purple wavelengths.
When the three coloured light bulbs all shine on the same surface, we see all the wavelengths from red through to purple, which we perceive as white.
With these three coloured lights you can make shadows of seven different colours:
Blue, red, green, black, cyan (blue-green), magenta (pink), and yellow.
If you block two of the three lights, you get a shadow of the third color.
Block the red and green lights and you get a blue shadow.Block all three lights, you get a black shadow.Block one of the three lights, you get a shadow whose colour is a mixture of the two other colours.Learn more about colour spectrum here:
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A force of 40 N is required to hold a spring that has been stretched from its natural length of 10 cm to a length of 15 cm. How much work is done in stretching the spring from 15 cm to 18 cm
0.36 J of work is done in stretching the spring from 15 cm to 18 cm.
To find the correct answer, we need to know about the work done to strech a string.
What is the work required to strech a string?Mathematically, the work done to strech a string is given as 1/2 ×K×x². K is the spring constant.What will be the spring constant, if 40N force is required to hold a 10 cm to 15 cm streched spring?The force experienced by a streched spring is given as Kx. x is the length of the spring streched from its natural length. Then K = Force / x. Here x = 15 - 10 = 5 cm = 0.05 mK = 40/0.05 = 800N/m.What will be the work required to strech that spring from 15 cm to 18 cm?Work done = 1/2×k×x²Here x= 18-15=3cm or 0.03 mSo, W= 1/2×800×0.03² = 0.36 J.Thus, we can conclude that the work done is 0.36 J.
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A ball is thrown straight upward at 10 m/s. Ideally (no air resistance), the ball will return to the thrower's hand with a speed of
The ball will return to the thrower's hand with a speed of 10 m/s.
What is straight upward motion:
It is the motion when an object is projected upward, it moves in the opposite direction of the force of gravity.
The velocity is negative while the object moves up and positive while it moves downward due to upward motion.
Here,
A ball is thrown straight upward, u = 10 m/s
final velocity since ball momentarily stops at highest point, v= 0 m/s
According to Newton's 3rd equation of motion:
2gh = V² - u²where,
g = acceleration due to gravity = -9.8 m/s²
h = height
substituting the values,
2(-9.8)h = (0)² - (10)²
h = 100 / 19.6
h = 5.10 m/s
Now, we consider downward motion:
2gh = v² - u²
where,
g = 9.8 m/s²
h = height = 5.10 m
v = return velocity of ball
u = 0 m/s
substituting the values,
2(9.8)(5.10 m) = V² - (0)²
V = √(99.96)
V = 9.99 m/s
V ≈ 10 m/s
Hence,
the ball will return to the thrower's hand with a speed of 10 m/s.
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