Answer: 1.348 meters
Explanation: Although the sign is missing from the location of the 4.00 kg object, it is assumed to be positive. The net moment of all the objects about the center of mass must be zero. Let the center of mass be on the y axis at a point c . Adding the four moments together, we get:
(2.00)(3.00−c)+(3.00)(2.50−c)+(2.50)(0−c)+(4.00)(0.500−c)=0
6.00−2.00c+7.50−3.00c+0−2.50c+2.00−4.00c=0
11.5c=15.50
c= 1.348 metres
The center of mass is on the y axis at y = 1.348 metres.
If the internal energy of a system is decreased, which of the following is impossible?
a
Work done by the system is larger than heat
released.
b
Work done on the system is smaller than
heat released.
C
Work done by the system is larger than heat
absorbed.
d
Work done on the system is smaller than
heat absorbed.
Work done on the system is smaller than heat absorbed.
What happens when internal energy decreases?A cell's internal energy drops when it does work or expels heat. There won't be a net change in internal energy if the work performed by a cell matches the energy transferred in by heat or if the work performed on a cell matches the energy transported out by the heat.The energy within remains constant. The ideal gas law states that the temperature decreases according to the volume when a gas is compressed while maintaining a constant pressure. In this instance, more energy is lost as heat from the system is gained through work. Internal energy levels drop.Ideal gases' internal energy and enthalpy depend solely on temperature; neither volume nor pressure play a role. Using property relations, we may demonstrate these characteristics of ideal gases.
If the internal energy of a system is decreased, which of the following is impossible:
C) Work done on the system is smaller than heat absorbed.
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How is faraday's law applicable in Electronic Drum
Faraday's law is applicable in the mechanism behind electric generators, credit cards, metal detectors, computer hard drives and electronic drum
What is Faraday's law?Faraday's law states that a changing magnetic field through an area or equivalently, a changing area with constant field will cause a voltage.
So therefore, Faraday's law is applicable in the mechanism behind electric generators, credit cards, metal detectors, computer hard drives and electronic drum
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The oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the:__________
The oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the arterial oxygen.
What does the oxygen–hemoglobin dissociation curve depicts?The oxygen-hemoglobin dissociation curve (OHDC) indicates the relationship between the oxygen saturation of hemoglobin and the partial pressure of arterial oxygen. This curve can change its position or shifted to another level depending on various factors.
So we can conclude that the oxygen–hemoglobin dissociation curve depicts the relationship between the partial pressure of oxygen (pao2) and the arterial oxygen.
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16) Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 10^26 kg, and use an orbital radius of 3.00 x 105 km. (G= 6.67 × 10-11 N·m2/kg2) A) 19.5 km/s B) 27.5 km/s *C) 11.2 km/s D) 20.5 km/. orbital speed?
The orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s. The correct answer is option C
What does Orbital speed depend on ?The speed of an object travelling around a circle depends on two quantities namely;
Its angular velocity wIts distance from the center of the circle.Given that an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 10^26 kg, and use an orbital radius of 3.00 x 105 km. (G= 6.67 × 10-11 N·m2/kg2)
The given parameters are:
The mass of Saturn = 5.68 x 10^26 kgThe orbital radius = 3.00 x 105 kmG = 6.67 × 10-11 N·m2/kg2Let us first calculate the gravitational field strength on the Saturn.
g = GM/r²
Substitute all the necessary parameters and convert km to m
g = (6.67 × [tex]10^{-11}[/tex] × 5.68 × [tex]10^{26}[/tex]) ÷ (300000 × 1000)²
g = 3.79 × [tex]10^{16}[/tex] ÷ 9 × [tex]10^{16}[/tex]
g = 0.421 m/s²
The orbital speed will be
V² = gr
V² = 0.4211 × 300000 × 1000
V² = 126333333.3
V = √126333333.3
V = 11239.8 m/s
Convert it to Km/s by dividing the answer by 1000
V = 11239.8/1000
V = 11.2 Km/s
Therefore, the orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s
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A certain force F has an c component of 46N and a y component of 80N. Find the magnitude of this force. A- 73.8N B- 103.8N C 92.3N D-67.6N E-none
Answer:
X component= 46 N
Y component= 80 N
Magnitude =( 46 ^2 + 80^2 )^0.5 = 92.3 N
A grinding wheel 0.35 m in diameter rotates at 2600 rpm .
a) Calculate its angular velocity in rad/s .
Express your answer using three significant figures.
b)What is the linear speed of a point on the edge of the grinding wheel?
Express your answer to two significant figures and include the appropriate units.
c)What is the acceleration of a point on the edge of the grinding wheel?
Express your answer to two significant figures and include the appropriate units.
It is calculated that a) The angular velocity of the wheel is 272.13 rad/s,
b) On the edge of the grinding wheel, the linear speed is 47.62 m/s,
and c) On the edge of the grinding wheel, the acceleration is 12958.08 m/s².
Calculation of angular velocity, linear speed & acceleration:
Provided that,
the diameter of the wheel = 0.35 m
So, the radius, r = 0.35/2 = 0.175 m
As 1 revolution = 2π rad
(a) the angular velocity, ω = 2600 rpm = [tex]\frac{2600 * 2\pi }{60}[/tex] rad/s
⇒ω = 272.13 rad/s
So, the angular velocity is 272.13 rad/s.
(b) The linear speed, v = r * ω
⇒v = 0.175 * 272.13
⇒v= 47.62 m/s
(c) The angular acceleration, [tex]a=\frac{v^{2} }{r}[/tex]
[tex]a = \frac{(47.62)^{2} }{0.175}[/tex]
⇒[tex]a[/tex] = 12958.08 m/s²
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What is meant by significant figures
Answer:
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation . The number of significant figures in an expression indicates the confidence or precision with which an engineer or scientist states a quantity.
Answer:
each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
Explanation:
An internal explosion breaks an object, initially at rest, into two pieces: A and B. Piece A has 1.9 times the mass of piece B. The energy of 7900 J is released in the explosion.
a)Determine the kinetic energy of piece A after the explosion.
Express your answer to two significant figures and include the appropriate units.
b)Determine the kinetic energy of piece B after the explosion.
Express your answer to two significant figures and include the appropriate units.
Kinetic energy of pieces A and B are 2724 Joule and 5176 Joule respectively.
What is the relation between the masses of A and B?Let mass of piece A = MaMass of piece B = Mb
Velocities of pieces A and B are Va and Vb respectively.As per conservation of momentum,Ma×Va = Mb×Vb
Here, Ma=1.9MbSo, 1.9Mb × Va = Mb×Vb
=> 1.9Va = Vb
What are the kinetic energy of piece A and B?Expression of kinetic energy of piece A = 1/2 × Ma × Va²Kinetic energy of piece B = 1/2 × Mb × Vb²Total kinetic energy= 7900J=>1/2 × Ma × Va² + 1/2 × Mb × Vb² = 7900
=> 1/2 × Ma × Va² + 1/2 × (Ma/1.9) × (1.9Va)² = 7900
=> 1/2 × Ma × Va² ×(1+1.9) = 7900 j
=> 1/2 × Ma × Va² = 7900/2.9 = 2724 Joule
Kinetic energy of piece B = 7900 - 2724 = 5176 JouleThus, we can conclude that the kinetic energy of piece A and B are 2724 Joule and 5176 Joule respectively.
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A vector in the xy plane has components -14.0 units in the x-direction and 30.0 units in the y-direction. What is the magnitude of the vector? What is the angle between the vector and the positive x-axis?
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
We would calculate the magnitude by applying pythagorean theorem:
[tex]\longrightarrow \sf{Magnitude= \sqrt{(-14)^2 } + 30^2}[/tex]
[tex]\longrightarrow \sf{Magnitude = 33.12}[/tex]
[tex]\longrightarrow \sf{The \: vector \: is \: (- 14, 30)}[/tex]
The angle between two vectors is given by the formula:
[tex]\sf{\longrightarrow \small \cos \emptyset = \dfrac{(a1b1 + a2b2)}{ \sqrt{(a1)^2 + (a2)^2√(b1)^2 + (b2)^2} } }[/tex]
In two dimensional, the x axis of vector form is:
[tex]\small\sf{\longrightarrow (b1, b2) = (1, 0) }[/tex]
[tex]\sf{\longrightarrow \small \cos \: \emptyset = \dfrac{(14 * 1 + 30 x 0)}{( \sqrt{(-14)^2 + (30)^2)(√(1)^2 + (0)^2)} } }[/tex]
[tex]\small\longrightarrow \sf{ \dfrac{14}{33.12} }[/tex]
[tex]\small\longrightarrow \sf{\emptyset \: = arcCos (\dfrac{ - 14}{33.12} )}[/tex]
[tex]\small\longrightarrow \sf{\emptyset= 115^\circ}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \small\bm{The \: angle \: between \: the \: vector \: }[/tex]
[tex]\small\bm{and \: \: the \: \: positive \: \: x \: \: axis \: \: is \: \: \: 115^\circ .}[/tex]
Which of the following phrases describes power?
A. How much energy is lost in friction
B. How much energy is lost in heat
OC. The rate energy is consumed
OD. The rate an object is moving
The rate energy is consumed this statement describes power.
Hence, Option C is correct answer.
How can we understand that this statement can describe power?Power is related to energy by that it is the rate at which energy is transferred.
What is Power ?It is a measure of the rate at which work is done.
According to the definition of power, Power is the amount of energy transferred or converted or consumed per unit time.
SI unit of power is watt.
By definition, 1 watt is equal to one joule of work done per second. So if P represents power in watts, E is the change in energy (number of joules) and t is the time taken in seconds then:
P=[tex]\frac{E}{t}[/tex]= [tex]\frac{1 Joule}{1 Second}[/tex]= 1 Watt.
Thus from the above conclusion we can say that, The rate energy is consumed describes power.
Hence, Option C is correct answer
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A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom.
1. The cylinder is replaced with one that has the same density and diameter, but with half the height.
2. Some of the water is removed from the glass.
3. A liquid with a density of 1.06 g/cm3 is poured into the glass.
4. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
5. A liquid with a density of 0.76 g/cm3 is poured into the glass.
6. The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
Options are: Increase, Decrease, No change
Each side has to have at least 44 horses
F61160 N. This is further explained below.
What is the force?Generally, We are only interested in the component that operates horizontally since the vertical components all cancel each other out. The pressure difference works on the hemisphere to generate a normal force all over the surface, but we are only concerned with that force's horizontal component. This may be determined by supposing the hemispheres to be two flat circular plates of the same radius as the hemispheres that have been forced together.
Therefore, force is equal to pressure multiplied by area, which is
F= (970 -15 )( * (0.45 m)2)
F=60754 N for each side.
Therefore, each side has to have at least 44 horses
44* 1390 = 61160 N
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When the current through a circular loop is 5.7 A, the magnetic field at its center is 3.9 ✕ 10−4 T. What is the radius (in m) of the loop?
Radius of the circular loop is 0.0091m.
What is magnetic field?Magnetic field is the area around a magnet where the magnetism influence is felt .
What is the magnetic field at the centre of a circular loop?The formula for magnetic field at the centre of a loop isB =(μ)I/2r
where B= Magnetic field at the centre of a circular loopμ= Magnetic permeability =4(π)*10^(-7)
I= current flowing through the loop
r= radius of the loop
Thus, radius of the loop =(4(π)×10^(-7)×5.7)/(2×3.9×10^(-4))=0.0091m
Thus, we can conclude that the radius of the loop is 0.0091m .
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A worker uses a pulley system to raise a 225
N carton 16.5 m. A force of 129 N is exerted
and the rope is pulled 33.0 m. What is the IMA
of the system?
Answer:
1.74
Explanation:
"How do you calculate the mechanical advantage of a block and tackle pulley?
To calculate the mechanical advantage, we can either divide the weight of the object being lifted by the force required to lift it or we can divide the amount of rope we have to pull by the distance the object moves."
If we use the rope method the mech advantage is 33.0/16.5 = 2
now if we use the forces MA = 225/129 =1.74 <==== this is not equal to '2' as we first found due to energy being lost to friction/deformation of rope etc. SO I would say the true mechanical advantage = 1.74
Efficiency = 1.74/2 = 87%
a)Calculate the angular velocity of the Earth in its orbit around the Sun.
Express your answer using three significant figures.
b) Calculate the angular velocity of the Earth about its axis.
Express your answer using three significant figures.
The earth's orbital angular velocity around the Sun is 0.986° per day, and its axial angular velocity is 15.041° per hour.
Calculation:
The speeds, not the velocities, are what we require in this case, therefore that is how I will approach it.
Regular speed is calculated by dividing the distance traveled by the travel time.
So, speed = [tex]\frac{distance -travelled}{time}[/tex]
The angular velocity is essentially the same.
Hence, it's divided by the amount of time it took to turn the angle.
(a) Calculation of Earth's orbit around the Sun :
The Earth orbits the Sun in a circle that is 2 radians in diameter (360 degrees). It also takes a year, as we are aware (approx 365 days)
360°/365.25636 days = 0.986°/day ≈ 1° per day
(b) Next, we have to calculate Earth's angular velocity on its axis:
determining the Earth's angular velocity as it fulfills a complete revolution on its axis (a solar day)-
This one requires more precision because a day does not always have 24 hours. Depending on how we define a day,If the day is defined as the time between the Sun's highest and lowest points in the sky, a year's worth of data equals an average of 24 hours.If we define a day as the duration of time it requires for a planet to get to the same location in the sky the following night, then it is 23 hours 56 minutes 4.09 seconds.According to this, the angular speed of rotation = 360°/ 23h 56min 4.09s = 15.041° / hour.
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Piston 1 in the figure has a diameter of 1.87 cm.
Piston 2 has a diameter of 9.46 cm. In the absence of friction, determine the force F, necessary to support an object with a mass of 991 kg placed on piston 2. (Neglect the height difference between the bottom of the two pistons, and assume that the pistons are massless).
The force F, necessary to support an object with a mass of 991 kg placed on piston 2 is 373.8 N.
What is the force required to support the weight on piston 2?The force, F required to support the weight on piston 2 is calculated as follows:
F = F₂ * A₁/A₂f = 991 * 9.81 = 9721.71 N
A₂ = (9.46/2)² = 22.373
A₁ = (1.87/2)² = 0.874
F = 9721.71 * 0.874/22.373
F = 373.8 N
Inc conclusion, a smaller force is applied to lift the larger force at Piston 2.
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What does the Q stand for in the enthalpy of fusion equation?
The Q in the enthalpy of fusion equation stands for heat energy absorbed or released.
What is enthalpy?In thermodynamics, enthalpy is a measure of the heat content of a chemical or physical system.
The enthalpy of fusion is the amount of heat energy required to convert a unit mass of a solid at its melting point into a liquid without an increase in temperature.
Its units are usually Joules per gram (J/g) or calories per gram (cal/g).
The enthalpy of fusion equation is given as follows:
Q = m·ΔHf
Where;
Q = heat energym = massΔHf = heat of fusionTherefore, the Q in the enthalpy of fusion equation stands for heat energy absorbed or released.
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A 0.550 kg air-track glider is attached to each end of the track by two coil springs. It takes a horizontal force of 0.500 N to displace the glider to a new equilibrium position, x= 0.070 m.
1. Find the effective spring constant of the system.
2. The glider is now released from rest at x= 0.070 m. Find the maximum x-acceleration of the glider.
3. Find the x-coordinate of the glider at time t= 0.650T, where T is the period of the oscillation.
4. Find the kinetic energy of the glider at x=0.00 m.
(1) The effective spring constant of the system is 7.14 N/m.
(2) The maximum x-acceleration of the glider is 0.9 m/s².
(3) The x-coordinate of the glider at time t= 0.650T is 0.28 m.
(4) The kinetic energy of the glider at x=0.00 m is zero.
The effective spring constant of the system
The effective spring constant of the system is calculated as follows;
F = kx
where;
k is spring constantk = F/x
k = 0.5/0.07
k = 7.14 N/m
Maximum acceleration of the glidera = ω²x
where;
ω is angular speedω = √k/m
ω = √(7.14/0.55)
ω = 3.6 rad/s
a = (3.6)² x 0.07
a = 0.9 m/s²
Period of the oscillationT = 2πx/v
T = 2πx/(ωx)
T = 2π/ω
T = 2π/(3.6)
T = 1.75 seconds
t = 0.65T
t = 0.65 x 1.75
t = 1.14 seconds
x = vt
x = (ωx)t
x = (3.6 x 0.07) x 1.14
x = 0.28 m
kinetic energy of the gliderAt position x = 0, the glider is at rest, the velocity is zero and the kinetic energy will be zero.
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PLEASE read this carefully.
A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'r or f or s' are possible answers in some of the cases.
The new sphere has a radius of r < r0 and a mass of m > m0.
The new sphere has a mass of m > m0 and a density of ρ < ρ0.
The new sphere has a density of ρ < ρ0 and a radius of r > r0.
For each of the given scenarios and based on the volume, mass, and density of the spheres, the water level is given as follows:
Scenario 1: The water level will rise; r
Scenario 2: The water level may rise or fall; r or f
Scenario 3: The water level will fall; f
What is the relationship between volume, density, and mass of the objects?The density, volume and mass of an object are related by the formula below:
Density = mass/volumeThe rise in the level of fluid when an object is placed in that fluid depends on the weight, volume and density of that object.
This is given by Archimedes' principle which states that the upthrust acting on a body immersed fully or partially in a fluid, is equal to the weight of the fluid displaced.
Based on the above, the water level in each of the scenarios is described thus:
Scenario 1: The new sphere has a radius of r < r0 and a mass of m > m0.
The new has a smaller volume and a greater mass and density. The water level will rise.
Scenario 2: The new sphere has a mass of m > m0 and a density of ρ < ρ0.
The new sphere has a greater volume and will float. Therefore, the water level may rise or fall.
Scenario 3: The new sphere has a density of ρ < ρ0 and a radius of r > r0.
The new sphere has a greater volume but less mass. Therefore, the water level will fall.
In conclusion, the rise or fall of the water level in the container depends on the volume, mass, and density of the spheres.
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A child in a boat throws a 5.90-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 25.0 kg and the mass of the boat is 38.4 kg. (Figure 1)
Calculate the velocity of the boat immediately after, assuming it was initially at rest.
Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the velocity is in the direction of the velocity of the box and negative value if the direction of the velocity is in the direction opposite to the velocity of the box.
-0.930 m/s is the velocity of the boat.
Given:Mass of child and boat , [tex]m_1[/tex] = (25.0 + 38.4 )kg
= 63.4 kg
Mass of the package, [tex]m_2[/tex] = 5.90 kg
Velocity of package thrown from boat , [tex]v_2[/tex] = 10.0m/s
[tex]v_1 =?[/tex]
Initial velocity v = 0 m/s
As the boat is at rest, [tex](m_1 + m_2) v=0[/tex]
According, to the law of conversation of momentum;
∴ Momentum before = Momentum after
[tex]( m_1 + m_2 ) v = m_1v_1 + m_2v_2\\0 = m_1v_1 + m_2v_2\\0 = 63.4 v_1 + 5.90*10.0\\63.4 v_1 = - 5.9\\v_1 = - 0.930 m/s[/tex]
Negative direction shows the velocity in the direction opposite to the motion of the package.
Therefore, -0.930 m/s is the velocity of the boat.
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A 5 Ω and a 5 Ω resistor are in parallel. What is their total resistance?
A. 10 Ω
B. 2.5 Ω
C. 25 Ω
D. 5 Ω
Answer:
B. 2.5 Ω
Explanation:
[tex]\frac{1}{5} +\frac{1}{5}=0.4[/tex]
Put a one on top of the 0.4
[tex]\frac{1}{0.4} =2.5[/tex]
The following coplanar forces pull on a ring 200N at 30 degrees and 500N at 80 degrees and 300N at 240 degrees and an unknown force. Find the magnitude and direction of the unknown force of the ring is to be in equilibrium
MAGNITUDE AND DIRECTION OF A VECTOR
Given a position vector →v=⟨a,b⟩,the magnitude is located by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)
What is the formula of magnitude?
The formula to determine the extent of a vector (in two dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem. the procedure to determine the magnitude of a vector (in three dimensional space) V = (x, y, z) is: |V| = √(x2 + y2 + z2)
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main answer is given below,
Find the center of mass of the three-mass system shown in the figure relative to the mass m = 1.03 kg . (Figure 1)
Express your answer to two significant figures and include the appropriate units.
The center of mass of the three-mass system is 0.433m.
A position established in relation to an object or set of objects is the center of mass. It represents the system's average location as weighted by each component's mass. In a collection of unconnected items, the center of mass can also be established.
Given:Mass of the object, m₁ = 1.03kg
Mass of the object, m₂= 1.50kg
Mass of the object, m₃= 1.10
Taking the location of m as the origin and towards right as positive X-axis.
x₁=0
x₂=0.50m
x₃=0.25+0.50 = 0.75m
The X-coordinate of the center of mass [tex]x_c[/tex] of a system of three masses m₁, m₂ and m₃ located at the positions x₁, x₂ and x₃ on X-axis is given by,
[tex]x_c=\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}[/tex]
[tex]x_c=\frac{0+1.50*0.50+1.10*0.75}{1.03+1.50+1.10}\\x_c= 0.433 m[/tex]
Therefore, the center of mass of the three-mass system is 0.433m.
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A weight lifter lifts a mass of 250 kg with a force of 5000N to a height of 5m. a. What is the workdone by the weight lifter? b. What is the workdone by the gravity? c. What is the net workdone on the object?
hii friends
Answers are:
a. The work done by the weight lifter W = 25000 Joule
b. The work done by the gravity W = 12250 Joule
c. The net work done on the object W = 12750 Joule
What is Work ?
Work is the product of force and distance in the direction of the force applied. That is, W = F x h
The S.I unit is Joule.
Given that a weight lifter lifts a mass of 250 kg with a force of 5000N to a height of 5m.
The given parameters are;
Mass m = 250 kgForce F = 5000 NHeight h = 5 ma. The work done by the weight lifter will be
W = F x h
W = 5000 x 5
W = 25000 Joule
b. The work done by the gravity will be
W = mg x h
W = 250 x 9.8 x 5
W = 12250 Joule
c. The net work done on the object will be
W = 25000 - 12250
W = 12750 Joule
Since the work done by the gravity is in opposite direction to the work done by the weight lifter, the net work done on the object will be the difference between the two.
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If the velocity of an object is -8 m/s and its momentum is -32 kgm/s, what is its mass?
Glucose solution is administered to a patient in a hospital. The density of the solution is 1.308 kg/l. If the blood pressure in the vein is 35.7 mmHg, then what is the minimum necessary height of the IV bag above the position of the needle?
The minimum necessary height of the IV bag above the position of the needle is 0.37 m.
Minimum necessary heightThe minimum necessary height of the IV bag above the position of the needle is calculated as follows;
P = ρgh
where;
ρ is density = 1.308 kg/L = 1308 kg/m³g is acceleration due to gravity = 9.8 m/s²p is pressure = 35.7 mmHg = 4759.609 Pah is height, (m) = ?Substitute the given parameters and solve for minimum height
h = P/ρg
h = (4759.609) / (9.8 x 1308)
h = 0.37 m
Thus, the minimum necessary height of the IV bag above the position of the needle is 0.37 m.
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Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 1026 kg, and use an orbital radius of 3.00 x 105 km. (G = 6.67 × 10-11 N ∙ m2/kg2)
19.5 km/s
27.5 km/s
11.2 km/s
20.5 km/s
The orbital speed of an ice cube in the rings of Saturn is 355358.97m/s
Law of gravitationAccording to the gravitation law, the force of gravitation is directly proportional to the product of the masses and inversely proportional to the distance between them. Mathematically;
F = GMm/r²
where
m = mass of ice cube and
s = Gm1/r^2
Hence,
F = sm2
On rearranging,
s = m2/F
let V = orbital speed
centripetal acceleration = V^2/r
Such that;
V²/r = Gm/r²
V² = Gm/r
V = √Gm/r
Substitute the given parameters
V = √6.67×10^-11 * 5.68 x 10^26 / 3.00 x 10^5
V = 355358.97m/s
Hence the orbital speed of an ice cube in the rings of Saturn is 355358.97m/s
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The CM of an empty 1300-kg car is 2.45 m behind the front of the car.
How far from the front of the car will the CM be when two people sit in the front seat 2.70 m from the front of the car, and three people sit in the back seat 3.65 m from the front? Assume that each person has a mass of 60.0 kg .
Express your answer to three significant figures and include the appropriate units.
The center of mass of the car with all people seated will be 3.20 m far from the front of the car.
Taking the front of the car as reference:
m₁x₁ + m₂x₂ + m₃x₃ = mx
where,
m₁ = mass of empty car = 1300 kg
x₁ = distance of center of mass of empty car from front = 2.45 m
m₂ = mass of 2 people sitting in front = 2 x 60 kg = 120 kg
x₂ = distance of center of mass of 2 people sitting in front from the front = 2.7 m
m₃ = mass of 3 people sitting in back seat = 3 x 60 kg = 180 kg
x₃ = distance of center of mass of 3 people sitting in the back seat from the front = 3.65 m
m = total mass of car with all people = 1300 kg + 120 kg + 180 kg = 1600kg
x = distance of center of mass of the car from the front when all are seated
Therefore,
(1300 kg)(2.45 m) + (120 kg)(2.7 m) + (180kg)(3.65 m) = (1300 kg)x
x = 4166 kg.m/1300 kg
x = 3.20 m
Therefore, the center of mass of the car with all people seated will be 3.20 m far from the front of the car.
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A child rolls a ball on a level floor 5.2 m to another child.
If the ball makes 15.0 revolutions, what is its diameter?
Express your answer to two significant figures and include the appropriate units.
Diameter of the ball = 11.03cm
The ball rolled by the child must cover a distance in a linear motion which will be then equal to the circumference of the ball after one complete revolution.
Linear distance = 5.2m
d = diameter of the ball =?
Total revolutions = 15
S = 2πr
S = πd
For 15 revolutions
S = 15πd
The Diameter of a ball is double the radius of the ball thus we use D instead of 2r in the formula
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How much time is required for reflected sunlight to travel from the Moon to Earth if the distance between Earth and the Moon is 3.85 × 105 km?
1.3 second of time will be required for reflected sunlight to travel from the Moon to Earth if the distance between Earth and the Moon is 3.85 × 105 km
What is Speed ?Speed is the distance travelled per time taken. It is a scalar quantity. And the S.I unit is meter per second. That is, m/s
In the given question, we want to find how much time is required for reflected sunlight to travel from the Moon to Earth if the distance between Earth and the Moon is 3.85 × 10^5 km.
What are the parameters to consider ?
The parameters are;
The distance S = 3.85 × [tex]10^{5}[/tex] kmThe Speed of Light C = 3 × [tex]10^{8}[/tex] m/sThe time taken t = ?Speed = distance S ÷ Time t
Convert kilometer to meter by multiplying it by 1000
C = S/t
3 × [tex]10^{8}[/tex] = 3.85 × [tex]10^{8}[/tex] / t
Make t the subject of formula
t = 3.85 × [tex]10^{8}[/tex] / 3 × [tex]10^{8}[/tex]
t = 1.2833
t = 1.3 s
Therefore, 1.3 second of time will be required for reflected sunlight to travel from the Moon to Earth if the distance between Earth and the Moon is 3.85 × 105 km
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Is it possible for an object to be in equilibrium (no net force), if only one force is acting on it ?
