The center of the mass of a one-meter long rod, made of 50 cm of iron (density 8gcm3) and 50 cm of aluminum (density 2.7gcm3) is 37.62(cm)
Calculations and Parametersλ Fe =8g/cm,λ Al =2.7g/cm
There is a metal rod 1 meter long, with the first 50cm being iron and the other 50cm aluminum. the problem is solved in a one-dimensional case meaning it's a thin rod.
Next, we would solve by definition of the center of mass
We would also note that the masses of iron and aluminum are just the product of their length and linear density.
[tex]X_C_M[/tex]= [tex]\frac{8(g/cm). \frac{2500(cm^2)}{2} + 2.7 (g/cm). \frac{7500(cm^2)}{2} }{8(g/cm).50(cm) + 2.7(g/cm). 50 (cm)}[/tex]
= 37.62(cm)
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A Skier starting from rest rolls down a 35.0 m ramp. When he arrives at the bottom of the ramp his speed is 10.43 m/s. (a) Determine the magnitude of his acceleration, assumed to be constant, (b) If the ramp is inclined at 60.0 degrees with respect to the ground, what is the component of his acceleration that is parallel to the ground. (c) Provide me with a free body diagram, one for the 35 m ramp situation. Also, provide a nice sketch of the skier.
We obtain the magnitude of the acceleration as 1.55 m/s^2 while its component parallel to the ground is 0.775 m/s^2.
What is acceleration?The acceleration refers to change of speed with time. From the question;
distance covered = 35.0 m final velocity = 10.43 m/sIt the follows that;
v^2 = u^2 + 2as
And;
u = 0m/s owing to the fact that motion started from rest
v^2 = 2as
a = v^2/2s
a = (10.43 m/s)^2/2 * 35.0 m
a = 1.55 m/s^2
For the acceleration component which is parallel to the ground;
ax = a sin θ
ax = 1.55 m/s^2 cos 60
ax = 0.775 m/s^2
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What are 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.
Hope its helpful!
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.
Explanation:
a 600 g pool ball moving at 2.0m/s hits a second pool of the same mass at rest. the first ball moves off at 1.5m/s at an angle of 30 degrees from the original direction. assume the surface of the pool table to b frictionless find the angle at which the second ball moves off and the speed of the second ball after impact.
The speed of the second ball after impact is 1.43 m/s at 60.8⁰.
Speed of the second ballApply the principle of conservation of linear momentum;
in y direction0.6(2) = 0.6(1.5 sin30) + 0.6(vy)
1.2 = 0.45 + 0.6vy
0.6vy = 0.75
vy = 0.75/0.6
vy = 1.25 m/s
in x direction0.6(2) = 0.6(1.5 cos30) + 0.6(vx)
1.2 = 0.78 + 0.6vx
0.6vx = 0.42
vx = 0.42/0.6
vx = 0.7 m/s
Resultant speedv = √(vy² + vx²)
v = √(1.25² + 0.7²)
v = 1.43 m/s
Direction of second massθ = arc tan(vy/vx)
θ = arc tan (1.25/0.7)
θ = 60.8⁰
Thus, the speed of the second ball after impact is 1.43 m/s at 60.8⁰.
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Which action will cause the magnetic force to push two magnets closer together?
The action that will cause the magnetic force to push two magnets closer together: is that of attraction which happens when opposite poles of the magnets approach.
Meaning of magnetic forcemagnetic force can be defined as the effect that is felt by magnetic objects that causes attraction and repulsion.
A magnetic force attracts two magnets when they are in opposite poles and repels them if they are in the same pole.
In conclusion, The action that will cause the magnetic force to push two magnets closer together: is that of attraction which happens when opposite poles of the magnets approach.
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By what percent does the braking distance of a car decrease, when the speed of the car is reduced by 10.3 percent? Braking distance is the distance a car travels from the point when the brakes are applied to when the car comes to a complete stop. (Hint: the answer is not 10.3 percent)
The percent of the braking distance is mathematically given as
P=91.5128%
What percent does the braking distance of a car decrease, when the speed of the car is reduced by 10.3 percent?Generally, the equation for is mathematically given as
V^2=U^2+2as
Therefore
V^2=u^2+2(-a)s
[tex]s=\frac{u^2}{-2a}[/tex]
Hence.
u'=u-u×0.103
u'=0.206u
v^2=u^2+2as
0=(0.206)^2+2(-a)s'
Hence
[tex]s'=\frac{0.042436u^2}{a}[/tex]
In conclusion,The reduction percentage is
[tex]P=\frac{s-s'}{s}*100\\\\P=\frac{(\frac{u^2}{-2a})-(\frac{0.042436u^2}{a} )}{ \frac{u^}{-2a}}*100\\\\P=\frac{(0.5-0.042436 )}{ 0.5}*100[/tex]
P=91.5128%
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Imagine that the Earth's size shrunk by a factor of 5.70 from a radius of 1120 km to a radius of 6370 km. However, Earth's mass has remained the same at 5.98×1024 kg. If a person's mass is 80.7 kg, calculate their weight before and after Earth's shrinkage in Newtons and pounds
The weight of the person in the first case is 25759.44 N while in the second it is 790.86 N.
What is weight?Weight is the product of mass and acceleration due to gravity. We have to find the acceleration due to gravity in both cases.
g = GM/r^2
g1 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/(1120 * 10^3 m)^2
g1 = 3.99 * 10^14/1.25 * 10^12
g1 = 319.2 m/s^2
g2 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/( 6370 * 10^3 m)^2
g2 = 3.99 * 10^14/4.06 * 10^13
g2 = 9.8 m/s^2
The weight of the person in the first case is; 80.7 kg * 319.2 m/s^2
= 25759.44 N
The weight of the person in the second case is; 80.7 kg * 9.8 m/s^2
= 790.86 N
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Drag each label to the correct location on the table sort the sentences based on weather thy are correct or incorrect
The statement that water boils at a temperature below 100 degrees in a pressure cooker is correct
What is freezing?The term freezing refers to the temperature at which a liquid is turned into a solid.
The following is the sorting of the statements into those that are correct and incorrect.
Water boils at a temperature below 100 degrees at high altitudes - correct
Water expands on freezing - correct
Water contracts on freezing - incorrect
Water boils at a temperature below 100 degrees in a pressure cooker - correct
Water boils at 100 degrees under normal pressure - correct
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(15 Points)
1. Two builders carry a sheet of drywall up a ramp.
Assume that W = 1.80 m, L = 3.30 m, θ = 24.0°, and that the lead builder carries a (vertical) weight of 147.0 N (33.0 lb). What is the (vertical) weight carried by the builder at the rear? (First Figure)
2. The builder at the rear gets tired and suggest that the drywall should be held by its narrow side. What is the weight (in N) he must now carry? (Second Figure)
The vertical weight carried by the builder at the rear end is F = 308.1 N
Calculations and ParametersGiven that:
The weight is carried up along the plane in rotational equilibrium condition
The torque equilibrium condition can be used to solve
We can note that the torque due to the force of the rear person about the position of the front person = Torque due to the weight of the block about the position of the front person
This would lead to:
F(W*cosθ) = mgsinθ(L/2) + mgcosθ(W/2)
F(1cos20)= 197/2(3.10sin20 + 2 cos 20)
Fcos20= 289.55
F= 308.1N
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When a mass of m = 29 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12∘ with the horizontal as shown in (Figure 1) . The elastic modulus for aluminum is 7.0×1010N/m2. Determine the radius of the wire
The solution to the given question is that the radius of the wire will be 0.378 millimetre approximately
At equilibrium,
Lets assume Tension T in the wire
mass of the block is given as 29 Kg
T sin 12° + T sin 12° = mg
T sin 12° + T sin 12° = 29 × 9.8
2T sin 12° = 29 × 9.8
T = ( 29 × 9.8 )/2 sin 12°
T = 141.1 / sin 12°
T = 141.1 / 0.2
T = 705.5 Newton
Stress = K × Strain
where K is the elastic modulus of the metal
elastic modulus is given as 7.0 × 10¹⁰ N/m²
T/A = 7.0 × 10¹⁰ × (Δl/l)
A = T × (l/Δl) × (1/ (7.0 × 10¹⁰) )
A = π r² = T / ( (7.0 × 10¹⁰) × ( (1/cos 12°) - 1) )
π r² = 705.5 / ( (7.0 × 10¹⁰) × 0.02234 )
r = √( 705.5 / ( π × (7.0 × 10¹⁰) × 0.02234 ) ) metre
r = √( 705.5 / ( 4910.33 × 10⁶ ) ) metre
r = √( 0.1436 × 10⁻⁶ ) metre
r = ( 0.378 × 10⁻³ ) metre
r = 0.378 millimetre
Thus we have find the radius of the wire by applying stress strain relation which came out to be 0.378 millimetre.
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What is the force between two balloons with a negative charge of 1.6 × 10−10 C if the balloons are 0.05 m apart?
Considering the Coulomb's Law, the force between the two ballons is 9.216×10⁻⁸ N.
Coulomb's LawCharged bodies experience a force of attraction or repulsion on approach.
From Coulomb's Law it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.
From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:
[tex]F=k\frac{Qq}{d^{2} }[/tex]
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).Q and q are the values of the two point charges. They are measured in Coulombs (C).d is the value of the distance that separates them. It is measured in meters (m).K is a constant of proportionality called the Coulomb's law constant. It depends on the medium in which the charges are located. Specifically for vacuum k is approximately 9×10⁹ [tex]\frac{Nm^{2} }{C^{2} }[/tex].The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.
Force between two balloonsIn this case, you know that two balloons have a negative charge of 1.6×10⁻¹⁰ C and the balloons are 0.05 m apart.
Replacing in the Coulomb's Law, you get:
[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{(-1.6x10^{-10} C)x(-1.6x10^{-10} C)}{(0.05 m)^{2} }[/tex]
Solving:
[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{2.56x10^{-20} C^{2} }{(0.05 m)^{2} }[/tex]
[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } 1.024x10^{-17}\frac{ C^{2} }{m^{2} }[/tex]
F= 9.216×10⁻⁸ N
Finally, the force between the two ballons is 9.216×10⁻⁸ N.
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A motor has coils with a resistance of 10.0 ohms and is supplied by a voltage of V = 1.20 x 102 V. When the motor is running at its maximum speed, the back emf is 70.0 V. Find the current in the coils (a) when the motor is first turned on and (b) when the motor has reached its maximum rotation rate.
Hi there!
a)
When the motor is first turned on, the coils are initially stationary. Thus, there is no change in magnetic flux and, consequently, no induced emf.
Therefore:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Since there's no back emf:
[tex]iR = \epsilon[/tex]
Solving for i using Ohm's Law:
[tex]i = \frac{\epsilon}{R}\\\\i = \frac{120}{10} = \boxed{12.0 A}[/tex]
b)
We are given that at max speed, the back EMF is 70.0 V.
Using the same equation as above:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Plugging in the values:
[tex]10i = 120 - 70 \\\\10i = 50 \\\\[/tex]
Solving for current:
[tex]i = \frac{50}{10} = \boxed{ 5.0 A}[/tex]
Animals change their feature according to their environment
Hydroelectric plants are used to produce electricity. Electric generators are used in such plants that are linked to water-wheels. As these water-wheels rotate, electricity is generated. Which of the following best explains the relationship between energy and motion in the process described
Hydroelectric plants are used to produce electricity is the statement that best explains the relationship between energy and motion.
Explains the relationship between energy and motion in the process?There is direct relationship between energy and motion in the process because if we increase the motion of the turbines, more electricity is produced in the generator and vice versa.
So we can conclude that the relationship between energy and motion in the process is directly proportional to each other.
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How much did mary pay in social securty taxes
The amount that Mary will pay in social security taxes will be $1550.
How to compute the value?It should be noted that the current tax for the social security is 6.2% for the employer and 6.2% for the employee.
In this case, let's assume that the income for Mary is $25000, the amount that Mary will pay will be:
= 6.2% × $25000
= 0.062 × $25000
= $1550
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Which graph describes the motion of a car that moves at constant speed, stops for some time and then moves again at a slower speed?
a. A
b. B
c. C
d. D
Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball B is twice that of ball A. a. Calculate the angle above the horizontal of the motion of mass A + B after the collision. b. What is the ratio of the final velocity of the mass A + B to the initial velocity of ball A, /? c. What is the ratio of the final energy of the system to the initial energy of the system, /? Is the collision elastic or inelastic?
The angle above the horizontal of the motion of mass A + B after the collision. as well as others are mathematically given as
[tex]\theta f = 26.3 \deg[/tex]vf/vA= 0.942vf^2 / 5vA^2 = 0.35What is Collison equilibrium?
According to the collision hypothesis of chemistry, chemical reactions happen when two molecules or atoms collide.
Generally, the equation for Collison equilibrium is mathematically given as
For horizontal motion
mvAx+m2vAx = 2mvfx
For vertical motion
-mvAy+m2vAy = 2mvfy
vfy = 1/2 vAy
[tex]\tan \theta f = vfy/vfx \\\\\tan \theta f = 1/3 vAy/vAx \\\\\tan \theta f = vAy/vAx \\\\\theta f = tan-1 ( 1/3 tan (56) )\\\\[/tex]
[tex]\theta f = 26.3 \deg[/tex]
(b)
[tex]v fy = vf sin \theta f\\\\vAy = vA sin theta i\\\\vf/vA = vfy/vAy sin( \theta i)/sin(\theta f)\\\\vf/vA = 1/2 sin(56)/sin(26.3) \\\\[/tex]
vf/vA= 0.94
(c)
[tex]Ef/Ei = \frac{(1/2 * (2m) * (vf)^2) }{ (1/2 * m * (vA)^2) + 1/2*m*(2vA)^2) ]}[/tex]
2vf^2 / 5vA^2 = 0.35
In conclusion, The angle above the horizontal of the motion of mass A + B after the collision. as well as others
[tex]\theta f = 26.3 \deg[/tex]
vf/vA= 0.94
2vf^2 / 5vA^2 = 0.35
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During the 2020 general election, GOP incumbent Donald Trump is once again successful in his bid for the presidency. Mr. Trump amasses 307 electoral votes compared to the 231 electoral votes Beto O'Rourke, the Democratic candidate, received. Following a selective state recount of the presidential election results, poll workers discover that Green Party Candidate Jill Stein actually won the popular vote in Pennsylvania, Michigan and Wisconsin, resulting in a deduction of 47 electoral votes from the GOP incumbent Donald Trump’s total. As a result of the deduction Mr. Trump now possesses 260 electoral votes. The recount also reveals a loss of two electoral votes to O'Rourke due to the non-votes by two faithless electors in Florida. O'Rourke’s final number now rests at 229 electoral votes. What would be the next step(s) in deciding which candidate becomes the next President of the United States?
The election would be given to the members of the House of Representatives who would be able to select either O'Rourke, or Trump only, because they were the only candidates who received more than 15% of the available electoral votes.
What is the role of house of representative?The house of representatives are those that has been given the authority to make and pass federal laws.
They are supposed to handle and mischief during elections that may affect the process on order to ascertain the rightful leader.
From the excerpt given, since a recount of the votes where made and the three parties involved had a miscount, the final decision should be made by the house of representatives.
This is because, the house of representatives has the authority to elect the president from the three presidential candidates that received the highest votes.
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Discuss how oxygen is used in spacecraft in at least 2 paragraphs.
Oxygen is used in spacecraft by the persons for respiration.
Why do spaceships need oxygen?Rocket engines carry oxygen gas for combustion because combustion need oxygen. Rockets carry an liquid oxygen up to space with them as a fuel.
Astronauts sealed in a spacecraft that need a continuous supply of oxygen for respiration. Without this oxygen, no person can survive in the spacecraft.
So we can conclude that oxygen is used in spacecraft by the persons for respiration.
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Oxygen is required in spacecrafts for the following:
Oxygen is mixed with fuel to power the engines,Oxygen is used in pressurized spacesuits for breathing.What is the importance of oxygen in spacecraft?Spacecraft refers to vehicles which are used to travel to space.
In space, their is little or no oxygen. Thus oxygen is used in the following ways:
Oxygen is mixed with fuel to power the engines,Oxygen is used in pressurized spacesuits for breathing.In conclusion, oxygen is important for combustion of fuel of the spacecraft engines as well as for breathing by the astronauts.
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A charge of 5.4 C experiences a force of 25.0 in an electric field. What is the strength of electric field at that point ? If the 5.4 C is replaced by a charge of half the magnitude, 2.7 C, how much force would this charge experience at that point ? Remember to identity all of your data, write the equation, and show your work. (5 points)
The strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and 12.38 N.
What is the electric field strength?The electric field strength is defined as the ratio of electric force to charge.
Given data;
q₁ = 5.4 C
F₁ is the electric force in case1
E is the electric field =?
F₂ is the electric force in case 2
q₂ is the charge 2
The strength of the electric field at that point is;
F₁=Eq₁
E₁=F/q₁
E₁=25.0 N / 5.4 C
E₁=4.587 N/C
The force would this charge experience at that point when the charge is 2.7 C;
F₂=Eq₂
F₂=4.587 N/C × 2.7 C
F₂ = 12.38 N
Hence the strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and 12.38 N.
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Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1,000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.56 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.3 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate. Answer the following:
1.hardwood floor magnitude
2.hardwood floor duration
3.carpeted floor magnitude
4.carpeted floor duration
This question is health related and seeks to compute the details surrounding a traumatic head injury. See the explanation below.
What is a traumatic head injury?Traumatic brain injury (TBI), a form of acquired brain injury, occurs when a sudden trauma causes damage to the brain.
TBI can result when the head suddenly and violently hits an object, or when an object pierces the skull and enters brain tissue
What are the details surrounding the head injury?Final velocity before hitting the ground
V² = 2g*0.56
V² = 2 * 9.8 * 0.56
V = √10.976
V = 3.312 m/s
*** Note that g which is the acceleration of gravity is about 9.8 meters.
1a) Where there is a hardwood floor
-u^2 = -2as
a = 3.312^2/2*0.0019
a = 1,042.08 m/s^2
1b) Duration
t = u/a
= 3.312/1,042.08
t = 3.18 ms
2a) Where there is a carpet on the floor
a = 3.312^2/2*0.013
a = 713.01 m/s^2
t = u/a
= 3.312/713.01
t = 4.65 ms
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An object has a weight of 9 n when it is in air and 7.2 n when it is submerged into water. what is the specific gravity of the object’s material?
The specific gravity of the object’s material is 5.09.
To calculate the specific gravity of the object:Weight difference = 9 - 7.2 = 1.8 N = Buoyant force of water
Buoyant Force in water(Fb) = density of water x g x volume of the body(Vb)
1.8 = 1000 x 9.81 x Vb
Vb = 1.8/9810 cubic meter
Now, in the air;
Weight of body = mg = 9 N
Mass of body,m = 9/9.81 Kg
So,
Density of body = m/ Vb
= 9/9.81 ÷ 1.8/9810
= 5094.44 kg per cubic meter
The specific gravity of body = density of body ÷ density of water
= 5094.44 ÷ 1000
= 5.09
Therefore, Specific gravity of body = 5.09
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Question 4
Newton's first law of motion is also known as the law of inertia. Which of the following BEST
describes inertia?
Inertia depends on an objects mass and velocity
Objects at rest stay at rest until an outside force acts on them
An unbalanced force causes an object to move
An object's tendency to resist change in motion
Answer:
It is the tendency
of an object to resist any change in its state of motion .
Explanation:
if I am right mark my answer as brainliest
A boat moves through the water with two forces acting on it. One is a 1,800-N forward push by the water on the propeller, and the other is a 1,200-N resistive force due to the water around the bow.
(a) What is the acceleration of the 1,400-kg boat?
0.25
m/s 2
(b) If it starts from rest, how far will the boat move in 20.0 s?
m
(c) What will its velocity be at the end of that time?
m/s
(a)The acceleration of the 1,400-kg boat will be 0.425 m/sec²
(b) If it starts from rest, the distance through which the boat moves in 20.0 s will be 85 m.
(c)Velocity at the end of that time will be 8.5 m/sec.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
Given data;
Forwad force acting on the boat,v₁ = 1,800-N
Resistive force acting on the boat,v₂ = 1,200-N
The acceleration of the boat,a
Mass of boat,m = 1,400-kg
Initial velocity of boat,u= 0 m/sec
Distance travelled by boat,S = ?
Time for the boat travels,t = 20.0 s
Final velocity,V = ? m/sec
The net force on the boat;
F = F₁ - F₂
F = 1800 N - 1200 N
F = 600 N
From the defination of force;
F= ma
a = F / m
a = 600 N / 1400 kg
a = 0.425 m/sec²
b)
The distance through which the boat moves is 20.0 s;
[tex]\rm x_f = x_ 0 + v_0 t + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}at^2 \\\\ x_f = 0+0 + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}\times 0.425 \times (20 )^ 2 \\\\ x_f = 85 \ m[/tex]
c)
The velocity at the end of that time is found as;
[tex]\rm v_f = v_ 0 + at \\\\ v_f =- 0+ at \\\\ v_f = 8.5[/tex] m/sec
Hence the acceleration of the boat, the distance through which the boat moves in 20.0 s, and velocity at the end of that time will be 0.425 m/sec²,85 m, and 8.5 m/sec.
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A person walks first at a constant speed of 5.00 m.s-1
along a straight line from point A to
point B and then back along the line from B to A at a constant speed of 3.00 m.s-1
.
(a) Calculate her average speed over the entire trip.
The average speed of the person over the entire trip is 3.75 m/s.
Average speed of the personAverage speed = total distance/total time
Average speed = (d + d)/(d/Va + d/Vb)
where;
d is the distance in a single tripVa is speed from point AVb is the speed from point BAverage speed = (2Vavb)/(Va + Vb)
Average speed = (2 x 5 x 3)/(5 + 3)
Average speed = 3.75 m/s
Thus, the average speed of the person over the entire trip is 3.75 m/s.
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An aircraft, initially stationary on a runway, takes off with a speed of 85 km h¹ in a distance of no
more than 1.20 km.
What is the minimum constant acceleration necessary for the aircraft?
A 0.23ms-²
B 0.46ms ²
C 3.0ms ²
D 6.0m
Answer:
A. 0.23 ms⁻²
Explanation:
Using the equation:
v² = u² + 2as
where:
v = final velocity (85 kmh⁻¹ = 85 x 0.278 = 23.6 ms⁻¹)
u = initial velocity (0 ms⁻¹)
a = acceleration (? ms⁻²)
s = displacement (1.20 km = 1.2 x 1000 = 1200 m),
[tex](23.6)^2 = (0)^2 + 2 (a) (1200)[/tex]
⇒ [tex]a = \frac{23.6^2}{2(1200)}[/tex]
⇒ a = 0.23 ms⁻²
A housefly with a mass of 0.00100 kilograms zooms through the room at a rate of 2.20 m/s. How much kinetic energy does it have?
0.00110 J
0.00220 J
0.00242 J
The height of the fly above the ground must be known to answer this question.
Considering the definition of kinetic energy, the housefly has a kinetic energy of 0.00242 J.
Kinetic energyKinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and in a rest position, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its rest state by applying a force to it.
The kinetic energy is represented by the following expression:
Ec= ½ mv²
Where:
Ec is the kinetic energy, which is measured in Joules (J).m is the mass measured in kilograms (kg).v is the speed measured in meters over seconds (m/s).Kinetic energy of a houseflyIn this case, you know:
m= 0.00100 kgv= 2.2 m/sReplacing in the definition of kinetic energy:
Ec= ½ ×0.00100 kg× (2.20 m/s)²
Solving:
Ec= 0.00242 J
Finally, the housefly has a kinetic energy of 0.00242 J.
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A uniform rod with a mass of m = 1.94 kg and a length of l = 2.10 m is attached to a horizontal surface with a hin ge. The rod can rotate around the hin ge without friction.
Initially the rod is held at rest at an angle of θ = 70.4° with respect to the horizontal surface. Then the rod is released.
1. What is the angular speed of the rod, when it lands on the horizontal surface?
2. What is the angular acceleration of the rod, just before it touches the horizontal surface?
Hello!
1.
To solve, we can use the work-energy theorem.
Initially, the rod is at rest. Its center of mass is some height above the surface, so it contains gravitational potential energy.
Finally, the rod has rotational kinetic energy.
To find the initial energy, we have to find where the center of mass is. It is located at the midpoint of the rod, or l/2. To find its height above, though, we have to find its sine component with respect to the angle:
[tex]E_i = mg{\frac{l}{2}}}sin(\theta)[/tex]
Its final energy:
[tex]E_f = \frac{1}{2}I\omega^2[/tex]
About the pivot point, a rod's moment of inertia (I) is 1/3ml².
[tex]E_f = \frac{1}{2}(\frac{1}{3}ml^2) = \frac{1}{6}ml^2\omega^2[/tex]
Now, solving for angular speed:
[tex]E_i = E_f\\\\mg\frac{l}{2}sin\theta = \frac{1}{6}ml^2 \omega^2\\\\3gsin\theta = l\omega^2 \\\\\omega = \sqrt{\frac{3gsin\theta}{l}}[/tex]
Plugging in the values and solving:
[tex]\omega = \sqrt{\frac{3(9.8)sin(70.4)}{2.1}} = \boxed{3.63 rad/s}[/tex]
2.
Let's determine where to place our pivot point. To minimize the number of torques to take into account, let's put the pivot point at the base of the rod.
Now, the only torque we must consider is that produced by the force of gravity.
Recall the equation for torque:
[tex]\tau = r \times F[/tex]
This is a cross-product, where 'r' is the lever arm of the force. This is the perpendicular distance between the line of action of the force and the pivot point.
In this instance, based on our reference angle, this would be the COSINE.
[tex]\tau = rFcos\theta[/tex]
r = distance from pivot point to center of the rod (1.05 m)
F = Force of gravity, mg (19.03 N)
θ = angle of rod from horizontal
Using the rotational equivalent of Newton's Second Law:
[tex]I\alpha = rFcos\theta[/tex]
'I' is the rod's moment of inertia about the pivot point. For a uniform rod, its moment of inertia at its end is 1/3ml².
Therefore:
[tex]I = \frac{1}{3}(1.94)(2.1^2) = 2.85 kgm^2[/tex]
Now, we can solve for the function for angular acceleration.
[tex]\alpha(\theta) = \frac{rF}{I}cos\theta\\\\\alpha(\theta) = \frac{(1.05)(19.03)}{2.85}cos\theta = 7cos\theta[/tex]
This is the angular acceleration of the rod as a function of theta.
Substituting in θ = 0°:
[tex]\alpha(0) = 7cos(0) = \boxed{7 rad/s^2}[/tex]
**Note, we couldn't just use rotational kinematics because the angular acceleration is NOT constant.
a jet of water of cross section area and velocity v impinges normally on a stationary flat plate the mass per unit volume of water ρ
by dimensional analysis determine and expression for the force f exerted by the jet against the plate.
Explained in the attachment !
Hope it helps you!!How much time is required for a sound to travel 1 mile (5,280.0 ft) if the air temperature is 0°C?
The time is required for a sound to travel 1 mile (5,280.0 ft) if the air temperature is 0°C is 4.85 sec.
What is velocity?Velocity is largely a vector quantity. It is the fee of alternate distance. The speed of an item transferring can by no means be negative. The pace of a transferring item may be zero.
The velocity of sound waves at zero degrees Celsius is 1087 ft/sec.
Velocity = Distance/Time
Time= Distance/Velocity
The distance to be traveled by sound is 5280 ft
The velocity of sound is 1087 ft/sec
Time = 5280 ft/ 1087 ft/sec
Time = 4.85 sec.
The time required by sound to travel 1 mile at zero degrees Celsius is 4.85 sec.
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what role do supernovae explosions play in galactic recycling?
Explanation:
Supernovae play a fundamental role in a great cosmic recycling program. We believe that almost all of the elements in the Universe that are heavier than hydrogen and helium are created either in the centres of stars during their lifetimes or in the supernova explosions that mark the demise of larger stars.