Given:
The mass of the elephant is M = 2750 kg
The mass of the sprinter is m = 66.5 kg
The speed of the sprinter is v = 9.5 m/s
The kinetic energy of the sprinter is equal to the kinetic energy of the elephant.
Required: The speed of the elephant
Explanation:
The kinetic energy of the sprinter is equal to the kinetic energy of the elephant.
The speed of the elephant can be calculated by the formula
[tex]\begin{gathered} K.E._{elephant}=K.E._{sprinter} \\ \frac{1}{2}MV^2=\frac{1}{2}mv^2 \\ V=\sqrt{\frac{mv^2}{M}} \end{gathered}[/tex]On substituting the values, the speed of the elephant will be
[tex]\begin{gathered} V=\sqrt{\frac{66.5\times(9.5)^2}{2750}} \\ =1.48\text{ m/s} \end{gathered}[/tex]Thus, the speed of the elephant is 1.48 m/s
Final Answer: The speed of the elephant is 1.48 m/s
You see a blue star directly over Avalon's equator. It appears to be moving north at 5.0 arcseconds per year. How far away is this star from Avalon (in parsecs - a parsec is ).
The distance of the star from the sun is 1.25 parsecs.
What quantity is measured in arcseconds?
The distance of the sun to other celestial bodies is measured in arcseconds.
The distance from the sun to a celestial object is the reciprocal of the angle, measured in arcseconds, of the object's apparent movement caused by parallax.
2 arcseconds = 0.5 parsecs
5 arcseconds = ?
= (5 arcseconds x 0.5 parsecs) / (2 arcseconds)
= 1.25 parsecs
Thus, the star appears to be moving north at 1.25 parsecs per year.
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choose the 200 kg refrigerator. set the applied force to 400 n (to the right). be sure friction is turned off. what is the net force acting on the refrigerator?
Answer:
Explanation:
Ginen:
m₁ = 200 kg
F₂ = 400 N
g ≈ 10 m/s²
__________
R - ?
F₁ = m₁·g = 200· 10 = 2000 N
R = √ (F₁² + F₂²) = √ ( 2000² + 400²) ≈ 2040 N
The net force acting on the refrigerator having a mass of 200 kg and the applied force to 400 n (to the right) is 2040 Newtons.
What is force?Force is the influence of either pull or pushes in the body. Basically, gravitation forces, nuclear forces, and friction forces are the types of forces. For e.g. when the wall is hit by a hand then a force is exerted by the hand on the wall as well as the wall also exerts a force on the hand. There are different laws given to Newton to understand force.
Newton is a unit of force used by physicists that is part of the International System (SI). The force required to move a body weighing one kilogram one meter per second is known as a newton.
Given:
The mass of the refrigerator, m = 200 kg,
The force, F = 400 N,
Calculate the net force by the formula given below,
F = m × g
here, g is the gravitational acceleration.
Substitute the values,
F= 200 × 10 = 2000 N
[tex]R = \sqrt{F_1^2 +F_2^2}[/tex]
where R is the net force
[tex]R = \sqrt{2000^2 +400^2}[/tex]
R = 2040 Newton
Therefore, the net force acting on the refrigerator having a mass of 200 kg and the applied force to 400 n (to the right) is 2040 Newtons.
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A car is driving around a turn with a radius of 20.7 m. If the coefficient of friction between the tires and the road is 2.07, what is the maximum speed the car can maintain around the turn without slipping?
Answer:
A car completes a turn that has a radius of 20 meters. The coefficient of friction between the tires and road is 0.50. What maximum speed can the car safely maintain in order to complete the turn without skidding? (A) 5 m/s (B) 10 m/s (C) 15 m/s (D) 20 m/s (E) 25 m/s
A raindrop has a mass of 7.7 × 10-7 kg and is falling near the surface of the earth. Calculate the magnitude of the gravitational force exerted (a) on the raindrop by the earth and (b) on the earth by the raindrop.(a)Fraindrop= _________________ units ________(b)Fearth= _________________ units_____________
ANSWER:
a) Fraindrop
[tex]F=7.546\cdot10^{-6}N[/tex](b) Fearth
[tex]F=-7.546\cdot10^{-6}N[/tex]STEP-BY-STEP EXPLANATION:
(a)
We calculate the force, multiplying the value of the mass by gravity, just like this:
[tex]\begin{gathered} F=m\cdot a \\ F=7.7\cdot10^{-7}\cdot9.8 \\ F=7.546\cdot10^{-6}N \end{gathered}[/tex](b)
by newton's 3rd law they are are equal and opposite so:
[tex]F=-7.546\cdot10^{-6}N[/tex]What is the average velocity of a car that travels 48 km north in 2.0 h?
Answer: 3.7 seconds. :)
Explanation:
Answer:
Explanation:
Given:
L = 48 km
t = 2.0 h
__________
V - ?
V = L / t = 48 / 2.0 = 24 km/h
Philip jumps up with to a height of 3 m above the ground. What was Philip's initial velocity? round to the tenth.
The initial velocity of Philip was 7.66 m/s
Given data:
The vertical height is h=3 m.
Considering ground as the reference, then the initial potential energy of Philip is zero, i.e., PEi=0
The formula for the kinetic energy is given by,
[tex]KE_i=\frac{1}{2}mv^2[/tex]Here, m is mass and v is the velocity.
After reaching the height of 3 m Philip comes to a stop. It means the final kinetic energy is zero, i.e. KEf=0.
The final potential energy is given by,
[tex]PE_f=mgh[/tex]Here, g is the gravitational acceleration.
Applying the conservation of energy between initial position and final position.
[tex]\begin{gathered} KE_i+PE_i=KE_f+PE_f \\ \frac{1}{2}mv^2+0=0+mgh \\ v=\sqrt[]{2gh} \\ v=\sqrt[]{2\times9.8\times3} \\ v=7.66\text{ m/s} \end{gathered}[/tex]Thus, the initial velocity of Philip was 7.66 m/s.
1.Can money by happiness?why and Why not?
2.Are you happy with the possession you have? Yes/No Why?
Answer:
Explanation:
1) No it can't
2)Yes I am
Answer:
yes it's can be, but Don't put money first
Given the wave described by y(x,t)=5cos[π(4x-3t)], in meters. Find the following. Giveexact answers with units.
Answer:
a) 5 m
b) 0.667 s
c) 0.5 m
d) 0.75 m/s
e) -5 m
Explanation:
In an equation of the form
y(x, t) = Acos(kx - ωt)
A is the amplitude, ω = 2π/T where T is the period, and k = 2π/λ where λ is the wavelength. In this case, the equation os
y(x,t) = 5cos(π(4x - 3t)
y(x,t) = 5cos(4πx - 3πt)
So, A = 5, k = 4π, and ω = 3π. Then, we can find each part as follows
a) Amplitude
The amplitude is A, so it is 5 m.
b) the period
Using the equation ω = 2π/T and solving for T, we get:
[tex]T=\frac{2\pi}{\omega}=\frac{2\pi}{3\pi}=\frac{2}{3}=0.667\text{ s}[/tex]So, the period is 0.667 s
c) the wavelength.
using the equation k = 2π/λ and solving for λ, we get:
[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{4\pi}=0.5\text{ m}[/tex]So, the wavelength is 0.5 m
d) The wave speed
The wave speed can be calculated as the division of the wavelength by the period, so
[tex]v=\frac{\lambda}{T}=\frac{0.5\text{ m}}{0.667\text{ s}}=0.75\text{ m/s}[/tex]e) The height of the wave at (2, 1)
To find the height, we need to replace (x, t) = (2, 1) on the initial equation, so
[tex]\begin{gathered} y(x,t)=5\cos(\pi(4x-3t)) \\ y(2,1)=5\cos(\pi(4\cdot2-3\cdot1)) \\ y(2,1)=5\cos(\pi(8-3)) \\ y(2,1)=5\cos(\pi(5)) \\ y(2,1)=5\cos(5\pi) \\ y(2,1)=5(-1) \\ y(2,1)=-5 \end{gathered}[/tex]Then, the height of the wave is -5 m.
Therefore, the answers are
a) 5 m
b) 0.667 s
c) 0.5 m
d) 0.75 m/s
e) -5 m
An arrangement of two pulleys, as shown in the figure, is used to lift a 64.3-kg crate a distance of 4.36 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical.What is the change in the potential energy of the crate when it is lifted a distance of 4.36 m? (kJ)How much work must be done to lift the crate a distance of 4.36 m? (kJ)What length of rope must be pulled to lift the crate 4.36 m? (m)
Given data:
* The mass of the crate is m = 64.3 kg.
* The height of the crate is h = 4.36 m.
Solution:
(a). The potential energy of the crate at the initial state is zero (as the height of the crate is zero at the initial state), thus, the change in the potential energy of the crate is,
[tex]\begin{gathered} dU=\text{mgh}-0 \\ dU=mgh \end{gathered}[/tex]where g is the acceleration due to gravity,
Substituting the known values,
[tex]\begin{gathered} dU=64.3\times9.8\times4.36 \\ dU=2747.4\text{ J} \\ dU=2.75\times10^3\text{ J} \\ dU=2.75\text{ kJ} \end{gathered}[/tex]Thus, the change in the potential energy is 2.75 kJ.
(b). The work done to lift the crate is equal to the change in the potential energy of the crate.
Thus, the work done on the crate is 2.75 kJ.
(c). As the single is pulling the two ropes to increase the height of the crate, thus, the length of the rope pulled in terms of the height of the crate is,
[tex]l=2h[/tex]Substituting the known values,
[tex]\begin{gathered} l=2\times4.36 \\ l=8.72\text{ m} \end{gathered}[/tex]Thus, the length of the rope pulled to lift the crate is 8.72 meters.
What are the answers for a, b and c in MJ?
Given:
The orbital height of the satellite, h=94 km=94000 m
The mass of the satellite, m=1045 kg
The new altitude of the satellite, d=207 km=207000 m
To find:
a) The energy needed.
b) The change in the kinetic energy.
c) The change in the potential energy.
Explanation:
The radius of the earth, R=6.37×10⁶ m
The mass of the earth, M=6×10²⁴ kg
a) The orbital velocity is given by,
[tex]v=\sqrt{\frac{GM}{r}}[/tex]Where G is the gravitational constant and r is the radius of the satellite from the center of the earth.
Thus the initial orbital velocity of the earth,
[tex]\begin{gathered} v_1=\sqrt{\frac{6.67\times10^{-11}\times6\times10^{24}}{(6.37×10^6+94000)}} \\ =7868.43\text{ m/s} \end{gathered}[/tex]The orbital velocity after changing the altitude is,
[tex]\begin{gathered} v_2=\sqrt{\frac{6.67\times10^{-11}\times6\times10^{24}}{(6.37\times10^6+207000)}} \\ =7800.5\text{ m/s} \end{gathered}[/tex]Thus the total energy needed is given by,
[tex]E=(\frac{1}{2}mv_2^2-\frac{GMm}{(R+d)})-(\frac{1}{2}mv_1^2-\frac{GMm}{(R+h)})[/tex]On substituting the known values,
[tex]\begin{gathered} E=1045[(\frac{1}{2}\times7868.43^2-\frac{6.67\times10^{-11}\times6\times10^{24}}{(6.37\times10^6+207000)})-(\frac{1}{2}\times7800.5^2-\frac{6.67\times10^{-11}\times6\times10^{24}}{(6.37×10^6+94000)})] \\ =623\text{ MJ} \end{gathered}[/tex]b)
The change in the kinetic energy is given by,
[tex]\begin{gathered} KE=\frac{1}{2}mv_2^2-\frac{1}{2}mv_1^2 \\ =\frac{1}{2}m(v_2^2-v_1^2) \end{gathered}[/tex]On substituting the known values,
People weigh less on the moon than on the Earth because:the moon is smaller and has less gravity to pull on you.the Earth has less gravity than the Moon.people weigh the same on the moon as they do on Earth.the moon is magnetized.
Given
People weigh less on the moon than on the Earth
To find
The correct reason for the given statement
Explanation
The moon has much lesser mass than that of the earth. It is also just 60 percent as dense as the earth. So the gravitational pull on the moon is less than on the earth and thus people weigh less on the moon
Conclusion
The correct reason is
the moon is smaller and has less gravity to pull on you.
A small object of mass 0.500 kg is attached by a 0.440 m-long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 5.34 m/s.What is the magnitude of the radial acceleration of the object? What is the tension in the cord?
Given data:
* The mass of the object attached is m = 0.5 kg.
* The radius of the circle is r = 0.44 m.
* The speed of the object moving in circular motion is v = 5.34 m/s.
Solution:
(a). The radial acceleration of the object is also known as the centripetal acceleration of the object.
The value of centripetal acceleration in terms of the velocity of the object is,
[tex]a_c=\frac{v^2}{r}[/tex]Substituting the known values,
[tex]\begin{gathered} a_c=\frac{5.34^2}{0.44} \\ a_c=64.8ms^{-2} \end{gathered}[/tex]Thus, the radial acceleration of the object is 64.8 meters per second squared.
(b). The tension in the chord is equivalent to the centripetal force acting on the object which helps it to move in the circular motion.
Thus, the tension acting on the chord is,
[tex]F=ma_c[/tex]Substituting the known values,
[tex]\begin{gathered} F=0.5\times64.8 \\ F=32.4\text{ N} \end{gathered}[/tex]Thus, the tension acting in the chord is 32.4 N.
part 2 of 2 ASSUME BOTH snowballs are thrown with the same initial speed 39.9 m/s. the first snowball is thrown at an angle of 51 degrees above the horizontal. At what angle should you throw the second snowball to make it hit the same point as the first? how many seconds after the first snowball should you throw the second so that they arrive on target at the same time?
Explanation
Step 1
Let
a) for ball 1
[tex]\begin{gathered} \text{ Initial sp}eed=v_0=33.9\text{ }\frac{m}{s} \\ \text{ Angle=51 \degree} \end{gathered}[/tex]the formula for the distance is given by:
[tex]x=\frac{v^2_0\sin(2\theta)}{g}[/tex][tex]\begin{gathered} \text{hence, let v}_0=39.9,\text{ angle= 51 \degree , g=9.8 } \\ \text{replace to solve for x } \\ x=\frac{(39.9)^2\sin(2\cdot51)}{9.8} \\ x=158.9\text{ m} \\ \end{gathered}[/tex]hence, the horizontal distance reached by the ball 1 is 158.9 meters
Step 2
as the ball started from the same point at the same initial speed, the only way to make the second ball hits the same point as the first is thworing the second ball at the same angle, it is 51 °
You push a 2.1 kg object on a table with 42N of force. The box then slowly skids to a stop over 2.2 m. What is the force of friction?
If you push a 2.1 kg object on a table with 42N of force. The box then slowly skids to a stop over 2.2 meters, then the force of the friction would be 42 Newtons as per the concept of limiting friction.
What is friction?Friction is a type of force that resists or prevents the relative motion of two physical objects when their surfaces come in contact.
As given in the problem if push a 2.1 kg object on a table with 42N of force. The box then slowly skids to a stop over 2.2 m, then we have to find the force of the friction.
The force of the friction = The limiting friction force
If you apply 42N of force to a 2.1-kilogram item on a table. According to the theory of limiting friction, when the box gently slides to a halt over a distance of 2.2 meters, the force of friction would be 42 Newtons.
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7/21/22, 7:37 AMProblem Set ThreeNotes: Use 9.8 m/s 2 for the acceleration due to gravity. Formust be expressed in m/sLaw calculations, mass must be expressed in kg and velocity.A steady 45 N horizontal force is applied to a 15kg object on a table. The object slides against a friction force of 30 N. Calculate the acceleration of the object in m/s.
Given:
The mass of the object is
[tex]m=15\text{ kg}[/tex]The applied force on the object is
[tex]F=45\text{ N}[/tex]The frictional force on the object is
[tex]f=30\text{ N}[/tex]To find:
The acceleration of the object
Explanation:
The net force on the object is
[tex]\begin{gathered} F_{net}=F-f \\ =45-30 \\ =15\text{ N} \end{gathered}[/tex]The acceleration of the object is,
[tex]\begin{gathered} a=\frac{F_{net}}{m} \\ =\frac{15}{15} \\ =1\text{ m/s}^2 \end{gathered}[/tex]Hence, the acceleration is
[tex]1\text{ m/s}^2[/tex]orce and Motion Unit TestUse the following scenario to answer the question.Taj and Micah chose to go bowling. Taj rolled the ball toward the pins first, knocking them all down.Which of the following is affecting these objects?point)O Gravity is affecting these objects.O An unbalanced force is affecting the objects.O Inertia is affecting these objects.O A balanced force is affecting the objects.
So lets go through all four answer choices.
The easiest to choose is whether gravity is affecting these objects. Assuming that there is some sort of gravity that would pull the pins down, gravity does affect these objects
Second is inertia.
We know that if an object has inertia, it will try to resist moving/coming to rest. In this case, we know that the pins have inertia because the pins fell over, so we know that the pins do have inertia
The last part is whether these objects have an unbalanced or balanced force. If a balanced force did exist, there would need to a force that would equally counteract the force of the bowling ball, which there isn't. Which means there is an unbalanced force affecting these objects.
Given that the user must choose one, the correct answer would be that an unbla
this is a 2 part question2) Two drivers traveling side-by-side at the same speed suddenly see a deer in the road ahead of them and begin braking. Driver 1 stops by locking up his brakes and screeching to a halt; driver 2 stops byapplying her brakes just to the verge of locking, so that the wheels continue to turn until her car comes to a complete stop. (a) All other factors being equal, is the stopping distance of driver 1 greater than,less than, or equal to the stopping distance of driver 2? (b) Choose the best explanation from among thefollowing: 1. Locking up the brakes gives the greatest possible braking force.2. The same tires on thesame road result in the same force of friction.3. Locked-up brakes lead to sliding (kinetic) friction, which is less than rolling (static) friction.
The maximum static friction between two surfaces is greater than the kinetic friction between them.
If the wheels of a car get locked, the surface of the wheel slides through the floor and kinetic friction acts to stop the car.
If the wheels of the car don't get locked, they may turn fast enough to prevent the surface of the wheel from sliding through the floor and static friction acts on the car.
Since the force acting on the car with its wheel locked is less than the force acting on the car with the turning wheels, then, the stopping distance is greater for driver 1 than for diver 2.
Therefore, the answers are:
a) The stopping distance of driver 1 is greater than the stopping distance of driver 2.
b) The best explanation is:
3. Locked-up brakes lead to sliding (kinetic) friction, which is less than rolling (static) friction.
A jet engine applies a force of 300 N horizontally to the right against a 50 kg rocket. The force of air friction 200 N. If the rocket is thrust horizontally 2.0 m, the kinetic energy gained by the rocket is
We will have the following:
[tex](300N)(2m)+(-200N)(2m)=200J[/tex]Then, we from the work-kinetic force theorem we will have that the total kinetic energy gained by the rocket was 200 Joules.
The block of a mass 10.2 kg is sliding at an initial velocity of 3.40 m/s in the positive x-direction. The surface has a coefficient of kinetic friction of 0.153.
m = mass = 10.2 kg
vo = initial velocity = 3.40 m/s
u = coefficient of kinetic friction = 0.153
g= gravity = 9.8m/s^2
a)
Fr = force of kinetic friction = u m g
Fr = 0.153 x 10.2 x 9.8 = -15.30N
b) Block's acceleration
Newton's second law of motion:
F = m*a
a = F/m = -15.30 / 10.2 = -1.5 m/s^2
c) USe the third equation of motion:
2as = vf^2 - vo^2
Where:
Vf= final velocity= 0 m/s
s = displacement
2 * -1.5 * s = 0^2 - 3.40^2
-3s = -11.56
s= -11.56/-3
s= 3.85 m
Please do this step-by-step how do you do it when it’s between
Given:
• Mass of block A = 6.0 kg
,• Mass of block B = 7.0 kg
,• Mass of block C = 13.0 kg
,• Force, F = 13.0 N
Let's find the magnitude of the tension in the rope between B and C.
Let's first find the acceleration.
We have:
[tex]13-T_B+T_B-T_A+T_A=6a+7a+13a[/tex]Thus, we have:
[tex]\begin{gathered} 13=26a \\ \\ a=\frac{13}{26} \\ \\ a=0.5\text{ m/s}^2 \end{gathered}[/tex]To find the tension between blocks B and C, we have the equation:
[tex]\begin{gathered} F-T_B=M_C*a \\ \\ T_B=F-M_c*a \end{gathered}[/tex]Where:
F = 13 N
Mc is the mass of block C = 13 kg
a is the acceleration = 0.5 m/s²
Thus, we have:
[tex]\begin{gathered} T_B=13-13*0.5 \\ \\ T_B=13-6.5 \\ \\ T_B=6.5\text{ N} \end{gathered}[/tex]Therefore, the magnitude of the tension in the rope between blocks B and C is 6.5 N
ANSWER:
6.5 N
Which of the following water molecules have the greatest kinetic energy?Select one:a. Cool water.b. Warm water.c. Boiling water.d. They all have the same kinetic energy.
Since all the molecules in the boiling water will have more energy introduced by heat, then the molecules with the greatest kinetic energy are the ones from the boiling water.
A car initially at rest travels with a uniform acceleration of 8 m / s^2 . Calculate the distance covered by the car in 3 s .
We know that
• The initial velocity is zero because it starts from rest.
,• The acceleration is 8 m/s^2.
,• The time elapsed is 3 seconds.
Use a formula that relates initial velocity, acceleration, time, and distance.
[tex]d=v_0t+\frac{1}{2}at^2[/tex]Use the given magnitudes to find d.
[tex]\begin{gathered} d=0\cdot3\sec +\frac{1}{2}\cdot(8\cdot\frac{m}{s^2})(3\sec )^2 \\ d=4\cdot\frac{m}{s^2}\cdot9s^2 \\ d=36m \end{gathered}[/tex]Therefore, the distance covered is 36 meters.Physics
Hello how to solve this
2.15 mL of water will spill from the beaker when a 400mL glass beaker at room temperature is filled to the brim with cold water.
What is temperature and how come 2 mL of water spills off the beaker?Temperature as studied always is the measure for the degree of hotness or coldness.Here in the question is given a glass beaker of 400 mL which is at room temperature .Now the beaker is warmed up to 30 degree celsius, and then some of amount of water spilled.Change in volume = beta x v1 x change in temperature = 210 x 10^-4 x 400 x ( 30 - 4.4) = 2.15 mL.Hence the amount of water that will spill from the beaker would be 2.15 mL.To know more about temperature visit:
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An airplane traveling at 1008 meters above the ocean at 135 km/h is going to drop a box of supplies to shipwrecked victims below. How many seconds before the plane is directly overhead should the box be dropped?
The horizontal velocity of the airplane is,
[tex]v=135\text{ km/h}[/tex]The height of the airplane is,
[tex]h=1008\text{ m}[/tex]The vertical initial velocity of the box is zero as the airplane is moving in the horizontal direction.
let the time to reach the victim is t.
we can write,
[tex]\begin{gathered} h=\frac{1}{2}gt^2 \\ t=\sqrt[]{\frac{2h}{g}} \end{gathered}[/tex]Substituting the values we get,
[tex]\begin{gathered} t=\sqrt[]{\frac{2\times1008}{9.8}} \\ =14.3\text{ s} \end{gathered}[/tex]Hence the required time is 14.3 s
IBangkok, Thailand, and Lima, Peru, are located at opposite positions of Earth's surface. When a rock is dropped in both cities, observers would describe the motion of either rock with a word that means "down."
Where are the two rocks moving?
Responses
They are moving away from each other.
.
One rock is moving due east and the other is moving due west.
They are moving down, which is the same direction in both cities.
They are moving toward each other.
Answer :dawg you got snaids thats the answer awww man
Explanation:
answer is that of an answer
A circular loop of wire with a diameter of 13.478 cm is in the horizontal plane and carries a current of 1.607 A counterclockwise, as viewed from above. What is the magnetic field, in microTeslas, at the center of the loop?
Given:
The number of the loops, n = 1
The diameter of the loop is d = 2r = 13.478 cm
The current in the loop is I = 1.607 A
To find the magnetic field in micro Tesla
Explanation:
The magnetic field can be calculated by the formula
[tex]B\text{ =}\frac{n\mu_0I}{2r}[/tex]Here, the value of the constant is
[tex]\mu_0=\text{ 12.57}\times10^{-7}\text{ H/m}[/tex]On substituting the values, the magnetic field will be
[tex]\begin{gathered} B=\frac{1\times12.57\times10^{-7}\times1.607}{13.478\times10^{-2}} \\ =1.499\text{ }\times10^{-5}\text{ T} \\ =14.99\times10^{-6}\text{ T} \\ =14.99\text{ }\mu T \end{gathered}[/tex]The magnetic field is 14.99 micro Tesla
S=3-2t+3t^2
What is the instantaneous velocity and it’s acceleration at t=3s
At what time is the particle at rest
Answer:
Explanation:
Given:
X(t) = 3 - 2*t + 3*t²
t = 3 s
_______________
V(t) - ?
a(t) - ?
Speed is the first derivative of the coordinate, acceleration is the second.
1)
V(t) = X' = (3 - 2*t + 3*t²)' = 0 - 2 +6*t = 6*t - 2
V(3) = 6*3 - 2 = 16 m/s
2)
a(t) = X'' = V' = (6*t - 2)' = 6 m/s²
a(3) = 6 m/s²
3)
The body will stop (V = 0 ) in (t) seconds:
V(t) = 6*t - 2
0 = 6*t - 2
6*t = 2
t = 2/6 = 1/3 ≈ 0,33 s
why free-fall acceleration can be regarded as a constant for objects falling within a few hundred miles of Earth’s surface.
An archerfish squirts water with a speed 2 m/s at an angle 50 degrees above the horizontal, and aims for a beetle on a leaf 3cm above the water surface. (A) At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time? (B) How much time does the beetle have to react?
A ) The horizontal distance from the beetle, the archerfish should fire if it is to hit its target in the least time = 1.19 m
B ) The time beetle have to react = 0.93 s
T = ( [tex]u_{y}[/tex] + √ [tex]u_{y}[/tex]² - 2 g H ) / g
T = Total time taken
g = Acceleration due to gravity
H = Height above the ground
[tex]u_{y}[/tex] = Y-component of initial velocity
u = 2 m / s
θ = 50°
H = 3 cm
[tex]u_{y}[/tex] = u sin θ
[tex]u_{y}[/tex] = 2 * sin 50°
[tex]u_{y}[/tex] = 1.54 m / s
T = ( 1.54 + √ 1.54² - ( 2 * 9.8 * 3 ) ) / 9.8
T = ( 1.54 + √ 56.42 ) / 9.8
T = 9.1 / 9.8
T = 0.93 s
R = [tex]u_{x}[/tex] T
[tex]u_{x}[/tex] = u cos θ
[tex]u_{x}[/tex] = 2 * cos 50°
[tex]u_{x}[/tex] = 1.28 m / s
R = 1.28 * 0.93
R = 1.19 m
Therefore,
A ) The horizontal distance from the beetle, the archerfish should fire if it is to hit its target in the least time = 1.19 m
B ) The time beetle have to react = 0.93 s
To know more about Projectile launched from a height
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If an 800 kg roller coaster is at the top of its 50 m high track, it will have a potential energy 392,000 and a kinetic energy of 0J. This means the total mechanical energy is 392,000J. If the cart drops down to a new height of 10m, how much energy does the cart have now?
ANSWER:
313600 J
STEP-BY-STEP EXPLANATION:
We have that the gravitational potential energy is given by the following equation:
[tex]E_p=m\cdot g\cdot h[/tex]We substitute and calculate the potential energy, knowing that g is the acceleration of gravity and is equal to 9.8 m/s^2:
[tex]\begin{gathered} E_p=800\cdot9.8\cdot10 \\ E_p=78400\text{ J} \end{gathered}[/tex]We know that the total energy is 392,000 joules, so the energy it now carries would be the total minus the calculated potential energy:
[tex]\begin{gathered} E_k=392000-78400 \\ E_k=313600\text{ J} \end{gathered}[/tex]The energy carried by the cart is 313600 J