Calculate the horizontal distance travelled by a ball throw with a velcoity 20 sqrt 2 ms^(-1) without hitting the ceiling of an anditorium of heith 20 m. Use g= 10 ms^(-2). =(20√2)2sin2×45∘10=9800×1)10=80m .
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What is the name of the invisible line that runs
down the center of the axial region?
Answer:
An axis is an invisible line around which an object rotates, or spins. The points where an axis intersects with an object's surface are the object's North and South Poles.
Explanation:
The Earth's axis is represented by the red line. The white circle represents axial precission, the slow "wobble" of the axis.
A 1030 kg car has four 12.0 kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles
Answer:
The required fraction is 0.023.
Explanation:
Given that
Mass of a car, m = 1030 kg
Mass of 4 wheels = 12 kg
We need to find the fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles.
The rotational kinetic energy due to four wheel is
[tex]=4\times \dfrac{1}{2}I\omega^2\\\\=4\times \dfrac{1}{2}\times \dfrac{1}{2}mR^2(\dfrac{v}{R})^2\\\\=mv^2[/tex]
Linear kinetic Energy of the car is:
[tex]=\dfrac{1}{2}mv^2\\\\=\dfrac{1}{2}\times Mv^2[/tex]
Fraction,
[tex]f=\dfrac{mv^2}{\dfrac{1}{2}Mv^2}\\\\f=\dfrac{m}{\dfrac{1}{2}M}\\\\f=\dfrac{12}{\dfrac{1}{2}\times 1030}\\\\=0.023[/tex]
So, the required fraction is 0.023.
1) Consider an electric power transmission line that carries a constant electric current of i = 500 A. The cylindrical copper cable used to transmit this current has a diameter o = 2.00 cm and a length L = 150 km. If there are 8.43x10^28 free electrons per cubic meter (m^3 ) in the cable, calculate how long it would take for an electron to cross the entire length of the transmitter line.
Answer:
t = 1.27 x 10⁹ s
Explanation:
First, we will find the volume of the wire:
Volume = V = AL
where,
A = Cross-sectional area of wire = πr² = π(1 cm)² = π(0.01 m)² = 3.14 x 10⁻⁴ m²
L = Length of wire = 150 km = 150000 m
Therefore,
V = 47.12 m³
Now, we will find the number of electrons in the wire:
No. of electrons = n = (Electrons per unit Volume)(V)
n = (8.43 x 10²⁸ electrons/m³)(47.12 m³)
n = 3.97 x 10³⁰ electrons
Now, we will use the formula of current to find out the time taken by each electron to cross the wire:
[tex]I =\frac{q}{t}[/tex]
where,
t = time = ?
I = current = 500 A
q = total charge = (n)(chareg on one electron)
q = (3.97 x 10³⁰ electrons)(1.6 x 10⁻¹⁹ C/electron)
q = 6.36 x 10¹¹ C
[tex]500\ A = \frac{6.36\ x\ 10^{11}\ C}{t}\\\\t = \frac{6.36\ x\ 10^{11}\ C}{500\ A}[/tex]
Therefore,
t = 1.27 x 10⁹ s
3. The figure below shows the motion of a car. It starts from the origin, O travels 8m
towards the east and then 12m towards the west.
D
8m.
X
X-8
12m.w
()What is the net displacement D from the origin to the final position?
(ii) What is the total distance travelled by the car?
Answer:
i. -4m
ii. 20m
Explanation:
The car travels 8m to the east, then travels 12m to the west which is the opposite of the east. Going west, the car travels 8m back to the origin point and then another 4m due west to make 12m. The displacement from the origin point is -4 (the negative sign shows the direction because displacement is a vector quantity)
Total distance = 8m going east + 8m back to origin + 4m west = 20m
A 6.90 kg block is at rest on a horizontal floor. If you push horizontally on the 6.90 kg block with a force of 12.0 N. It just
starts to move.
What is the coefficient of static friction?
Numeric Response
[tex]\mu = 0.177[/tex]
Explanation:
Let's look at the forces on the two axes:
[tex]x:\:\:\:F - f_n = F - \mu N = 0\:\:\:\:\:\;(1)[/tex]
[tex]y:\:\:\:N - mg = 0\:\:\:\:\:\:\:\:\:(2)[/tex]
Substituting (2) into (1) and solving for [tex]\mu[/tex], we get
[tex]F = \mu mg[/tex]
[tex]\mu = \dfrac{F}{mg} = \dfrac{12.0\:\text{N}}{(6.9\:\text{kg})(9.8\:\text{m/s}^2)} = 0.177[/tex]
1. A turtle and a rabbit are to have a race. The turtle’s average speed is 0.9 m/s. The rabbit’s average speed is 9 m/s. The distance from the starting line to the finish line is 1500 m. The rabbit decides to let the turtle run before he starts running to give the turtle a head start. If the rabbit started to run 30 minutes after the turtle started, can he win the race? Explain.
Answer:no
Explanation:because 0.9*(30*60)=0.9*1800=1620
The turtle has already won the race
Yes rabbit will win the race will distance in 3.2 hours and turtle will cover in 27 hours
What will be the speed of the rabbit and the turtle?It is given
[tex]V_{t} = 0.9 \frac{m}{s}[/tex]
[tex]V_{r} = 9 \frac{m}{s}[/tex]
[tex]D=1500 m[/tex]
Time taken by turtle
[tex]T= \dfrac{D}{V_{t} }=\dfrac{1500}{0.9_{} }[/tex]
[tex]T=1666 minutes= 27 hours[/tex]
Time taken by rabbit
[tex]T= \dfrac{D}{V_{r} }=\dfrac{1500}{9_{} }[/tex]
[tex]T=166 minutes[/tex]
since rabbit started 30 minutes after turtle then
[tex]T= 136+30=196 minutes[/tex]
[tex]T= 3.2 hours[/tex]
Hence Yes rabbit will win the race will distance in 3.2 hours and turtle will cover in 27 hours
To know more about average velocity follow
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An ideal parallel plate capacitor with a cross-sectional area of 0.4 cm2 contains a dielectric with a dielectric constant of 4 and a dielectric strength of 2 x 108 V/m. The separation between the plates of the capacitor is 5 mm. What is the maximum electric charge (in nC) that can be stored in the capacitor before dielectric breakdown
Answer: [tex]283.2\times 10^{-9}\ nC[/tex]
Explanation:
Given
Cross-sectional area [tex]A=0.4\ cm^2[/tex]
Dielectric constant [tex]k=4[/tex]
Dielectric strength [tex]E=2\times 10^8\ V/m[/tex]
Distance between capacitors [tex]d=5\ mm[/tex]
Maximum charge that can be stored before dielectric breakdown is given by
[tex]\Rightarrow Q=CV\\\\\Rightarrow Q=\dfrac{k\epsilon_oA}{d}\cdot (Ed)\quad\quad [V=E\cdot d]\\\\\Rightarrow Q=k\epsilon_oAE\\\\\Rightarrow Q=4\times 8.85\times 10^{-12}\times 0.4\times 10^{-4}\times 2\times 10^8\\\\\Rightarrow Q=28.32\times 10^{-8}\\\\\Rightarrow Q=283.2\times 10^{-9}\ nC[/tex]
Answer:
The maximum charge is 7.08 x 10^-8 C.
Explanation:
Area, A = 0.4 cm^2
K = 4
Electric field, E = 2 x 10^8 V/m
separation, d = 5 mm = 0.005 m
Let the capacitance is C and the charge is q.
[tex]q = CV\\\\q=\frac{\varepsilon o A}{d}\times E d\\\\q = \varepsilon o A E\\\\q = 8.85\times 10^{-12}\times0.4\times 10^{-4}\times 2\times 10^8\\\\q = 7.08\times 10^{-8}C[/tex]
Your forehead can withstand a force of about 6.0 kN before it fractures. Your cheekbone on the other hand can only handle about 1.3 kN before fracturing. If a 140 g baseball hits your head at 30.0 m/s and stops in 0.00150 s,
Required:
a. What is the magnitude of the ball's acceleration?
b. What is the magnitude of the force that stops the baseball?
c. What force does the baseball apply to your head? Explain?
d. Are you in danger of a fracture if the ball hits you in the forehead?
Answer:
Explanation:
a)
Final velocity v = 0 ; initial velocity u = 30 m/s , time t = .0015 s
v = u + a t
0 = 30 m/s + a x .0015 s
a = - 30 / .0015
= - 20000 m / s²
b )
Magnitude of force = m x a
= .140 kg x 20,000 m / s²
= 2800 N = 2.8 kN.
c )
The force applied by baseball = 2.8 kN .
d )
Since ball can withstand a force of 1.3 kN so it will break if 2.8 kN force acts on it . SO, head will fracture.
Calculate the minimum area moment of inertia for a rectangular cross-section with side lengths 6 cm and 4 cm.
52 cm4
72 cm4
32 cm4
24 cm4
2 cm4
Answer:
Minimum Area of rectangle = 24 centimeter²
Explanation:
Given:
Length of rectangle = 6 centimeter
Width of rectangle = 4 centimeter
Find:
Minimum Area of rectangle
Computation:
Minimum Area of rectangle = Length of rectangle x Width of rectangle
Minimum Area of rectangle = 6 x 4
Minimum Area of rectangle = 24 centimeter²
An evacuated tube uses an accelerating voltage of 55 kV to accelerate electrons to hit a copper plate and produce x rays. Non-relativistically, what would be the maximum speed of these electrons?
Answer:
v = 4.4 x 10⁷ m/s
Explanation:
The kinetic energy of the electrons will be equal to the energy supplied by the electric voltage:
Kinetic Energy = Electric Energy
[tex]\frac{1}{2}mv^2 = eV[/tex]
where,
m = mass of electron = 9.1 x 10⁻³¹ kg
v = speed of electron = ?
e = charge on electron = 1.6 x 10⁻¹⁹ C
V =Voltage = 55 kV = 55000 V
Therefore,
[tex]\frac{1}{2}(9.1\ x\ 10^{-31}\ kg)(v)^2 = (1.6\ x\ 10^{-19}\ C)(55000\ V)\\\\v^2 = \frac{(2)(8.8\ x\ 10^{-16}\ J)}{9.1\ x\ 10^{-31}\ kg}\\\\v = \sqrt{19.34\ x\ 10^{14}\ m^2/s^2}[/tex]
v = 4.4 x 10⁷ m/s
Electric field is always perpendicular to the equipotential surface.
a. True
b. False
Answer:
a: true.
Explanation:
We can define an equipotential surface as a surface where the potential at any point of the surface is constant.
For example, for a punctual charge, the equipotential surfaces are spheres centered at the punctual charge.
Or in the case of an infinite plane of charge, the equipotential surfaces will be planes parallel to our plane of charge.
Now we want to see if the electric field is always perpendicular to these equipotential surfaces.
You can see that in the two previous examples this is true, but let's see for a general case.
Now suppose that you have a given field, and you have a test charge in one equipotential surface.
So, now we can move the charge along the equipotential surface because the potential in the surface is constant, then the potential energy of the charge does not change. And because there is no potential change, then there is no work done by the electric field as the charge moves along the equipotential surface.
But the particle is moving and the electric field is acting on the particle, so the only way that the work can be zero is if the force (the one generated by the electric field, which is parallel to the electric field) and the direction of motion are perpendiculars.
Then we can conclude that the electric field will be always perpendicular to the equipotential surfaces.
The correct option is a.
A bird has a kinetic energy of 3 J and a potential energy of 25 J. What is the mechanical energy of the bird?
Answer:
28 j
Explanation:
because when you add you get 28
3. Three blocks of masses m, 2m and 3m are suspended from the ceiling using ropes as shown in diagram. Which of the following correctly describes the tension in the three rope segments?
a. T1< T2 < T3
b. T1< T2 = T3
c. T1 = T2 = T3
d. T1> T2 > T3
please help.show how and which?
see attachment for more detail.
Option d (T₁ > T₂ > T₃) correctly describes the tension in the three rope system.
Let's evaluate each tension.
Case T₃.
[tex] T_{3} - W_{3} = 0 [/tex]
For the system to be in equilibrium, the algebraic sum of the tension force (T) and the weight (W) must be equal to zero. The minus sign of W is because it is in the opposite direction of T.
[tex] T_{3} = W_{3} [/tex]
Since W₃ = mg, where m is for mass and g is for the acceleration due to gravity, we have:
[tex] T_{3} = W_{3} = mg [/tex] (1) Case T₂.
[tex] T_{2} - (T_{3} + W_{2}) = 0 [/tex]
[tex] T_{2} = T_{3} + W_{2} [/tex] (2)
By entering W₂ = 2mg and equation (1) into eq (2) we have:
[tex] T_{2} = T_{3} + W_{2} = mg + 2mg = 3mg [/tex]
Case T₁.
[tex] T_{1} - (T_{2} + W_{1}) = 0 [/tex]
[tex] T_{1} = T_{2} + W_{1} [/tex] (3)
Knowing that W₁ = 3mg and T₂ = 3mg, eq (3) is:
[tex] T_{1} = 3mg + 3mg = 6mg [/tex]
Therefore, the correct option is d: T₁ > T₂ > T₃.
Learn more about tension and weight forces here: https://brainly.com/question/18770200?referrer=searchResults
I hope it helps you!
Correct answer: D. [tex]T_{1} > T_{2} > T_{3}[/tex]
First, we must construct the Equations of Equilibrium for each mass based on Newton's Laws of Motion, then we solve the resulting system for every Tension force:
Mass m:
[tex]\Sigma F = T_{3}-m\cdot g = 0[/tex] (1)
Mass 2m:
[tex]\Sigma F = T_{2}-2\cdot m \cdot g -T_{3} = 0[/tex] (2)
Mass 3m:
[tex]\Sigma F = T_{1}-3\cdot m\cdot g - T_{2} = 0[/tex] (3)
The solution of this system is: [tex]T_{3} = m\cdot g[/tex], [tex]T_{2} = 3\cdot m\cdot g[/tex] and [tex]T_{1} = 6\cdot m\cdot g[/tex], which means that [tex]T_{1} > T_{2} > T_{3}[/tex]. (Correct answer: D.)
What is the magnitude of force required to accelerate a car of mass 1.7 * 10 ^ 3 kg by 4.75 m/s
What is the magnitude of force required to accelerate a car of mass 1.7 × 10³ kg by 4.75 m/s²
Answer:
F = 8.075 N
Explanation:
Formula for force is;
F = ma
Where;
m is mass
a is acceleration
F = 1.7 × 10³ × 4.75
F = 8.075 N
find the exit angle relative to the horizontal in an isosceles triangle with 36 °
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If you stand next to a wall on a frictionless skateboard and push the wall with a force of 44 N , how hard does the wall push on you
Answer:
44 N
Explanation:
Given that,
If you stand next to a wall on a frictionless skateboard and push the wall with a force of 44 N, then we need to find the force the wall push on you.
It is based on Newton's third law of motion which states that for an action there is an equal and opposite reaction. If the you push the wall with a force of 44 N, the wall push on you is 44 N also as it is based on Newton's third law of motion.
Two point charges, the first with a charge of 4.47 x 10-6 C and the second with a charge of 1.86 x 10-6 C, are separated by 17.4 mm. What is the magnitude of the electrostatic force experienced by charge 2
Answer: [tex]247.12\ N[/tex]
Explanation:
Given
Magnitude of the charges
[tex]q_1=4.47\times 10^{-6}\ C[/tex]
[tex]q_2=1.86\times 10^{-6}\ C[/tex]
Distance between them [tex]d=17.4\ mm[/tex]
As both charges are of same sign, they must repel each other
Force experienced by second charge is
[tex]\Rightarrow F_{21}=\dfrac{kq_1q_2}{d^2}\\\\\Rightarrow F_{21}=\dfrac{9\times 10^9\times 4.47\times 10^{-6}\times 1.86\times 10^{-6}}{(17.4\times 10^{-3})^2}\\\\\Rightarrow F_{21}=\dfrac{74.82\times 10^{-3}}{302.76\times 10^{-6}}\\\\\Rightarrow F_{21}=0.2471\times 10^3\\\Rightarrow F_{21}=247.12\ N[/tex]
Thus, charge 2 experience a force of [tex]247.12\ N[/tex]
Answer:
The force between the two charges is 247.15 N.
Explanation:
Charge, q = 4.47 x 10^-6 C
charge, q' = 1.86 x 10^-6 C
distance, d = 17.4 mm
Let the force is F.
The force is given by the Coulomb's law:
[tex]F = \frac{K q q'}{r^2}\\\\F =\frac{9\times 10^9\times 4.47\times 10^{-6}\times1.86\times 10^{-6}}{(17.4\times 10^{-3})^2}\\\\F = 247.15 N[/tex]
Một ống dây điện thẳng dài có lõi sắt, tiết diện ngang của ống S = 20 cm2
, chiều dài
1 m, hệ số tự cảm L = 0,44 H. Cường độ từ trường trong ống dây là H = 0,8.103 A/m. Từ
thông gửi qua tiết diện ngang của ống bằng
3
0
1,6.10 Wb
. Cường độ dòng điện chạy
qua ống dây là
Answer:
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Use the image of Potential vs. position in 1D to match each scenario with subsequent motion.
A (+) charge is placed at A and can only move in the x-direction. When it is released, what will happen?
Correct answer:
It will move to the left
A (-) charge is placed at A and can only move in the x-direction. When it is released, what will happen?
Incorrect answer:
It remains at where it was placed.
A (-) charge is placed at B and can only move in the x-direction. When it is released, what will happen?
Correct answer:
It remains at where it was placed.
A (+) charge is placed at B and pushed slightly to the right; it can only move in the x-direction. What will happen?
Correct answer:
It will move to the right.
A (-) charge is placed at B and pushed slightly to the right; it can only move in the x-direction. What will happen?
Correct answer:
It will oscillate around B
Continuing the previous exercise, determine the nature of work (for each force listed, not net force), KE and PE for:
1. A + charge moving away from a + charge, from rest, under field force only.
KE
[ Select ]
0 PE
[ Select ]
0 Work
[ Select ]
0
2. A + charge moving away from a + charge, from rest, with applied force slowing it.
Work is
[ Select ]
0
3. A - charge moving toward a + charge under field force only.
KE
[ Select ]
0 PE
[ Select ]
0 Work is
[ Select ]
0
4. A - charge moving toward a + charge with applied force slowing it.
Work is
[ Select ]
0
5. An applied force pulls a negative charge away from a positive charge.
Work is
[ Select ]
6. An applied force pushes 2 like charges together.
Work is
[ Select ]
Answer:
incorporators and it is the one you for the delay to get it for now that the new to me to the same as last week to week in my opinion of your
What is inertia of motion?
Explanation:
Inertia of motion
It is also known as Newton's first law of motion.
It states that,
An object remains in a state of rest or of uniform motion in a straight line unless compelled to change its state by an applied external force.
8. A boat moving initially at 6.5 km hr due southwest crosses a river that is flowing due south at 3 km hr.
What is the magnitude and direction of the boat relative to the ground? If the river is 1.5 mi wide how long
does it take the boat to cross?
Answer:
a) v = 8,878 km / h, θ’= 238.8º, b) t = 1890.9 s
Explanation:
a) In this exercise we must find the resulting speed of the boat.
Let's use trigonometry to break down the speed of the boat (v1)
cos 225 = v₁ₓ / v₁
sin 225 = v_{1y} / v₁
v₁ₓ = v₁ soc 225
v_{1y} = v₁ sin 225
v₁ₓ = 6.5 cos 225 = -4.596 km / h
v_{1y} = 6.5 sin 225 = -4.596 km / h
to find the velocity we add each component
vₓ = v₁ₓ
vₓ = - 4,596 km / h
v_y = v_{1y} + v₂
v_y = -4.596 - 3
v_y = - 7,596 km / h
Now let's compose the speed
Let's use the Pythagorean theorem for the module
v = [tex]\sqrt{v_x^2 + v_y^2 }[/tex]
v = Ra 4.596² + 7.596²
v = 8,878 km / h
Let's use trigonometry for the direction
tan θ = v_y / vₓ
θ = tan⁻¹ v_y / vₓ
θ = tan⁻¹ ( [tex]\frac{-7.596}{ -4.596}[/tex] )
θ = 58.8º
measured from the positive side of the x-axis
θ'= 180 + 58.8
θ’= 238.8º
b) Let's reduce the river width to the SI system
x = 1.5 miles (1,609 km / 1 mile) = 2,414 km
to cross the river the speed is on the x axis which is the width of the river
v = x / t
t = x / v
t = 2.414 /4.596
t = 0.525 h
let's reduce to the SI system
t = 0.525 h (3600 s / 1h)
t = 1890.9 s
How does this work?
Why won't it fall?
Why can't you continue building the tower forever?
From what I've been told, if the center of mass leaves it's support area, the object falls.
But the object on the tops center of mass is certainly outside of its support area (the object at the bottom)
Please explain! Thank you in advance. : )
Answer with explanation:
*Pre-condition: The mass of all blocks are evenly distributed.
As you add more and more blocks, the center of mass of the system changes.
Let the first block be the support. The maximum distance that can be unsupported (hung over) by the second block is equal to half the length of second block.
Why?
Let's take a look at our formula for torque. Torque, [tex]\tau[/tex], is given by:
[tex]\tau=rF\sin \theta[/tex], where [tex]r[/tex] is radius, [tex]F[/tex] is force, and [tex]\theta[/tex] is the angle between the radius and level arm.
[tex]\sin \theta[/tex] is used to calculate the relevant component of a force producing torque. In this case, the only force acting on the object is the force of gravity. Therefore, [tex]\theta =90^{\circ}[/tex] and recall [tex]\sin 90^{\circ}=1[/tex].
Conceptually, it's more important to look at the [tex]r[/tex] term here. From our formula, we can see that if [tex]r=0[/tex], there is no torque.
The point of pivot will be at the center of mass. Here's the important part:
As long as the point of pivot is supported, [tex]r[/tex] will remain zero and no torque will be created from the force of gravity. As you keep stacking blocks, as long as the center of mass of the entire system remains supported from your first support, the tower will not fall.
In the given picture shown, that first block will be your support.
The 6 blocks on top of that first block form a center of mass that is still on that first block, thus allowing the tower to remain standing.
The position of the image obtained by convex lens when object is kept beyond 2F1(F: principal focus of the convex lens)
A. between F2 and 2F2
B. at 2F2
C. beyond 2F2
D. at infinity
Answer:
Between F2 and 2F2
Explanation:
Diagram attached from Teachoo.
Link to website if you need to refer
https://www.teachoo.com/10838/3118/Convex-Lens---Ray-diagram/category/Concepts/
A stone dropped from the top of a 80m high building strikes the ground at 40 m/s after falling for 4 seconds. The stone's potential energy with respect to the ground is equal to its kinetic energy … (use g = 10 m/s 2)
A) at the moment of impact.
B) 2 seconds after the stone is released.
C) after the stone has fallen 40 m.
D) when the stone is moving at 20 m/s.
At the moment of impact both Kinetic Energy and Potential Energy should be 0, right? So it can't be A), right? Or is this wrong? Is it indeed A)? Please show work and explain it well.
Answer:
Explanation:
The answer is C because the building is 80 meters high. Before the stone is dropped, it has ONLY potential energy since kinetic energy involves velocity and a still stone has no velocity. At impact, there is no potential energy because potential energy involves the height of the stone relative to the ground and a stone ON the ground has no height; here there is ONLY kinetic.
From the First Law of Thermodynamics, we know that energy cannot be created or destroyed, it can only change form. Therefore, that means that at the halfway point of 40 meters, half of the stone's potential energy has been lost, and it has been lost to kinetic energy. Here, at 40 meters, there is an equality between PE and KE. It only last for however long the stone is AT 40 meters, which is probably a millisecond of time, but that's where they are equal.
When placed 1.18 m apart, the force each exerts on the other is 11.2 N and is repulsive. What is the charge on each
Answer:
[tex]q=41.62\ \mu C[/tex]
Explanation:
Given that,
Force between two objects, F = 11.2 N
Distance between objects, d = 1.18 m
We need to find the charge on each objects. The force between charges is as follows :
[tex]F=\dfrac{kq^2}{r^2}\\\\q=\sqrt{\dfrac{Fr^2}{k}} \\\\q=\sqrt{\dfrac{11.2\times (1.18)^2}{9\times 10^9}} \\\\q=41.62\ \mu C[/tex]
So, the charge on each sphere is [tex]41.62\ \mu C[/tex].
A stone is dropped from a bridge. It takes 4s to reach the water below. How high is the bridge above the water?
Answer:
height is 78.4m
Explanation:
h=u.t + 0.5.g.t^2
= 0 + 0.5x9.8x4^2
= 78.4m
At what angle torque is half of the max
A 1,071.628 N painter needs to climb d=1.926 m up a ladder (measured along its length from the point where the ladder contacting the ground), without the ladder slipping. The uniform ladder is 12.014 m long and weighs 250 N. It rests with one end on the ground and the other end against a perfectly smooth vertical wall. The ladder rises at an angle of theta=51.96 degrees above the horizontal floor. What is friction force in unit of N that the floor must exert on the ladder? Use g = 10 m/s2 if you need to .
The frictional force in unit of N that the floor must exert on the ladder is approximately 232.216 N
The known values are;
The weight of the painter = 1,071.628 N
The height to which the painter needs to climb along the ladder = 1.926 m
The length of the ladder = 12.014 m
The weight of the ladder = 250 N
The points where one of the ladder's ends is resting = On the ground
The points where the other end of the ladder is resting = A perfectly smooth wall
The angle with which the ladder rises above the horizontal floor = 51.96°
The acceleration due to gravity, g ≈ 10 m/s²
The unknown values include;
The friction force that the floor must exert on the ladder
The strategy to be used;
At equilibrium, the sum of moments about a point is zero
Finding the moments about the point of contact where the ladder rests on the wall, P, is given as follows;
At equilibrium, the sum of clockwise, [tex]M_{CW}[/tex], moment about P = The sum of the counterclockwise, [tex]M_{CCW}[/tex]moment about P
[tex]\mathbf{M_{CCW}}[/tex] = (12.014 - 1.926) × cos(51.96°) × 1,071.628 + (12.014/2) × cos(51.96°) × 250
[tex]\mathbf{M_{CW}}[/tex] = 12.014 × cos(51.96°) × [tex]\mathbf{F_N}[/tex]
Where;
[tex]\mathbf{F_N}[/tex] = The normal reaction of the of the ground on the end of the ladder that rests on the floor
[tex]\mathbf{M_{CCW}}[/tex] = [tex]\mathbf{M_{CW}}[/tex]
∴ (12.014 - 1.926) × cos(51.96°) × 1,071.628 + (12.014/2) × cos(51.96°) × 250 = 12.014 × cos(51.96°) × [tex]F_N[/tex]
We get;
6,665.3068846 N·m = 7.40316448688 m × [tex]F_N[/tex]
[tex]\mathbf{F_N}[/tex] = 6,665.3068846 N·m/(7.40316448688 m) = 900.332135 N
The normal reaction of the floor on the ladder, [tex]\mathbf{F_N}[/tex] = 900.332135 N
Taking moment about the point the ladder rests on the floor, R, gives;
[tex]M_{CCW}[/tex] = 12.014 × sin(51.96°) × [tex]F_W[/tex]
Where;
[tex]\mathbf{F_W}[/tex] = The normal reaction at the wall
[tex]M_{CW}[/tex] = 1.926 × cos(51.96°) × 1,071.628 + (12.014/2) × cos(51.96°) × 250
At equilibrium, we have, [tex]M_{CCW}[/tex] = [tex]M_{CW}[/tex]
Therefore;
12.014 × sin(51.96°) × [tex]F_W[/tex] = 1.926 × cos(51.96°) × 1,071.628 + (12.014/2) × cos(51.96°) × 250
9.46199511627 m × [tex]F_W[/tex] = 2,197.22861125 N·m
[tex]F_W[/tex] = 2,197.22861125 N·m/(9.46199511627 m)
The reaction of the wall, [tex]\mathbf{F_W}[/tex] = 232.216206 N
We note that also at equilibrium, the sum horizontal forces = 0
The horizontal forces acting on the ladder = The normal reaction on the, [tex]F_W[/tex] wall and the friction force on the ground, [tex]\mathbf{F_f}[/tex]
∴ At equilibrium; [tex]\mathbf{F_W}[/tex] + [tex]\mathbf{F_f}[/tex] = 0
[tex]\mathbf{F_f}[/tex] = -[tex]\mathbf{F_W}[/tex]
[tex]\mathbf{F_W}[/tex] = 232.216206 N
Therefore;
The frictional force in unit of N that the floor must exert on the ladder, [tex]\mathbf{F_f}[/tex] = 232.216206 N ≈ 232.216 N.
(The coefficient of friction, μ = [tex]\mathbf{F_N}[/tex]/[tex]\mathbf{F_W}[/tex] = 900.332135/232.216206 ≈ 3.877).
Learn more about the force of friction here;
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Why must scientists be careful when studying
nanotechnology?
Answer:
When studying nanotechnology, scientists must be aware that their ideas may not work out. Their work could be very time consuming and cost a lot of money. Finally, scientists do not yet know all of the effects of nanotechnology on human health.
Hope it helps u:)
the momentum of a spring coil when the external compressing force is removed b the difference between the final momentum and the initial momentum of the object c the backward momentum felt by an object or person exerting force on another object d the difference between the total momentum of the system after impact and the total momentum of the system before impact
Answer:
the correct one is b
the difference between the final moment and the initial moment
Explanation:
The momentum is related to the moment
I = ΔP
∫ F dt = p_f - p₀
where p_f and p₀ are the final and initial moments, respectively
When checking the different answers, the correct one is b
the difference between the final moment and the initial moment
