A 15 m uniform ladder weighing 500 N rests against a frictionless wall. The ladder makes a 60° angle with horizontal. (a) Find the horizontal and vertical forces that the earth exerts on the base of the ladder when an 800 N firefighter is 4 m from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is 9 m up, what is the coefficient of static friction between ladder and ground?
Answers
Answer:
a) F₁ = 267.3 N, N₁ = 1300 N, b) μ = 0.324
Explanation:
For this exercise we use the rotational equilibrium condition, we have a reference system is the floor and the anticlockwise rotations as positive, in the adjoint we can see a diagram of the forces
let's use subscript 1 for the ladder and 2 for the firefighter
∑ τ = 0
-W₁ x₁ - W₂ x₂ + N₁ y = 0
N₁ = [tex]\frac{W_1 x_1 + W_2 x_2}{y}[/tex] (1)
the center of mass of the ladder is at its geometric center,
d = L / 2 = 15/2 = 7.5 m
cos 60 = x₁ / d₁
x₁ = d₁ cos 60
x₁ = 7.5 cos 60
x₁ = 3.75 m
for the firefighter d₂ = 4 m
cos 60 = x₂ / d₂
x₂ = d₂ cos 60
x₂ = 4 cos 60 = 2 m
for the fulcrum d₃ = 15 m
sin 60 = y / d₃
y = d₃ sin 60
y = 15 sin 60
y = 13 m
we look for the Normal by substituting in equation 1
N₂ = [tex]\frac{500 \ 3.75 \ + 800 \ 2}{13}[/tex]
N₂ = 267.3 N
now let's use the translational equilibrium relations
X axis
F₁ - N₂ = 0
F₁ = N₂
F₁ = 267.3 N
Axis y
N₁ - W₁ -W₂ = 0
N₁ = W₁ + W₂
N₁ = 500 + 800
N₁ = 1300 N
b) for this case change the firefighter's distance d₂ = 9 m
x₂ = 9 cos 60
x₂ = 4.5 m
we substitute in 1
N₂ = \frac{500 \ 3.75 \ + 800 \ 4.5}{13}
N₂ = 421.15 N
of the translational equilibrium equation on the x-axis
fr = F₁ = N₂
fr = 421.15 N
friction force has the expression
fr = μ N
in this case the reaction of the Earth to the support of the ladder is N1 = 1300N
μ = fr / N₁
μ = 421.15 / 1300
μ = 0.324
Related Questions
please help me out with these !! 50 points would greatly appreciate it.
Answers
Answer:
Its nymber 2
Explanation:
A wheelbarrow is pushed 10 meters with a force of 75 N for 30 seconds. What is the work done?
How much power is needed?
Answers
Power= work done/ time taken.
Work done = 75N x 10m
= 750Nm/ 750J( Joules)* joules is the SI unit of work.
Power is the rate at which work is done. Suppose two men were carrying a heavy box, man A has a force of 10N , man B has a force of 10N and both carries the box of a distance 3m. Both have done the same work. But if suppose man A takes 2 seconds to carry the box while man B takes 3 seconds, their power needed are different.
Man A , power= 30J/ 2s which is 15 joules per second ( SI unit of power is “watts”)
Man B, power= 30J/ 3s which is 10 joules per second. MAN A HAS MORE POWER.
so, the work done for the wheelbarrow is 750J, divide it by the time taken( 30 seconds) 750J/30s= 25 J/s. <— this is the power needed.
A ball is dropped from a building taking 3sec to fall to the ground. Calculate:
Speed when falling to the ground
The height of the building
Answers
Answer:
Vf = 29.4 m/s
h = 44.1 m
Explanation:
Data:
Initial Velocity (Vo) = 0 m/sGravity (g) = 9.8 m/s²Time (t) = 3 sFinal Velocity (Vf) = ?Height (h) = ?==================================================================
Final Velocity
Use formula:
Vf = g * tReplace:
Vf = 9.8 m/s² * 3sMultiply:
Vf = 29.4 m/s==================================================================
Height
Use formula:
[tex]\boxed{h=\frac{g*(t)^{2}}{2}}[/tex]Replace:
[tex]\boxed{h=\frac{9.8\frac{m}{s^{2}}*(3s)^{2}}{2}}[/tex]Multiply time squared:
[tex]\boxed{h=\frac{9.8\frac{m}{s^{2}}*9s^{2}}{2}}[/tex]Simplify the s², and multiply in the numerator:
[tex]\boxed{h=\frac{88.2m}{2}}[/tex]It divides:
[tex]\boxed{h=44.1\ m}[/tex]What is the velocity when falling to the ground?
The final velocity is 29.4 meters per seconds.
How high is the building?
The height of the building is 44.1 meters.
what is a Lever?
what is wedge
what is a inclined Plane/screw
what is a wheel and axle
what is a Pulley?
Answers
Wedge: a tool used to go in between object to put them in place
Incline plane : a ramp it’s used to help rise heavy things
Pulley: it’s a wheel that supports movement and change of direction
Answer:lever
Explanation:
1. In calculating the work W necessary to stretch a spring from its natural length of 8 centimeters to a length of 12 centimeters, we need some more information about the spring. There are two distinct kinds of information, each of which separately would provide the necessary assistance so we could find W. Describe what the two additional kinds of information are.
Answers
Answer:
* displacement from equilibrium position
* The spring constant,
Explanation:
The work done by a spring is two times the expressions
W = ∫ F. dx
in a spring the force is given by hooke's law
F = - k Δx
we substitute
W = - k ∫ x dx cos θ
In the case of the spring, the displacement is in the same direction of work, therefore the angle is zero and the cosine is equal to 1
we integrate
W = ½ k Δx²
we can see that we need two parts to calculate the work
* displacement from equilibrium position
Δx = 12 -8 = 4 cm
* The spring constant, this constant can be found from the displacement measurements as a function of the applied force.
Peter, a 100 kg basketball player, lands on his feet after completing a slam dunk and then immediately jumps up again to celebrate his basket. When his feet first touch the floor after the dunk, his velocity is 5 m/s downward; when his feet leave the floor 0.50 s later, as he jumps back up, his velocity is 4 m/s upward. a. What is the impulse exerted on Peter during this 0.50 s
Answers
Answer:
Explanation:
Impulse = change in momentum
Initial momentum = mass x initial velocity = 100 x 5 = 500 kg m/s
final momentum = mass x final velocity = 100 x - 4 = -400 ( - ve sign due to reversal of direction )
change in momentum = final momentum - initial momentum
= - 400 - 500 = - 900 kg m/s .
As it is - ve , it acts upwards .
So magnitude of impulse on Perter = 900 kg m/s
Rank the four fundamental forces from strongest to weakest. Use 1 to indicate the strongest force and 4 to indicate the weakest force. The gravitational force: The electromagnetic force: The strong nuclear force: The weak nuclear force:
Answers
Answer:
4
2
1
3
Explanation:
Be safe, lovelies <3
Suppose you had 10 identical molecules enclosed by a box. At a given instant, one molecule has an energy of 100 Joules, and the others are all stationary. (A) What is the average kinetic energy of the 10 molecules
Answers
Answer:
the average kinetic energy of the 10 molecules is 10 J.
Explanation:
Given;
energy on one molecule in motion, E = 100 J
number of molecules, n = 10
(A) The average kinetic energy of the 10 molecules
since the remaining 9 molecules are at rest, their kinetic energy = 0
[tex]E_{Avg} = \frac{E_1 + E_9}{10} \\\\E_{Avg} = \frac{100J+ 0}{10} \\\\E_{Avg} = \frac{100J}{10} \\\\E_{Avg} = 10J[/tex]
Therefore, the average kinetic energy of the 10 molecules is 10 J.
A 200-N force acts on a 10-kg object. The acceleration of the object is
Answers
NEED HELP WITH THIS PLEASE
Answers
Answer:
A
Explanation:
A π meson of rest energy 139.6 MeV moving at a speed of 0.921c collides with and sticks to a proton of rest energy 938.3 MeV that is at rest. (a) Find the total relativistic energy of the resulting composite particle. (b) Find the total linear momentum of the composite particle. (c) Using the results of (a) and (b), find the rest energy of the composite particle.
Answers
Answer:
A) 1268 MeV
B) 299MeV/c
C) 1268 MeV
Explanation:
Given :
π meson rest energy = 139.6 MeV
Speed = 0.921c
proton at rest energy = 938.3 MeV
a) Find the total relativistic energy of resulting composite particle
E = E(meson) + E(proton)
= [tex]\frac{(mc^2)_{meson} }{\sqrt{1-\frac{v^2}{c^2} } } + (mc^2)_{proton}[/tex]
= [tex]\frac{139.6MeV}{\sqrt{1-\frac{(0.906c)^2}{c^2} } } + 938.3[/tex]
E = 1268 MeV
B) determine the total linear momentum of the composite particle
= 299MeV/c
attached below is the detailed solution
C) Determine the rest energy of the composite particle
E = 1268 MeV
The electric potential inside a living cell is lower than the potential outside. Suppose the electric potential difference between the inner and the outer cell wall is 0.095 V, a typical value. To maintain the internal electrical balance, the cell pumps out sodium ions. How much work must be done to remove a single sodium ion (charge e)
Answers
Answer:
1.52 × 10⁻²⁰ J
Explanation:
The electrical potential difference is defined as the amount of work done in carrying a unit charge from one point to another point in an electric field. Electric potential difference is measured in volts. It is given by the formula:
ΔV = ΔU / q
ΔV is electric potential difference between the two points, ΔU is the work done and q is the unit charge.
Given that ΔV = 0.095 V, q = 1.6 × 10⁻¹⁹ C. Hence:
ΔU = ΔV.q
ΔU = 0.095 V * 1.6 × 10⁻¹⁹ C
ΔU = 1.52 × 10⁻²⁰ J
The electric potential difference is the amount of effort done in an electrical field to shift a unit charge from one spot to another.The electric potential difference will be 1.52×10⁻²⁰J.
What is the electric potential difference ?
The electrical potential difference is the amount of effort done in an electrical field to shift a unit charge from one spot to another.
Traditional current flows from positive to negative terminals, signifying positive charge transfer in that direction.
The given data in the problem is
[tex]\triangle V[/tex] is the electric potential difference between the inner and the outer cell wall = 0.095 V
[tex]\triangle U[/tex] is the amount of work done
q is the charge on the electron =1.6×10⁻¹⁹C
Electric potential difference is given by the formula
[tex]\triangle V=\frac{\triangle U}{q} \\\\ \triangle U=\triangle Vq\\\\\triangle U=0.095 V\times1.6\times10^{-19}\\\\ \triangle U=1.52\times10^{-20}J[/tex]
Hence the electric potential difference will be 1.52×10⁻²⁰J.
To learn more about the electric potential difference refer to the link;
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Starting from the front door of your ranch house, you walk 55.0 mm due east to your windmill, turn around, and then slowly walk 40.0 mm west to a bench, where you sit and watch the sunrise. It takes you 25.0 ss to walk from your house to the windmill and then 37.0 ss to walk from the windmill to the bench.
Required:
a. For the entire trip from your front door to the bench, what is your average velocity?
b. For the entire trip from your front door to the bench, what is your average speed?
Answers
Answer:
a) V = 0.24 m/s
b) v = 1.53 m/s
Explanation:
In this case, we are asked to find two values that are pretty similar and use the same units, however, there are differences between them.
The average velocity is often referred to a vector quantity, therefore, if time is a scalar magnitude, we need to find the vector quantity of distance. In this case, is the displacement, which is also referred as a vector.
So, to calculate the average velocity we need to determine first the displacement of the person. As the person heads east and then west, his total displacement (D) is:
D = 55 - 40 = 15 m
Now the total time would be the time taken to go to the windmill and then, to a bench:
t = 25 + 37 = 62 s
Finally, the average speed is:
V = D/t
V = 15 / 62
V = 0.24 m/sThe average speed is a scalar magnitude, so we use the covered distance by the person (d) and the total time:
d = 40 + 55 = 95 m
Then, the speed:
v = 95/62
v = 1.53 m/sHope this helps
A body is dropped from the roof of a 20 m high building by how much:
Does it take to reach the ground? How fast does it hit the ground?
Answers
Answer:
t = 2.01 s
Vf = 19.7 m/s
Explanation:
It's know through the International System that the earth's gravity is 9.8 m/s², then we have;
Data:
Height (h) = 20 mGravity (g) = 9.8 m/s²Time (t) = ?Final Velocity (Vf) = ?==================================================================
Time
Use formula:
[tex]\boxed{t=\sqrt{\frac{2*h}{g}}}[/tex]Replace:
[tex]\boxed{t=\sqrt{\frac{2*20m}{9.8\frac{m}{s^{2}}}}}[/tex]Everything inside the root is solved first. So, we solve the multiplication of the numerator:
[tex]\boxed{t=\sqrt{\frac{40m}{9.8\frac{m}{s^{2}}}}}[/tex]It divides:
[tex]\boxed{t=\sqrt{4.08s}}[/tex]The square root is performed:
[tex]\boxed{t=2.01s}[/tex]==================================================================
Final Velocity
use formula:
Vf = g * tReplace:
Vf = 9.8 m/s² * 2.01 sMultiply:
Vf = 19.7 m/s==================================================================
How long does it take to reach the ground?
Takes time to reach the ground in 2.01 seconds.
How fast does it hit the ground?
Hits the ground with a speed of 19.7 meters per seconds.
Why do birds not get shock when they
sit on high power live wire but we do?
Answers
Answer:
Their bodies don't conduct electricity like we do.
Explanation:
Answer:
birds dont get shocked because they sit on their talons and their talons are a different type of skin then the rest of their body
Explanation:
An electric vehicle starts from rest and accelerates at a rate of 2.3 m/s2 in a straight line until it reaches a speed of 29 m/s. The vehicle then slows at a constant rate of 1.5 m/s2 until it stops. (a) How much time elapses from start to stop
Answers
Answer:
t = 12.6 seconds
Explanation:
Given that,
Initial velocity, u = 0
Acceleration of an electric vehicle, a = 2.3 m/s²
Final velocity, v = 29 m/s
We need to find the time elapses from start to stop. The acceleration of an object is given by the relation as follows :
[tex]a=\dfrac{v-u}{t}\\\\t=\dfrac{v-u}{a}\\\\t=\dfrac{29-0}{2.3}\\\\t=12.6\ s[/tex]
So, 12.6 seconds is elapsed from start to stop.
Postural deviations can result in
Answers
Answer:
Postural deviations can cause poor balance, muscle pain and skeletal stress.
Explanation:
The mass percent of hydrogen in CH₄O is 12.5%.
What is the mass percent?Mass percent is the mass of the element divided by the mass of the compound or solute.
Step 1: Calculate the mass of the compound.
mCH₄O = 1 mC + 4 mH + 1 mO = 1 (12.01 amu) + 4 (1.00 amu) + 1 (16.00 amu) = 32.01 amu
Step 2: Calculate the mass of hydrogen in the compound.
mH in mCH₄O = 4 mH = 4 (1.00 amu) = 4.00 amu
Step 3: Calculate the mass percent of hydrogen in the compound.
%H = (mH in mCH₄O / mCH₄O) × 100%
%H = 4.00 amu / 32.01 amu × 100% = 12.5%
The mass percent of hydrogen in CH₄O is 12.5%.
CO2 = 1.580 grams H2O = 0.592 grams Lookup the molar mass of each element in the compound Carbon = 12.0107 Hydrogen = 1.00794 Oxygen = 15.999 Calculate the molar mass of CH4O by adding the total masses of each element used. 12.0107 + 4 * 1.00794 + 15.999 = 32.04146 Now calculate how many moles of CH4O you have by dividing by the molar mass. m = 1.15 g / 32.04146 g/mole = 0.035891 mole Now figure out how many moles of carbon and hydrogen you have. Carbon = 0.035891 moles Hydrogen = 0.035891 moles *
Therefore, The mass percent of hydrogen in CH₄O is 12.5%.
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a. Use the graph and the element made in question 2 to determine the mass of the star.
Answers
Which is the weakest of the four fundamental forces?
strong nuclear
weak nuclear
electromagnetic
gravitational
Answers
Answer:
Gravitational
Explanation:
gravitational
Answer:
Gravitational
Explanation:
In order from strongest to weakest.
Strong nuclear
Electromagnetic
Weak nuclear
Gravitational
I love buying physics toys. I recently broke out my new electromagnetic field meter and started playing with it. After turning it on, I noticed the device kept showing an electric field value of 200 N/C towards the ground, without being near anything obvious (e.g., an electronic device) that would be producing the electric field. I even took a long walk to check if the reading was somehow localized to my house, but I got the same result. How might you explain the reading (assuming the device is working properly)
Answers
Answer:
ionized particles from the sun.
* interactions in radiation belts.
* the friction of the planet in the solar wind
q = +9 10⁵ C
Explanation:
Due to being made up of matter, the planet Earth has a series of positive and negative charges, in general these charges should be balanced and the net charge of the planet should be zero, but there are several phenomena that introduce unbalanced charges, for example:
* ionized particles from the sun.
* interactions in radiation belts.
* the friction of the planet in the solar wind
This creates that the planet has a net electrical load
We can roughly calculate the charge of the planet
E = k q / r²
q = E r² / k
let's calculate
q = 200 (6.37 10⁶)²/9 10⁹
q = +9 10⁵ C
I have a massive rock weighing 3,000 Newtons but I can only accelerate it to 500 m/s2 what is its mass?
Answers
Answer:
6 kg
Explanation:
F=ma
F is Force(newtons)
m is mass(kg)
a is acceleration(m/s^2)
Plug in the numbers
3000 = m(500)
divide both sides by 500 to cancel out the 500.
3000/500=6
6 = m
6kg is the mass
help? its a short question
Answers
Answer:
i think its ancestor
Explanation:
sry if im wrong
Answer:
scientists compare organisms DNA to support the theory that all species share a common Ancestor.
The design of interior spaces is relatively unimportant to good
architecture?
Answers
Suppose a cat climbs a tree to a height of 2 meters. If the cat doubles its height to 4 meters, its potential energy will
1)not change
2)reduce to halve
3)double
4)quadruple
Answers
If h doubles Ep=m*g*2h
Meaning Ep=1*1*2
Ep=2
So 3)potential energy doubles.
Can someone please help me with this worksheet. It’s due today and I have no idea what to do.
Answers
As an electromagnetic wave travels, what is the relationship between the
magnetic field and the electric field along its path?
A. They are parallel to each other.
B. The angle between them decreases with an increase in energy
O C. The angle between them increases with an increase in energy.
D. They are at a 90° angle to each other.
Answers
Answer:
Its D
Explanation:
They are at a 90° angle to each other.
Do good on your tests :]
The answer is D) They are at a 90° angle to each other.
What is an electromagnetic wave?One of the waves which are propagated with the aid of simultaneous periodic versions of electrical and magnetic subject depth and consists of radio waves, infrared, seen mild, ultraviolet, X-rays, and gamma rays.
Radio waves, microwaves, seen light, and x-rays are all examples of electromagnetic waves that range very differently in wavelength. (a) Longer wavelength; (b) shorter wavelength. Electromagnetic waves are produced by means of the motion of electrically charged debris.
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6 An object can never have
A. a positive speed.
B. a negative speed.
C. a positive velocity.
D. a negative velocity.
Answers
Answer:
B
Explanation:
Speed is the magnitude of the velocity vector, so it can never be negative.
An object can never have a negative velocity. Therefore, option (D) is correct.
What is velocity?Velocity is a vector quantity that describes an object's speed and direction of motion. If an object is moving in a positive direction, it has a positive velocity. If it is moving in the opposite direction, it has a negative velocity.
However, an object can never have a negative speed. Speed is a scalar quantity that describes an object's rate of motion, and it is always positive. The speed of an object can be positive or negative, depending on the direction of its velocity, but the magnitude of its speed is always positive.
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what are the precautions to be taken while performing a rectangular glass prism experiment
Answers
Answer:
PRECAUTIONS
-The refracting faces of the glass prism should be smooth, transparent and without any air bubble or broken edge. ...
-Use a sharp pencil to draw boundary of the prism and rays of light.
-The alpins should have sharp tip and should be fixed exactly vertical to the plane of the paper.
Explanation:
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1. li took 2 } seconds for a car's vclocity to change from 20 m/s to 15 m/s. The mass of the car was 1370 kg. What force was required to cause the acceleration? (Hint: First calculate the acceleration.
Answers
Answer:
Do you still need help??
Explanation:
A body moves on a coordinate line such that it has a position sequalsf(t)equalstsquaredminus4tplus3on the interval 0less than or equalstless than or equals7,with s in meters and t in seconds.a. Find the body's displacement and average velocity for the given time interval.b. Find the body's speed and acceleration at the endpoints of the interval.c. When, if ever, during the interval does the body change direction?
Answers
Answer:
A) Δf = - 49 m, B) v (7) = -56 m / s, a = - 8 m / s², C) t = 0.866 s
Explanation:
A) In this exercise ask to find the displacement and the average velocity, give the function of the movement
f (t) = - 4t² +3
and the range of motion 0≤ t ≤ 7
the displacement is
for t = 0
f (0) = 3
for t = 7 s
f (7) = - 4 7² +3
f (7) = -46 m
the total displacement is
Δf = f (7) - f (0)
Δf = -46 - 3
Δf = - 49 m
the average speed is defined as the displacement between the time interval
v = Df / Dt
v = -49 / 7
v = - 7 m / s
B) the speed and acceleration of the end points of the motion
the speed of defined by
v = [tex]\frac{dx}{dt}[/tex]
in this case
v = [tex]\frac{df}{dt}[/tex]
v = -8t
let's calculate
v (7) = -8 7
v (7) = -56 m / s
acceleration is defined by
a = [tex]\frac{dv}{dt}[/tex]
a = - 8 m / s²
acceleration is constant throughout the movement
C) the point where the direction changes.
This point is a point where the position goes from positive to negative, the point f = 0
0 = -4t² +3
t = √¾
t = 0.866 s
