1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
satela [25.4K]
2 years ago
11

A 15 m uniform ladder weighing 500 N rests against a frictionless wall. The ladder makes a 60° angle with horizontal. (a) Find t

he 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?
Physics
1 answer:
scoray [572]2 years ago
8 0

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 = \frac{W_1 x_1 + W_2 x_2}{y}          (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 = \frac{500 \ 3.75 \ + 800 \ 2}{13}

         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

You might be interested in
How might the climate be affected if you were people drove automobiles and more people road bikes or use public transportation l
Hoochie [10]
The level of greenhouse gases in our atmosphere would decrease, due to less automobiles.
8 0
2 years ago
What do scientist use to determine the temperature of a star
REY [17]

Color is what scientist use to determine the temperature of a star!

hope this helps!

4 0
3 years ago
Marisol drives north at 64.3 km/h. How far does Marisol travel after 5.8 h?
Nady [450]

Answer:

372.94 km

d= st

= (64.3 km/h)(5.8h)

=372.94 km

3 0
3 years ago
Read 2 more answers
You attach a meter stick to an oak tree, such that the top of the meter stick is 1.87 meters above the ground. Later, an acorn f
Verdich [7]

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. We will calculate the initial velocity of the object, and from it, we will calculate the final position. With the considerations made in the statement we will obtain the total height. Initial velocity of the acorn,

u = 0m/s

Also, it is given that the acorn takes 0.201s to pass the length of the meter stick.

s = ut+\frac{1}{2} at^2

Replacing,

1 = u(0.141)+ \frac{1}{2} (9.8)(0.141)^2

u =6.4013m/s

The height of the acorn above the meter stick can be calculated as,

v^2 = u^2 +2gh

h = \frac{v^2-u^2}{2g}

h = \frac{6.4013^2-0^2}{2(9.8)}

h = 2.0906m

Also the top of the meter stick is 1.87m above the ground hence the height of the acorn above the ground is

h = 2.0906+1.87

h = 3.9606m

4 0
3 years ago
Pada setiap tumbukan berlaku hukum
sweet-ann [11.9K]
Hij ane les spoona sudhea alldor oakie
6 0
2 years ago
Other questions:
  • What velocity must a car with a mass of 1280 kg have in order to have the same momentum as a 2230?
    11·1 answer
  • Starting from rest, a 4.10-kg block slides 2.10 m down a rough 30.0° incline. The coefficient of kinetic friction between the bl
    14·1 answer
  • An example of unprofessional behavior is?
    10·2 answers
  • A watt is a unit of<br><br>light<br>power<br>force<br>motion<br>energy
    6·1 answer
  • Acceleration is defined as the rate of change for which of the following?
    14·2 answers
  • QUESTION 7
    8·1 answer
  • Which physical property of iron is being tested in the picture
    6·1 answer
  • 1.
    14·2 answers
  • Una onda sonora se produce durante 1,5 s. Posee una longitud de onda de 2,4 m y una velocidad de 340 m/s.
    13·1 answer
  • If you touch the two probes together while the DMM is set to resistance, what will happen?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!